基于核方法的雷达高分辨距离像目标识别技术研究
|
摘要
雷达高分辨距离像(HRRP)可以反映目标散射点在纵向距离上的分布情况,提供了目标重要的结构信息,并且相对于基于雷达目标像(包括SAR及ISAR像)的目标识别技术,基于HRRP的目标识别不要求目标相对于雷达平台有一定的转角,因而更易获取,对雷达具有更大的适应性,因此基于HRRP的雷达目标识别技术将受到更为广泛的关注和研究。近十几年来,基于核函数的方法也已经成功地用于解决机器学习领域的各种问题。基于核函数的算法相当于线性算法的一种非线性版本,它通过一个非线性函数将输入向量预先投影到一个高维空间中,我们只需要利用核函数计算各向量的内积便可在该高维空间中应用模式分析的各种算法,不仅提高了算法性能也节约了大量的运算时间。而在HRRP识别当中,由于目标的机动性,目标之间存在着复杂的非线性关系。因此,本论文主要围绕着“十五”国防预研项目“目标识别技术”(项目编号:413070501)和“十一五”国防预研项目“雷达高分辨距离像特征提取及识别”(项目编号:51307060601)的研究任务,针对高分辨距离像目标识别,从基于核函数的特征提取、分类器设计以及核函数优化算法等三个方面展开了较为深入的研究,另外,论文也对目标方位角划分和距离像的特征选择技术进行了研究。本论文的主要内容概括如下:
1、简单回顾了核方法的研究背景,介绍了核函数的基本概念和性质。并且,为了展示基于核函数的方法相对线性方法的优越性,我们针对雷达HRRP的目标姿态敏感性、平移敏感性和闪烁效应的特点改进了核主分量分析(Kernel PCA),从而将其应用于雷达自动目标识别任务中。
2、线性判别分析( Linear Discriminant Analysis,LDA)是被广泛应用于模式识别领域中的一种线性降维方法,但是它对数据有较强的限制,例如各类数据均为协方差矩阵相同但均值向量不同的多元正态分布,并且每类数据都是单聚类结构。为了克服这些局限性,近来子类判别分析(Subclass Discriminant Analysis,SDA)已经被提出。我们提出一种基于核函数的子空间判别分析(Kernel SDA),简称为KSDA。同时,我们给出了一个新的SDA表示公式从而避免了在特征空间中的一些复杂而且不直观的推导过程。
3、提出一种简单而有效的方法通过减少在决策函数中出现的支撑向量的个数来加速其决策过程。尽管支撑向量机已经成功地应用于数据分类与回归等领域,但鉴于在决策阶段测试数据必须和所有支撑向量结合构成核函数的原因,与其他方法相比,在获得相似的性能时其测试速度相对较慢。实际上,投影数据只是位于高维核空间的一个子空间中,所以我们能够找到一组基向量来表示所有的支撑向量,而这些基向量的个数通常小于支撑向量的个数。
4、针对核函数优化问题进行了研究。这部分工作主要分三个内容:(1)提出一种针对雷达一维高分辨距离像的核函数优化算法。该算法基于对模-1距离高斯核和模-2距离高斯核的融合,结合两种核函数的不同特性,不仅优化了核函数,同时对HRRP的闪烁效应有抑制作用;(2)核函数是否与数据分布结构相“匹配”控制着基于核函数方法的性能,这个结论已被广泛认同。理想情况下,数据在期望的核函数定义的特征空间中能够线性可分,因此Fisher线性可分性准则可以作为一种核优化规则。然而在许多应用中,即使在核空间转换后数据仍未达到线性可分,例如多模结构数据,因此在这种情况下非线性分类器更能体现出其优越的性能,并且此时Fisher准则已不是核优化准则的最好选择。受此启发,我们提出了一种新的核优化算法,该方法依靠局部核Fisher准则,在特征空间最大化局部类可分性以增大特征空间中各类间的局部距离,从而使得非线性分类器在核函数定义的特征空间中的的分类性能得到改进;(3)另外,Fisher准则仅在各类数据均为协方差矩阵相同但均值向量不同的多元正态分布,并且每类数据都是单聚类结构的假设条件下,才是最优的。由于这个假设的限制,在一些应用中Fisher准则显然已不是核优化准则的最好选择。为了解决这一问题,近来许多改进的判别分析已经被提出。因此,为了将这些判别准则应用于核优化中,基于依赖数据的核函数形式,我们提出了一个统一的核优化框架,该优化框架能使用任何可以写为样本对的形式判别准则作为代价函数。在该优化框架下,如果需要应用不同的判别准则,仅修改对应的伴随矩阵即可,而不需要任何特征空间中复杂的公式推导。
5、首先从流形几何的角度来学习雷达高分辨距离像(HRRP)中的非线性结构。然后,针对目标的姿态敏感性,在假设HRRP位于一低维流形基础上,利用HRRP流形的弯曲率,提出了一种自适应分割角域的方法。
6、提出一种新的特征选择的方法。特征选择是机器学习领域中较难的一个组合任务,同时也具有较高的实用价值。我们的工作是,针对k近邻分类器提出一种大边界特征加权算法。该算法主要通过最小化一个代价函数学习相应的特征权值。代价函数的目的是利用一个较大的边界分离异类样本,同时拉近同类样本间的距离,并且使用尽可能少的特征。相应的优化问题可以使用线性规划算法有效得到最优解。
Target high-resolution range profile (HRRP) represents the projection of the complex returned echoes from the target scattering centers onto the radar line-of-sight (LOS), which contains the informative target structure signatures. Furthermore, different from the target recognition using radar target images including SAR and ISAR images, it is unnecessary for HRRP target recognition to require a rotation angle between the target and radar. It means that obtaining target HRRP is easier and the technique is more applicable to many types of radar. Consequently, radar HRRP target recognition has received intensive attention from the radar automatic target recognition (RATR) community. Kernel methods have been successfully applied in solving various problems in machine learning community. Kernel methods are algorithms that, by replacing the inner product with an appropriate positive definite function (kernel function), implicitly perform a nonlinear mapping of input data to a high dimensional feature space. The attractiveness of such algorithms stems from their elegant treatment of nonlinear problems and their efficiency in high-dimensional problems. Due to the non-cooperative and maneuvering, the different targets should be nonlinear separable. Therefore, from the three aspects, i.e. kernel feature extraction, the classifier designing and kernel optimization, this dissertation provide our researches for HRRP target recognition, which are supported by Advanced Defense Research Programs of China (No. 413070501 and No. 51307060601) and National Science Foundation of China (No. 60302009).
The main content of this dissertation is summarized as follows.
1. The first part summarily reviews the background of kernel methods and introduces the fundamental theories and characteristics. Moreover, in order to demonstrate the better performance of kernel methods than linear methods, an improved kernel principle component analysis (Kernel PCA) is proposed to deal with the target-aspect, time-shift and amplitude-scale sensitivity of HRRP samples.
2. LDA is a popular method for linear dimensionality reduction, which maximizes between-class scatter and minimizes within-class scatter. However, LDA is optimal only in the case that all the classes are generated from underlying multivariate Normal distributions of common covariance matrix but different means and each class is expressed by a single cluster. In order to overcome the limitations of LDA, recently subclass discriminant analysis (SDA) is proposed. We develop SDA into Kernel SDA (KSDA) in the feature space, which can result in a better subspace for the classification task since a nonlinear clustering technique can find the underlying subclasses more exactly in the feature space and nonlinear LDA can provide a nonlinear discriminant hyperplane. Furthermore, a reformulation of SDA is given to avoid the complicated derivation in the feature space.
3. The third section focuses on simply and efficiently reducing the number of support vectors (SV) in the decision function of support vector machine (SVM) to speedup the SVM decision procedure. SVM is currently considerably slower in test phase than other approaches with similar generalization performance, which restricts its application to real-time tasks. Because in practice the embedded data just lie into a subspace of the kernel-induced high dimensional space, we can search a set of basis vectors (BV) to express all the SVs approximately, the number of which is usually less than that of SVs.
4. The forth section is contributed on the optimization of kernel functions. The main work concerns the following three aspects: (1) we develop a kernel optimization method based on fusion kernel for High-resolution range profile (HRRP). In terms of the fusion of l1-norm and l2-norm Gaussian kernels, our method combines the different characteristics of them so that not only is the kernel function optimized but also the speckle fluctuations of HRRP are restrained; (2) ideally it is expected that the data is linearly separable in the kernel induced feature space, therefore, Fisher linear discriminant criterion can be used as a cost function to optimize the kernel function. However, the data may not be linearly separable even after kernel transformation in many applications, e.g., the data may exist as multimodally distributed structure, in this case, a nonlinear classifier is preferred, and obviously Fisher criterion is not a suitable choice as kernel optimization rule. Motivated by this issue, we propose a localized kernel Fisher criterion, instead of traditional Fisher criterion, as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space, which results in a better classification performance of kernel-based classifiers; (3) Fisher criteria is optimal only in the case that all the classes are generated from underlying multivariate Normal distributions of common covariance matrix but different means and each class is expressed by a single cluster. Due to the assumptions, Fisher criteria obviously is not a suitable choice as a kernel optimization rule in some applications. In order to solve this problem, recently many improved discriminant criteria (DC) have been also developed. Therefore, to apply these discriminant criteria to kernel optimization, in this paper based on a data-dependent kernel function we propose a unified kernel optimization framework, which can use any discriminant criteria formulated in a pairwise manner as the objective functions. Under the kernel optimization framework, if one would like to employ different discriminant criteria, what to do only is to change the corresponding affinity matrices without having to resort to any complex derivations in feature space.
5. In the fifth part, the manifold geometry in radar HRRP is firstly explored. And then according to the characteristics of target pose sensitivity, a method of adaptively segmenting the aspect sectors is proposed for HRRP recognition through evaluating the curvature of HRRP manifold.
6. Finally, we propose a novel feature selection algorithm. The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance. In this paper we present a large margin feature weighting method for k -nearest neighbor (kNN) classifier. The method learns the feature weighting factors by minimizing a cost function, which aims at separating points in different classes by a large margin, pulling closer together points from the same class and using as few features as possible. The consequent optimization problem can efficiently be solved by Linear Programming.
1、简单回顾了核方法的研究背景,介绍了核函数的基本概念和性质。并且,为了展示基于核函数的方法相对线性方法的优越性,我们针对雷达HRRP的目标姿态敏感性、平移敏感性和闪烁效应的特点改进了核主分量分析(Kernel PCA),从而将其应用于雷达自动目标识别任务中。
2、线性判别分析( Linear Discriminant Analysis,LDA)是被广泛应用于模式识别领域中的一种线性降维方法,但是它对数据有较强的限制,例如各类数据均为协方差矩阵相同但均值向量不同的多元正态分布,并且每类数据都是单聚类结构。为了克服这些局限性,近来子类判别分析(Subclass Discriminant Analysis,SDA)已经被提出。我们提出一种基于核函数的子空间判别分析(Kernel SDA),简称为KSDA。同时,我们给出了一个新的SDA表示公式从而避免了在特征空间中的一些复杂而且不直观的推导过程。
3、提出一种简单而有效的方法通过减少在决策函数中出现的支撑向量的个数来加速其决策过程。尽管支撑向量机已经成功地应用于数据分类与回归等领域,但鉴于在决策阶段测试数据必须和所有支撑向量结合构成核函数的原因,与其他方法相比,在获得相似的性能时其测试速度相对较慢。实际上,投影数据只是位于高维核空间的一个子空间中,所以我们能够找到一组基向量来表示所有的支撑向量,而这些基向量的个数通常小于支撑向量的个数。
4、针对核函数优化问题进行了研究。这部分工作主要分三个内容:(1)提出一种针对雷达一维高分辨距离像的核函数优化算法。该算法基于对模-1距离高斯核和模-2距离高斯核的融合,结合两种核函数的不同特性,不仅优化了核函数,同时对HRRP的闪烁效应有抑制作用;(2)核函数是否与数据分布结构相“匹配”控制着基于核函数方法的性能,这个结论已被广泛认同。理想情况下,数据在期望的核函数定义的特征空间中能够线性可分,因此Fisher线性可分性准则可以作为一种核优化规则。然而在许多应用中,即使在核空间转换后数据仍未达到线性可分,例如多模结构数据,因此在这种情况下非线性分类器更能体现出其优越的性能,并且此时Fisher准则已不是核优化准则的最好选择。受此启发,我们提出了一种新的核优化算法,该方法依靠局部核Fisher准则,在特征空间最大化局部类可分性以增大特征空间中各类间的局部距离,从而使得非线性分类器在核函数定义的特征空间中的的分类性能得到改进;(3)另外,Fisher准则仅在各类数据均为协方差矩阵相同但均值向量不同的多元正态分布,并且每类数据都是单聚类结构的假设条件下,才是最优的。由于这个假设的限制,在一些应用中Fisher准则显然已不是核优化准则的最好选择。为了解决这一问题,近来许多改进的判别分析已经被提出。因此,为了将这些判别准则应用于核优化中,基于依赖数据的核函数形式,我们提出了一个统一的核优化框架,该优化框架能使用任何可以写为样本对的形式判别准则作为代价函数。在该优化框架下,如果需要应用不同的判别准则,仅修改对应的伴随矩阵即可,而不需要任何特征空间中复杂的公式推导。
5、首先从流形几何的角度来学习雷达高分辨距离像(HRRP)中的非线性结构。然后,针对目标的姿态敏感性,在假设HRRP位于一低维流形基础上,利用HRRP流形的弯曲率,提出了一种自适应分割角域的方法。
6、提出一种新的特征选择的方法。特征选择是机器学习领域中较难的一个组合任务,同时也具有较高的实用价值。我们的工作是,针对k近邻分类器提出一种大边界特征加权算法。该算法主要通过最小化一个代价函数学习相应的特征权值。代价函数的目的是利用一个较大的边界分离异类样本,同时拉近同类样本间的距离,并且使用尽可能少的特征。相应的优化问题可以使用线性规划算法有效得到最优解。
Target high-resolution range profile (HRRP) represents the projection of the complex returned echoes from the target scattering centers onto the radar line-of-sight (LOS), which contains the informative target structure signatures. Furthermore, different from the target recognition using radar target images including SAR and ISAR images, it is unnecessary for HRRP target recognition to require a rotation angle between the target and radar. It means that obtaining target HRRP is easier and the technique is more applicable to many types of radar. Consequently, radar HRRP target recognition has received intensive attention from the radar automatic target recognition (RATR) community. Kernel methods have been successfully applied in solving various problems in machine learning community. Kernel methods are algorithms that, by replacing the inner product with an appropriate positive definite function (kernel function), implicitly perform a nonlinear mapping of input data to a high dimensional feature space. The attractiveness of such algorithms stems from their elegant treatment of nonlinear problems and their efficiency in high-dimensional problems. Due to the non-cooperative and maneuvering, the different targets should be nonlinear separable. Therefore, from the three aspects, i.e. kernel feature extraction, the classifier designing and kernel optimization, this dissertation provide our researches for HRRP target recognition, which are supported by Advanced Defense Research Programs of China (No. 413070501 and No. 51307060601) and National Science Foundation of China (No. 60302009).
The main content of this dissertation is summarized as follows.
1. The first part summarily reviews the background of kernel methods and introduces the fundamental theories and characteristics. Moreover, in order to demonstrate the better performance of kernel methods than linear methods, an improved kernel principle component analysis (Kernel PCA) is proposed to deal with the target-aspect, time-shift and amplitude-scale sensitivity of HRRP samples.
2. LDA is a popular method for linear dimensionality reduction, which maximizes between-class scatter and minimizes within-class scatter. However, LDA is optimal only in the case that all the classes are generated from underlying multivariate Normal distributions of common covariance matrix but different means and each class is expressed by a single cluster. In order to overcome the limitations of LDA, recently subclass discriminant analysis (SDA) is proposed. We develop SDA into Kernel SDA (KSDA) in the feature space, which can result in a better subspace for the classification task since a nonlinear clustering technique can find the underlying subclasses more exactly in the feature space and nonlinear LDA can provide a nonlinear discriminant hyperplane. Furthermore, a reformulation of SDA is given to avoid the complicated derivation in the feature space.
3. The third section focuses on simply and efficiently reducing the number of support vectors (SV) in the decision function of support vector machine (SVM) to speedup the SVM decision procedure. SVM is currently considerably slower in test phase than other approaches with similar generalization performance, which restricts its application to real-time tasks. Because in practice the embedded data just lie into a subspace of the kernel-induced high dimensional space, we can search a set of basis vectors (BV) to express all the SVs approximately, the number of which is usually less than that of SVs.
4. The forth section is contributed on the optimization of kernel functions. The main work concerns the following three aspects: (1) we develop a kernel optimization method based on fusion kernel for High-resolution range profile (HRRP). In terms of the fusion of l1-norm and l2-norm Gaussian kernels, our method combines the different characteristics of them so that not only is the kernel function optimized but also the speckle fluctuations of HRRP are restrained; (2) ideally it is expected that the data is linearly separable in the kernel induced feature space, therefore, Fisher linear discriminant criterion can be used as a cost function to optimize the kernel function. However, the data may not be linearly separable even after kernel transformation in many applications, e.g., the data may exist as multimodally distributed structure, in this case, a nonlinear classifier is preferred, and obviously Fisher criterion is not a suitable choice as kernel optimization rule. Motivated by this issue, we propose a localized kernel Fisher criterion, instead of traditional Fisher criterion, as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space, which results in a better classification performance of kernel-based classifiers; (3) Fisher criteria is optimal only in the case that all the classes are generated from underlying multivariate Normal distributions of common covariance matrix but different means and each class is expressed by a single cluster. Due to the assumptions, Fisher criteria obviously is not a suitable choice as a kernel optimization rule in some applications. In order to solve this problem, recently many improved discriminant criteria (DC) have been also developed. Therefore, to apply these discriminant criteria to kernel optimization, in this paper based on a data-dependent kernel function we propose a unified kernel optimization framework, which can use any discriminant criteria formulated in a pairwise manner as the objective functions. Under the kernel optimization framework, if one would like to employ different discriminant criteria, what to do only is to change the corresponding affinity matrices without having to resort to any complex derivations in feature space.
5. In the fifth part, the manifold geometry in radar HRRP is firstly explored. And then according to the characteristics of target pose sensitivity, a method of adaptively segmenting the aspect sectors is proposed for HRRP recognition through evaluating the curvature of HRRP manifold.
6. Finally, we propose a novel feature selection algorithm. The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance. In this paper we present a large margin feature weighting method for k -nearest neighbor (kNN) classifier. The method learns the feature weighting factors by minimizing a cost function, which aims at separating points in different classes by a large margin, pulling closer together points from the same class and using as few features as possible. The consequent optimization problem can efficiently be solved by Linear Programming.
引文
[1] W.G.Carrara, R.S.Goodman, R.M.Majewski. Spotlight synthetic aperture radar: signal processing algorithms . Boston: Artech House, 1995.
[2] 保铮,邢孟道,王彤. 雷达成像技术. 北京:电子工业出版社,2005.
[3] C.A.Wiley. Synthetic aperture radar. IEEE Trans. on AES, 1985, Vol. 21(3), 440-443.
[4] 杜兰,刘宏伟,保铮.一种基于距离-多谱勒二维联合的群目标分辨方法.电子学报.Vol.32 (6), 881-885, 2004.
[5] 杜兰,保铮,邢孟道.直升机雷达回波的分析与检测.西安电子科技大学学报, Vol.30 (5), 574-579, 2003.
[6] Moving and stationary target acquisition and recognition, Program technology review. Denver, CO. Nov. 1996. http://www.mbvlab.wpafb.af.mil/public/MBVDATA.
[7] 廖学军. 基于高分辨距离像的雷达目标识别. 博士研究生学位论文. 西安电子科技大学. 1999。
[8] 裴炳南. 高分辨雷达自动目标识别方法研究. 博士研究生学位论文. 西安电子科技大学. 2002.
[9] 刘宏伟, 杜兰, 袁莉, 保铮. 雷达高分辨距离像目标识别研究进展. 电子与信息学报. 2005 年 8 月, 27(8),1328-1334.
[10] 邢孟道. 基于实测数据的雷达成像方法研究. 博士研究生学位论文. 西安电子科技大学. 2002.
[11] 杜兰.雷达高分辨距离像目标识别方法研究. 博士研究生学位论文. 西安电子科技大学. 2007.
[12] 袁莉. 基于高分辨距离像的雷达目标识别方法研究。博士研究生学位论文. 西安电子科技大学. 2007.
[13] Jacobs S. P.. Automatic target recognition using high-resolution radar range profiles. Ph. D. Dissertation. Washington University. 1999.
[14] Li H.-J., Yang S.-H.. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. A.P., Vol. 41(3). 261-268, 1993.
[15] Anthony Zywechm and Robert E. Bogner, Radar target classification of commercial aircraft, IEEE Trans. on Aerospace and Electronic Systems, Vol. 32(2), 598-606, 1996.
[16] Anthony Zywechm and Robert E. Bogner, Coherent averaging of range profiles, in Proceedings of IEEE International Radar Conference, 456-461, 1995.
[17] Mitchell R. A., Dewall R.. Overview of high range resolution radar target identification. In Proceedings of Automatic Target Recognition Working Group,1994.
[18] Webb A. R.. Gamma Mixture Models for Target Recognition. Pattern Recognition. Vol. 33, 2045-2054, 2000.
[19] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Trans. on Signal Processing. Vol.54 (6). 2226-2238.
[20] M. Tipping and C.M. Bishop, Probabilistic Principal Component Analysis, J. Royal Statistical Soc. B, Vol. 21(3), 611-622, 1999.
[21] Rubin D., Thayer D.. EM algorithms for ML factor analysis. Psychometrika. Vol. 47(1). 69-76, 1982.
[22] Du Lan, Liu Hngwei, Bao Zheng. Radar HRRP statistical recognition: parametric model and model selection. IEEE Trans. on Signal Processing. In press.
[23] C. Cortes and V. Vapnik, Support-vector networks. Machine Learning, Vol. 20, 273-297, 1995.
[24] V. Vapnik, The nature of statistical learning theory. Springer, N. Y., 1995.
[25] C. J. C. Burges, A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, Vol. 2, 121–167, 1998.
[26] Hongwei Liu, Zheng Bao, Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel, LNCS 3174 (I) (2004) 531-536.
[27] R. Williams, J. Westerkamp, et al, Automatic target recognition of time critical moving targets using 1D high range resolution (HRR) radar, IEEE AES Magazine, April, 37-43, 2000.
[28] Xuejun Liao, Paul Runkle and Lawrence Carin, Identification of Ground Targets From Sequential High-Range-Resolution Radar Signatures, IEEE Trans. Aerospace and Electronic Systems, Vol. 38(4), 1230-1242, 2002.
[29] P. Bharadwaj, P. Runkle, L. Carin, et al, Multiaspect classification of airborne targets via physics-based HMMs and matching pursuits, IEEE Trans. AES, Vol.37(2), 595-606, 2001.
[30] Lan Du, Hongwei Liu, Zheng Bao and Mengdao Xing. Radar HRRP target recognition based on higher order spectra. IEEE transactions on Signal Processing, Vol. 53(7), 2359-2368, 2005.
[31] Xing M.-D., Bao Z., Pei B.. The properties of high-resolution range profiles. Optical Engineering. Vol. 41(2). 493-504, 2002.
[32] Rong Hu and Zhaoda Zhu, Research on Radar Classification based on High Resolution Range Profiles, in Proceedings of Aerospace and Electronics Conference, Vol.2, 951-955, 1997.
[33] 袁莉,刘宏伟,保铮. 雷达高分辨距离像分类器的参数自适应学习算法.电子与信息学报,已录用。
[34] Bo Chen, Hongwei Liu, Zheng Bao. Adaptively Segmenting Angular Sectors for Radar HRRP ATR. EURASIP Journal on Applied Signal Processing. In press.
[35] J.Portegies Zwart, R.van der Heiden, S.Gelsema and F.Groen. Fast translation invariant classification of HRR range profiles in a zero phase representation. IEE Proc.-Radar Sonar Navig., Vol.150(6), 411-418, 2003.
[36] 陈渤,刘宏伟,保铮. 一种基于零相位表示法的 HRRP 识别方法,西电学报,Vol. 32 (5), 657-662, 2005.
[37] 陈渤,刘宏伟,保铮. 基于三种不同绝对对齐方法的分类器的分析与研究。现代雷达, Vol. 28 (3), 58-62, 2006.
[38] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. Signal Processing. Vol. 49(9), 1875-1885, 2001.
[39] Bo Chen, Hongwei Liu, Zheng Bao. An Efficient Kernel Optimization Method for Radar High-resolution Range Profile Recognition, EURASIP Journal on Applied Signal Processing. Vol. 2007, Article ID 49597, 10 pages, 2007.
[40] 杜兰, 刘宏伟, 保铮, 张军英. 一种利用雷达高分辨距离像幅度起伏特性的特征提取新方法. 电子学报. Vol.33 (3). 411-415, 2005.
[41] 杜兰,刘宏伟,保铮,张军英.一种用于雷达 HRRP 功率谱的加权特征压缩方法. 西安电子科技大学学报. Vol. 33(2). 173-177, 2006.
[42] Bo Chen, Hongwei Liu, Zheng Bao. A Kernel Optimization Method Based on the Localized Kernel Fisher, Pattern Recognition, Vol. 41(3), 1098-1109, 2008.
[43] Bo Chen, Hongwei Liu, Zheng Bao. Large Margin Feature Weighting via Linear Programming. IEEE Transactions on Knowledge and Data Engineering. In revision.
[44] C. J. C.Burges. Simplified support vector decision rules. The Proc. of ICML’96 San Mateo, CA, 71-77, 1996.
[45] B. Sch?lkopf, S. Mika, C. J. C. Burges, P. knirsch, K. Muller, G. Ratsch, and A. J. Smola. Input space versus feature space in kernel-based methods. IEEE Trans. Neural Networks, 10, 1000-1017, 1999.
[46] DucDung Nguyen and Ho TuBao. An efficient method for simplifying support machines. The Proc. of ICML’05. Bonn, Germany, 2005.
[47] Bo Chen, Hongwei Liu, Zheng Bao. Speeding up SVM in Test Phase: Application to Radar HRRP ATR. The Proc. of ICONIP’06, Hongkong, China, 2006.
[48] John Shawe-Taylor and Nello Cristianini, Kernel Methods for Pattern Analysis, Cambridge Univerisity Press, 2004.
[49] B.E.Boser, I.M. Guyon, and V.N. Vapnik, A training algorithm for optimal margin classifiers, in Proceedings of the 5th annual ACM Workshop on Computational Learning Theory, D. Haussler, Ed., 144-152, 1992.
[50] B. Sch?lkopf, Support vector learning, Oldenbourg Verlag, Munich, 1997.
[51] V. N. Vapnik, Statistical Learning Theory, Wiley, New York, 1998.
[52] B. Sch?lkopf, C.J.C. Burges, and A.J. Smola. Advances in Kernel Methods—Support Vector Learning, MIT Press, Cambridge, MA, 1999.
[53] S. Mika, G. Ratsch, J. Weston, B. Sch?lkopf, and K.-R. Muller, Fisher discriminant analysis with kernels, in Neural Networks for Signal Precessing IX, Y.-H. Hu, J.Larsen, E. Wilson, and S. Douglas, Eds. 1999, 41-48, IEEE.
[54] V. Roth and V. Steinhage, Nonlinear discriminant analysis using kernel functions, in Advances in Neural Information Precessing Systems 12, S.A. Solla, T.K. Leen, and K.-R. Muller, Eds. 2000, 568-574, MIT Press.
[55] G. Baudat and F. Anouar, Generalized discriminant analysis using a kernel approach, Neural Computation, Vol.12 (10), 2385-2404, 2000.
[56] S. Mika, G. Ratsch, J. Weston, B. Sch?lkopf, and K.-R. Muller, Invariant feature extraction and classification in kernel spaces, in Advances in Neural Information Precessing Systems 12, S.A. Solla, T.K. Leen, and K.-R. Muller, Eds. 526-532, MIT Press, 2000.
[57] A. Smola, P. L. Bartlett, B. Scheolkopf and J. Schurmann (editors). Advances in Large Margin Classifiers. Cambridge, MA: MIT Press, 2000.
[58] B. Sch?lkopf, C.J.C. Burges, and A.J. Smola, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, Vol.10, 1299-1319, 1998.
[59] S. Mika, B. Scholkopf, A.J. Smola, K.-R. Muller, M. Scholz, and G. Ratsch, Kernel PCA and de-noising in feature spaces, in Advances in Neural Information Precessing Systems 11, M.S. Kearns, S.A. Solla, and D.A. Cohn, Eds. 536-542, MIT Press, 1999.
[60] Francis R. Bach and Michael I. Jordan, Kernel Independent Component Analysis, Journal of Machine Learning Research, Vol. 3, 1-48, 2002.
[61] Bo Chen, Hongwei Liu, Zheng Bao. Kernel Subclass Discriminant Analysis. Neurocomputing, Vol. 71, 455-458, 2007.
[62] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. Vol. 41(6), 2107-2119, 2008.
[63] Bo Chen, Hongwei Liu, Zheng Bao. PCA and Kernel PCA for Radar High Range Resolution Profiles Recognition. IEEE International Radar Conference in Arlington, Virginia USA, 528-533, 2005.
[64] T. Joachims, Text categorization with support vector machines: Learning with many relevant features, in Proc. Europ. Conf. Machine Learning. Berlin, Germany: Springer-Verlag, 137–142, 1998.
[65] S. Dumais, J. Platt, D. Heckerman, and M. Sahami, Inductive learning algorithms and representations for text categorization, in Proc. 7th Int. Conf. Inform. Knowledge Management, 1998.
[66] H. Drucker, D.Wu, and V. N. Vapnik, Support vector machines for span categorization, IEEE Trans. Neural Networks, Vol. 10, 1048–1054, 1999.
[67] K.-R. Müller, A. J. Smola, G. R?tsch, B. Sch?lkopf, J. Kohlmorgen, and V. N. Vapnik, Predicting time series with support vector machines, in Artificial Neural Networks—ICANN’97. Springer Lecture Notes in Computer Science, W. Gerstner, A. Germond, M. Hasler, and J.-D. Nicoud, Eds. Berlin, Germany: Springer-Verlag, Vol. 1327, 999–1004, 1997.
[68] D. Mattera and S. Haykin, Support vector machines for dynamic reconstructionof a chaotic system, in Advances in Kernel Methods—Support Vector Learning, B. Sch?lkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 211–242, 1999.
[69] M. P. S. Brown, W. N. Grundy, D. Lin, N. Cristianini, C. Sugnet, T.S. Furey, M. Ares, and D. Haussler, Knowledge-based analysis of microarray gene expression data using support vector machines, Proc. Nat. Academy Sci., Vol. 97(1), 262–267, 2000.
[70] T. Furey, N. Cristianini, N. Duffy, D. Bednarski, M. Schummer, and D. Haussler, Support vector machine classification and validation of cancer tissue samples using microarray expression data, Bioinformatics, Vol. 16, 906–914, 2000.
[71] A. Zien, G. R?tsch, S. Mika, B. Sch?lkopf, T. Lengauer, and K.-R. Müller, Engineering support vector machine kernels that recognize translation initiation sites in DNA, Bioinformatics, Vol. 16, 799–807, 2000.
[72] T. S. Jaakkola, M. Diekhans, and D. Haussler, A discriminative framework for detecting remote protein homologies. [online] http://www.cse.ucsc.edu/~research/compbio/research.html, Oct. 1999.
[73] D. Haussler, Convolution kernels on discrete structures, UC Santa Cruz, Tech. Rep. UCSC-CRL-99-10, July 1999.
[74] O. Chapelle, V. Vapnik, O. Bousquet, S. Mukherjee, Choosing multiple parameters for support vector machines, Machine Learning, Vol.46(1), 131-159, 2002.
[75] J. T. Kwok, The evidence framework applied to support vector machines, IEEE Trans. Neural Networks, Vol. 11(5), 1162–1173, 2000.
[76] P. Sollich, Bayesian methods for support vector machines: Evidence and predictive class probabilities, Machine Learning, Vol. 46(1-3), 21–52, 2002.
[77] M. M. S. Lee, S. S. Keerthi, C. J. Ong, and D. DeCoste, An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels, IEEE Trans. Neural Networks, Vol. 15(3), 750–757, 2004.
[78] Daoqiang Zhang, Songcan Chen and Zhi-Hua Zhou, Learning the kernel parameters in kernel minimum distance classifier, Pattern Recognition, Vol. 39(1), 133-135, 2006.
[79] N. Cristianini, J. Kandola, A. Elisseeff, J. Shawe-Taylor, On kernel target alignment, in: Advances in Neural Information Processing Systems (NIPS’01), MIT Press, Cambridge, MA, 367-373, 2001.
[80] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, M. I. Jordan, Learning the kernel matrix with semidefinte programming, J. Mach. Learn. Res. 5, 27-72, 2004.
[81] O. Bousquet and D. Herrmann. On the complexity of learning the kernel matrix, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[82] C. S. Ong, A. J. Smola, R. C.Williamson, Learning the kernel with hyperkernels, J. Mach. Learn. Res., Vol. 3, 1001-1030, 2003.
[83] K. Crammer, J. Keshet, Y. Singer, Kernel design using boosting, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[84] T. Hertz, A. B. Hillel, D. Weinshall, Learning a kernel function for classification with small training samples, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, 2006.
[85] H. L. Xiong, M. N. S. Swamy, M. Omair Ahmad, Optimizing the kernel in the empirical feature space, IEEE Trans. Neural Networks, Vol. 16(2), 460-474, 2005.
[86] S. Amari, S. Wu, Improving support vector machine classifiers by modifying kernel functions, Neural Networks, Vol. 12(6), 783–789, 1999.
[87] K. Fukunaga, Introduction to statistical pattern recognition. Boston, Academic Press Inc., 1990.
[88] M. Zhu and A. M. Martinez, Subclass discriminant analysis. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 28(8), 1274-1286, 2006.
[89] A. M. Martinez and M. Zhu, Where are linear feature extraction methods applicable?, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(12), 1934-1944, 2005.
[1] John Shawe-Taylor and Nello Cristianini, Kernel Methods for Pattern Analysis, Cambridge Univerisity Press, 2004.
[2] V. Vapnik, The nature of statistical learning theory. Springer, N. Y., 1995.
[3] Richard O. Duda, Peter E. Hart, and David G. Stork. Pattern Classification, Second Edition, John Wiley & Sons, 2001.
[4] G. S. Kimeldorf and G.Wahba. Some results on Tchebycheffian spline functions, J. Math. Anal. Applicat., Vol. 33, 82–95, 1971.
[5] A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Washington, D.C.: Winston, 1977.
[6] T. Poggio and F. Girosi. Regularization algorithms for learning that are equivalent to multilayer networks, Science, Vol. 247, 978–982, 1990.
[7] D. D. Cox and F. O’Sullivan. Asymptotic analysis of penalized likelihood and related estimates, Ann. Statist., Vol. 18(4), 1676–1695, 1990.
[8] H. Akaike. A new look at the statistical model identification, IEEE Trans. Automat. Control, Vol. AC-19, 716–723, 1974.
[9] J. Moody. The effective number of parameters: An analysis of generalization and regularization in nonlinear learning systems, in Advances in Neural Information Processings Systems 4, S. J. Hanson, J. Moody, and R. P. Lippman Eds., 847–854, San Mateo CA: Morgan Kaufman, 1992.
[10] N. Murata, S. Amari, and S. Yoshizawa. Network information criterion— determining the number of hidden units for an artificial neural network model, IEEE Trans. Neural Networks, Vol. 5, 865–872, 1994.
[11] V. N. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
[12] V. N. Vapnik and A. Y. Chervonenkis. Theory of Pattern Recognition (in Russian). Moscow, Russia: Nauka, 1974.
[13] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning 20, 273-297, 1995.
[14] K. P. Bennett and O. L. Mangasarian. Robust linear programming discrimination of two linearly inseparable sets, Optimization Methods Software, Vol. 1, 23–34, 1992.
[15] B.E.Boser, I.M. Guyon, and V.N. Vapnik. A training algorithm for optimal margin classifiers, in Proceedings of the 5th annual ACM Workshop on Computational Learning Theory, D. Haussler, Ed., 144-152, 1992.
[16] M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning, Automat. Remote Contr., Vol. 25, 821–837, 1964.
[17] S. Saitoh. Theory of Reproducing Kernels and Its Applications. Harlow, U.K.: Longman, 1988.
[18] J. Mercer. Functions of positive and negative type and their connection with the theory of integral equations, Philos. Trans. Roy. Soc. London, Vol. A 209,415–446, 1909.
[19] N. Aronszajn. Theory of reproducing kernels. Transactions of the American Mathe-matical Society, 68: 337-404, 1950.
[20] B. Sch?lkopf. Support vector learning, Oldenbourg Verlag, Munich, 1997.
[21] G. Wahba. Spline models for observational data, Vol. 59 of CBMS-NSF Regional conference series in applied mathematics, SIAM, Philadephia, 1990.
[22] F. Girosi. An equivalence between sparse approximation and support vector machines, Neural Computation, 10(6), 1455-1480, 1998.
[23] Roman Rosipal. Kernel-Based regression and objective nonlinear measures to assess brain functioning. PhD Thesis, 2001.
[24] G. Kimeldorf and G. Wahba. Some results on Tchebucheffian spline functions. Journal of Machematical Analysis and Applications, Vol.33, 82-95, 1971.
[25] G. Wahba. Support vector machines, Reproducing Kernel Hilbert Spaces, and Randomized GACV. In B. Sch?lkopf, C.J.C Burges, and A.J. Smola, editor, Advances in Kernel Methods-Support Vector Learning, 69-88. MIT press, Cambridge, MA, 1999.
[26] B. Sch?lkopf, C.J.C. Burges, and A.J. Smola. Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, Vol.10, 1299-1319, 1998.
[27] S. Mika, B. Scholkopf, A.J. Smola, K.-R. Muller, M. Scholz, and G. Ratsch. Kernel PCA and de-noising in feature spaces, in Advances in Neural Information Precessing Systems 11, M.S. Kearns, S.A. Solla, and D.A. Cohn, Eds. 1999, 536-542, MIT Press.
[28] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. 41(6): 2107-2119, 2008.
[29] Bo Chen, Hongwei Liu, Zheng Bao. A Kernel Optimization Method Based on the Localized Kernel Fisher, Pattern Recognition, Vol.41 (3), 1098-1109, 2008.
[30] Bo Chen, Hongwei Liu, Zheng Bao. An Efficient Kernel Optimization Method for Radar High-resolution Range Profile Recognition, EURASIP Journal on Applied Signal Processing. Vol. 2007, Article ID 49597, 10 pages, 2007.
[31] J. T. Kwok, The evidence framework applied to support vector machines, IEEE Trans. Neural Networks, Vol. 11(5), 1162–1173, 2000.
[32] P. Sollich, Bayesian methods for support vector machines: Evidence and predictive class probabilities, Machine Learning, Vol. 46(1-3), 21–52, 2002.
[33] M. M. S. Lee, S. S. Keerthi, C. J. Ong, and D. DeCoste. An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels, IEEE Trans. Neural Networks, Vol. 15(3), 750–757, 2004.
[34] Daoqiang Zhang, Songcan Chen and Zhi-Hua Zhou. Learning the kernel parameters in kernel minimum distance classifier. Pattern Recognition, Vol. 39(1), 133-135, 2006.
[35] N. Cristianini, J. Kandola, A. Elisseeff, J. Shawe-Taylor. On kernel target alignment, in: Advances in Neural Information Processing Systems (NIPS’01), MIT Press, Cambridge, MA, 367-373, 2001.
[36] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, M. I. Jordan, Learning the kernel matrix with semidefinte programming, J. Mach. Learn. Res., Vol. 5, 27-72, 2004.
[37] O. Bousquet and D. Herrmann. On the complexity of learning the kernel matrix, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[38] C. S. Ong, A. J. Smola, R. C.Williamson. Learning the kernel with hyperkernels, J. Mach. Learn. Res., Vol. 3, 1001-1030, 2003.
[39] K. Crammer, J. Keshet, Y. Singer. Kernel design using boosting, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[40] T. Hertz, A. B. Hillel, D. Weinshall. Learning a kernel function for classification with small training samples, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, 2006.
[41] James T. Kwok, Ivor W. Tsang. Learning with idealized kernels, in: Proceedings of the International Conference on Machine Learning, Washington DC, USA, 2003.
[42] H. L. Xiong, M. N. S. Swamy, M. Omair Ahmad. Optimizing the kernel in the empirical feature space, IEEE Trans. Neural Networks, Vol. 16(2), 460-474, 2005.
[43] Bo Chen, Hongwei Liu, Zheng Bao. PCA and Kernel PCA for Radar High Range Resolution Profiles Recognition. 2005 IEEE International Radar Conference in Arlington, Virginia USA: 528-533.
[44] I. T. Jolliffe. Principle Component analysis. New York: Springer-Verlag, 1986.
[45] Y.Linde, A.Buzo and R.M.Gray. An algorithm for vector quantizer design. IEEE Trans. Communications, Vol. 28(1), 84-95, 1988.
[46] András Kocsor and László Tóth. Kernel-Based feature extraction with a speech technology application. IEEE Trans on Signal Processing. 2004. 52(8): 2250-2263.
[47] Hongwei Liu and Zheng Bao. Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel. Springer Lecture Notes in Computer Science. Editors: Fuliang Yin, Jun Wang, Chengan Guo. Berlin: Springer-Verlag, 2004. 3174(I), 531-536.
[48] Anthony Zywechm, et al. Radar target classification of commercial aircraft. IEEE Trans. on Aerospace and Electronic Systems, 1996, Vol.32(2): 598-606.
[49] Xing mengdao and Bao zheng. The properties of range profile of aircraft. Optical Engineering. 2002. Vol.41(2): 493-504
[50] Anthony Zywechm and Robert E. Bogner. Coherent averaging of range profiles. Proceedings of IEEE International Radar Conference. Alexandria, VA, USA: IEEE, 456-461, 1995.
[51] 刘宏伟,马建华,保铮 . BOX-COX 变换提高雷达高分辨距离像识别性能的物理机理分析. 烟台:海军航空工程学院,2004. 254-357.
[52] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, Vol. 20, 273-297, 1995.
[1] K. Fukunaga, Introduction to statistical pattern recognition. Boston, Academic Press Inc., 1990.
[2] T.K., Kim and J. Kittler, Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(3), 318-327, 2005.
[3] Bo Chen, Hongwei Liu and Zheng Bao, A Kernel Optimization Method Based on the Localized Kernel Fisher Criterion, Pattern Recognition. In press.
[4] M. Zhu and A. M. Martinez, Subclass discriminant analysis. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 28(8), 1274-1286, 2006.
[5] A. M. Martinez and M. Zhu, Where are linear feature extraction methods applicable?, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(12), 1934-1944, 2005.
[6] G. Baudat and F. Anouar, Generalized discriminant analysis using a kernel approach, Neural Comput., 12, 2385-2404, 2000.
[7] S. Mika, G. Ratsch, J. Weston, B. Scholkopf, A. Smola and K.-R. Muller. Invariance feature extraction and classification in kernel spaces, Advances in neural information processing systems, 12, 526-532, 2000.
[8] B. Scholkopf and A. J. Smola. Learning with kernels. The MIT Press, Cambridge, MA, 2002.
[9] Sugiyama, M., Local Fisher discriminant analysis for supervised dimensionality reduction, In: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, 2006.
[10] J. Shawe-Taylor and N. Cristianini, Kernel methods for pattern analysis, Cambridge University Press, 2004.
[11] Sam Roweis. Finding the first few eigenvectors in a large space. Available from< http://www.cs.toronto.edu/~roweis/ >.
[12] B. Scholkopf, A. Smola and K.-R. Muller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, Vol. 10, 1299-1319, 1998.
[13] J., Lu, K. N. Plataniotis and A. N. Venetsanopoulos, Face recognition using kernel discriminant analysis algorithms, IEEE Trans. Neural Networks, Vol. 14(1), 117-126, 2003.
[14] J., Yang, A.F. Frangi, J. Yang, D. Zhang and Z. Jin. KPCA plus LDA: a complete kernel fisher discriminant framework for feature extraction and recognition, IEEE Trans. PAMI 27(2), 230-244, 2005.
[15] C., Blake, E., Keogh and C. J., Merz., UCI Repository of Machine Learning Databases. Dept. Inform. Comput. Sci., Univ. California, Irvine, CA, 1998. Available from< http://www.ics.uci.edu/mlearn>.
[16] B. Leibe and B. Schiele, Analyzing Appearance and Contour Based Methods for Object Categorization, Proc. IEEE Conf. Computer Vision and Pattern Recognition, June 2003.
[17] Bo Chen, Hongwei Liu, Zheng Bao. Kernel Subclass Discriminant Analysis. Neurocomputing, Vol. 71, 455-458, 2007.
[18] 刘宏伟,马建华,保铮 . BOX-COX 变换提高雷达高分辨距离像识别性能的物理机理分析. 烟台:海军航空工程学院. 254-357,2004.
[1] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, Vol. 20, 273-297, 1995.
[2] B. Schoelkopf, C. Burges, and A. Smola (editors). Advances in kernel methods: Support Vector Machines. Cambridge, MA: MIT Press, 1998.
[3] A. Smola, P. L. Bartlett, B. Scheolkopf and J. Schurmann (editors). Advances in Large Margin Classifiers. Cambridge, MA: MIT Press, 2000.
[4] V. Vapnik. The nature of statistical learning theory. N. Y.: Springer, 1995.
[5] C. J. C.Burges. Simplified support vector decision rules. The Proc. of ICML’96. San Mateo, CA, 71-77, 1996.
[6] B. Schoelkopf, S. Mika, C. J. C. Burges, P. knirsch, K. Muller, G. Ratsch, and A. J. Smola. Input space versus feature space in kernel-based methods. IEEE Trans. Neural Networks, Vol. 10, 1000-1017, 1999.
[7] DucDung Nguyen and Ho TuBao. An efficient method for simplifying support machines. The Proc. of ICML’05. Bonn, Germany, 2005.
[8] G. Baudat and F. Anouar. Feature vector selection and projection using kernels. Neurocomputing, Vol.5, 20-38, 2003.
[9] Bo Chen, Hongwei Liu and Zheng Bao. Speeding Up SVM In Test Phase: Application To Radar HRRP ATR. The Proc. of ICONIP’06. Hongkong, China, 2006.
[10] S. Theodoridis and K. Koutroumbas. Pattern Recognition, second edition. USA: Elsevier Science.
[11] A. J. Smola and B. Scheolkopf. Sparse greedy matrix approximation for machine learning. The Proc. of ICML’00. 2000: 911-918.
[12] Antoine Bordes, Seyda Ertekin, Jason Weston and Leon Bottou. Fast kernel classifiers with online and active learning. Journal of Machine Learning Research, Vol. 6, 1579-1619, 2005.
[13] C. Domingo and O.Watanabe. MadaBoost: a modification of AdaBoost. The Proc. of COLT’00. Berlin: Springer, 180–189, 2000.
[14] S. Sathiya Keerthi, Olivier Chapelle and Dennis DeCoste. Building Support Vector Machine with Reduced Classifier Complexity. Journal of Machine LearningResearch, Vol. 8, 1-22, 2006.
[15] A. J. Smola and P. L. Bartlett. Sparse greedy Gaussian process regression. The Proc. of NIPS’01, Cambridge, MA, 619-625, 2001.
[16] I. W. Tsang, J. T. Kwok, and P.-M Cheung. Core vector machines: Fast SVM training on very large data sets. Journal of Machine Learning Research, Vol. 6, 363-392, 2005.
[17] S. V. N. Vishwanathan, A. J. Smola, and M. Narasimha Murty. SimpleSVM. The Proc. of ICML’03, 760–767, 2003.
[18] Lan Du, Hongwei Liu, Zheng Bao and Mengdao Xing. Radar HRRP target recognition based on higher order spectra. IEEE Transactions on Signal Processing , Vol. 54(6): 2359-2368, 2006.
[19] Lan Du, Hongwei Liu, Zheng Bao and Junying Zhang. A two-distribution compounded statistical modelfor radar HRRP target recognition. IEEE Transactions on Signal Processing, Vol. 53(7), 2226-2238, 2005.
[20] 陈渤,刘宏伟,保铮. 一种针对高分辨距离像识别的融合核优化算法.电子学报, Vol.34 (6), 1146-1151,2006.
[21] Yoshua Bengio, Olivier Delalleau and Nicolas Le Roux. The curse of dimensionality for local kernel machines. Technical Report 1258, Dept. IRO, University of Montreal, Canada, 2005.
[22] C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, Vol. 2, 121–167, 1998.
[23] W J Duncan. Some devices for the solution of large sets of simultaneous linear equations, The London, Edinburgh, anf Dublin Philosophical Magazine and Journal of Science 1944, Series 7, 35, 660-670.
[24] M A Woodbury. Inverting modified matrices. Memorandum Report 42, Statistical Research Group, NJ: Princeton, 1950.
[1] N. Cristianini and J. Shawe-Taylor, An Introduction to support vector machines. Cambridge: Cambridge Univ. Press, 2000.
[2] B. Scholkopf and A. J. Smola, Learning with kernels, MIT Press, Cambridge, MA, 2002.
[3] V. Vapnik, Statistical learning theory. New York: Wiley, 1998.
[4] O. Chapelle, V. Vapnik, O. Bousquet and S. Mukherjee. Choosing multiple parameters for support vector machines, Machine Learning, Vol. 46(1), 131-159, 2002.
[5] J. T. Kwok. The evidence framework applied to support vector machines, IEEE Trans. Neural Networks, Vol.11(5), 1162–1173, 2000.
[6] P. Sollich. Bayesian methods for support vector machines: Evidence and predictive class probabilities, Machine Learning, Vol. 46(1-3), 21–52, 2002.
[7] M. M. S. Lee, S. S. Keerthi, C. J. Ong, and D. DeCoste. An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels, IEEE Trans. Neural Networks, Vol. 15(3), 750–757, 2004.
[8] Daoqiang Zhang, Songcan Chen and Zhi-Hua Zhou. Learning the kernel parameters in kernel minimum distance classifier, Pattern Recognition, Vol. 39(1), 133-135, 2006.
[9] N. Cristianini, J. Kandola, A. Elisseeff and J. Shawe-Taylor. On kernel target alignment, in: Advances in Neural Information Processing Systems (NIPS’01), MIT Press, Cambridge, MA, 2001, 367-373.
[10] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui and M. I. Jordan. Learning the kernel matrix with semidefinte programming, J. Mach. Learn. Res., Vol. 5, 27-72, 2004.
[11] O. Bousquet and D. Herrmann. On the complexity of learning the kernel matrix, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press,Cambridge, MA, 2003.
[12] C. S. Ong, A. J. Smola, R. C.Williamson. Learning the kernel with hyperkernels, J. Mach. Learn. Res., Vol. 3, 1001-1030, 2003.
[13] K. Crammer, J. Keshet, Y. Singer. Kernel design using boosting, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[14] T. Hertz, A. B. Hillel and D. Weinshall. Learning a kernel function for classification with small training samples, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, 2006.
[15] James T. Kwok and Ivor W. Tsang. Learning with idealized kernels, in: Proceedings of the International Conference on Machine Learning, Washington DC, USA, 2003.
[16] S. Amari and S. Wu. Improving support vector machine classifiers by modifying kernel functions, Neural Networks, Vol. 12(6), 783–789, 1999.
[17] H. L. Xiong, M. N. S. Swamy and M. Omair Ahmad, Optimizing the kernel in the empirical feature space, IEEE Trans. Neural Networks, Vol. 16(2), 460-474, 2005.
[18] Bo Chen, Hongwei Liu, Zheng Bao. A Kernel Optimization Method Based on the Localized Kernel Fisher, Pattern Recognition, Vol. 41(3), 1098-1109, 2008.
[19] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. Vol. 41(6): 2107-2119, 2008.
[20] Bo Chen, Hongwei Liu, Zheng Bao. An Efficient Kernel Optimization Method for Radar High-resolution Range Profile Recognition, EURASIP Journal on Applied Signal Processing. Vol. 2007, Article ID 49597, 10 pages, 2007.
[21] Bo Chen, Hongwei Liu, Zheng Bao. PCA and kernel PCA for radar high range resolution profiles recognition. The Proc of 2005 IEEE International Radar Conference. USA, 528-533, 2005.
[22] 保铮,邢孟道,王彤.雷达成像技术.电子工业出版社,北京,2005.
[23] Hongwei Liu and Zheng Bao. Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel. 2004 LNCS, 3174(I), 531-536.
[24] Shaohua Kevin Zhou and Rama Chellappa. From Sample Similarity to Ensemble Similarity: Probabilistic Distance Measures in Reproducing Kernel Hilbert Space. IEEE Trans. Pattern Analysis Machine Intelligence, Vol. 28(6), 917-929, 2006.
[25] C. Blake, E., Keogh and C. J., Merz, UCI Repository of Machine Learning Databases. Dept. Inform. Comput. Sci., Univ. California, Irvine, CA, 1998.[Online]. Available from< http://www.ics.uci.edu/mlearn>.
[26] S. Roweis and L. Saul. Nonlinear dimensionality reduction by locally linear embedding, Science, Vol. 290(22), 2323- 2326, 2000.
[27] T.K., Kim, J. Kittler. Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image. IEEE Trans. Pattern Anal. Mach. Intell., Vol. 27(3), 318-327, 2005.
[28] M., Sugiyama, Local Fisher discriminant analysis for supervised dimensionality reduction, Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, 2006.
[29] M., Zhu and Martinez, A. M., Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell., Vol. 28(8), 1274-1286, 2006.
[30] Yan, S., Xu, D., Zhang, B., Zhang, H., Yang, Q. and Lin, S., Graph embedding and extensions: a general framework for dimensionality reduction, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 29(1), 40-51, 2007.
[31] Huilin Xiong and Xue-wen Chen, Kernel-based distance metric learning for microarray data classification, BMC Bioinformatics, 2006, 7:299.
[32] Machine Learning, Neural and Statistical Classification, D. Michie, D.J. Spiegelhalter, C.C. Taylor, eds, Ellis Horwood, 1994, data sets available from.
[33] Sam Roweis, Finding the first few eigenvectors in a large space. Individual research note. Available from< http://www.cs.toronto.edu/~roweis/ >.
[34] Dai, J., Yan, S., Tang, X. and Kwok, J. T., Locally adaptive classification piloted by uncertainty. Proceedings of the International Conference on Machine Learning, 2006, Pittsburgh, PA.
[35] M. Loog and R.P.W. Duin. Linear dimensionality reduction via a heteroscedastic extension of LDA: the Chernoff criterion. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26(6), 32–739, 2004.
[36] Guang Dai, Dit-Yan Yeung, and Hong Chang, Extending kernel Fisher discriminant analysis with the weighted pairwise Chernoff criterion, in: Proceedings of ECCV 2006, 308-320, Springer-Verlag Berlin Heidelberg.
[37] I. Joliffe, Principal Component Analysis. Springer-Verlag, 1986.
[38] X. He, S. Yan, Y. Hu, P. Niyogi, and H. Zhang, Face recognition using laplacianfaces, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(3), 328-340, 2005.
[39] J. Tenenbaum, V. Silva, and J. Langford, A global geometric framework fornonlinear dimensionality reduction, Science, Vol. 290(22), 2319-2323, 2000.
[40] J., Yang, David Zhang, Jing-yu Yang and Ben Niu, Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 29(4), 650-664, 2007.
[1] Hudson S, Psaltis D. Correlation filters for aircraft identification from radar range profile. IEEE Trans. AES, Vol. 29(3), 741-748, 1993.
[2] Li H J, Yang S H. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. AP, Vol. 41(3), 261-268, 1993.
[3] Jacobs S P, O’sollivan J A. Automatic target recognition using sequences of high resolution radar-profiles. IEEE Trans. AES, Vol. 36(2), 364-380, 2000.
[4] Xing M D, Bao Z, Pei B N.The properties of high-resolution range profiles. Optical Engineering, Vol. 41(2), 493-504, 2002.
[5] 刘宏伟,杜兰,袁莉. 雷达高分辨距离像目标识别研究进展.电子与信息学报. 27(8), 1328-1334,2005.
[6] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition, IEEE Trans. on Signal Processing, Vol. 54(6), 2226- 2238, 2006.
[7] Anthony Zywechm and Robert E. Bogner, Radar target classification of commercial aircraft, IEEE Trans. on Aerospace and Electronic Systems, Vol. 32(2): 598-606, 1996.
[8] Anthony Zywechm and Robert E. Bogner, Coherent averaging of range profiles, Proc. IEEE International Radar Conference, 456-461, 1995.
[9] Lan Du, Hongwei Liu, Zheng Bao and Mengdao Xing, Radar HRRP target recognition based on higher order spectra. IEEE transactions on signal processing 53(7): 2359-2368. 2005.
[10] Rong Hu and Zhaoda Zhu, Research on Radar Classification based on High Resolution Range Profiles, in Proceedings of Aerospace and Electronics Conference, Vol. 2, 951-955, 1997.
[11] Xuejun Liao, Paul Runkle and Lawrence Carin, Identification of Ground Targets From Sequential High-Range-Resolution Radar Signatures, IEEE Trans. Aerospace and Electronic Systems, Vol. 38(4), 1230-1242, 2002.
[12] Yoshua Bengio and Martin Monperrus. Discovering shared structure in manifold learning. Technical Report 1250, Dept. IRO, University of Montreal, July 6, 2004.
[13] J. Tenenbaum, V. De Silva and J. Langford. A global geometric framework for nonlinear dimension reduction. Science, Vol. 290, 2319–2323, 2000.
[14] S. T. Roweis and L. K. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science, Vol. 290, 2323–2326, 2000.
[15] Z. Zhang and H. Zha. Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment. SIAM J. Scientific Computing, Vol. 26, 313–338, 2004.
[16] S. A. Gorshkov, S. P. Leschenko, V. M. Orlenko, S. Y. Sedyshev, and Y. D. Shirman, Radar Target Backscattering Simulation Software and User’s Manual. Artech House, Boston, MA, 2002.
[17] Li Q, Iiavarasan P, et al. Radar target identification using a combined early-time/late-time e-pulse technique, IEEE Trans. AP, 1998, Vol. 46(9), 1272-1278.
[18] J. Wang, Z. Zhang and H. Zha. Adaptive Manifold Learning. Technical Report CSE-04-21, Dept. CSE, Pennsylvania State University, 2004.
[19] Hongwei Liu and Zheng Bao. Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel, Springer Lecture Notes in Computer Science, 3174 (I), 531-536, 2004.
[1] A.K. Jain, R.P.W. Duin and J. Mao. Statistical pattern recognition: a review, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 22(1), 4–37, 2000.
[2] Fix, E. and Hodges, j.. Discriminatory analysis nonparametric discrimination: Consistency properties (Technical Report 4). USAF school of Aviation Medicine, 1951.
[3] Y. Yang and J.O. Pedersen. A comparative study on feature selection, in: Proceedings of ACM International Conference on Research and Development in Information Retrieval, 42–49, 1999.
[4] J. Mao and A.K. Jain. Artificial neural networks for feature selection and multivariate data projection, IEEE Trans. Neural Networks, Vol. 6(2), 296–317, 1995.
[5] R. Kohavi and G.H. John. Wrappers for feature subset selection, Artificial Intelligence, 273–324, 1997.
[6] I. Guyon and A. Elisseeff. An Introduction to Variable and Feature Selection, Journal of Machine Learning Research, Vol. 3, 1157-1182, 2003.
[7] Kononenko, I.. Estimating attributes: analysis and extensions of RELIEF. in: Proceedings of the European conference on machine learning on Machine Learning, 171–182, 1994.
[8] Gilad-Bachrach, R., Navot, A. and Tishby, N.. Margin based feature selection - theory and algorithms. ICML'04, 43-50, 2004.
[9] Yijun Sun. Iterative RELIEF for feeature weighting: algorithms, theories, and applications, IEEE Trans. on Pattern analysis and Machine Intelligence, vol. 29(6), 1-17, 2007.
[10] Kira, K. and Rendell, L. A.. A practical approach to feature selection. ICML'92, 249–256, 1992.
[11] Cor J. Veenman and David M.J. Tax. LESS: a Model-Based Classifier for Sparse Subspaces, IEEE Trans. on Pattern analysis and Machine Intelligence, Vol. 27(9), 1496-1500, 2005.
[12] Kilian Q. Weinberger, John Blitzer and Lawrence K. Saul. Distance metric learning for large margin nearest neighbor classification, NIPS 2006.
[13] L. Vandenberghe and S. P. Boyd. Semidefinite programming. SIAM Review, Vol. 38(1), 49–95, March 1996.
[14] C. Cortes and V. Vapnik, Support-vector networks. Machine Learning 20, 273-297, 1995.
[15] C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery 2, 121–167, 1998.
[16] Lerenzo Torresani and Kuang-chih Lee. Large margin component analysis, NIPS, 2006.
[17] Blake, C., Keogh, E. and Merz. C. J., UCI Repository of Machine Learning Databases. Dept. Inform. Comput Sci., Univ. California, Irvine, CA. [Online]. Available from< http://www.ics.uci.edu/mlearn>.
[18] J. Weston, S. Mukherjee, O. Chapelle, M. Pontil, T. Poggio and V. Vapnik. Feature selection for svms. In Neural Information Processing Systems, Cambridge, MA, 2001b. MIT Press.
[19] E.-J. Yeoh, M.E. Ross, S.A. Shurtleff, W.K. Williams, D. Patel, R. Mahrouz, F.G. Behm, S.C. Raimondi, M.V. Relling, A. Patel, C. Cheng, D. Campana, D. Wilkins,X. Zhou, J. Li, H. Liu, C.-H. Pui, W.E. Evans, C. Naeve, L. Wong, and J.R. Downing. Classification, Subtype Discovery, and Prediction of Outcome in Pediatric Lymphoblastic Leukemia by Gene Expression Profiling, Cancer Cell, Vol. 1, 133-143, 2002.
[20] Golub TR, Slonim DK, Tamayo P, Huard C, Gassenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA, Bloomfield CD, Lander ES. Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science, 286, 531-537, October 1999
[21] A.A. Alizadeh. Distinct types of diffuse large b-cell lymphoma identified by gene expression profiling. Nature, 403, 503–511, 2000.
[22] Pomeroy SL, Tamayo P, Gaasenbeek M, Sturla LM, Angelo M, McLaughlin ME, Kim JYH, Goumnerova LC, Black PM, Lau C, Allen JC, Zagzag D, Olson JM, Curran T, Wetmore C, Biegel JA, Poggio T, Mukherjee S, Rifkin R, Califano A, Stolovitzky G, Louis DN, Mesirov JP, Lander ES, Golub TR. Prediction of central nervous system embryonal tumor outcome based on gene expression. Nature, Vol. 415, 436-442, 2002.
[23] U. Alon, N. Barkai, D. Notterman, K. Gish, S. Ybarra, D. Mack, and A. Levine. Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon cancer tissues probed by oligonucleotide arrays. Cell Biology, Vol. 96, 6745–6750, 1999.
[24] L.J. van 't Veer, H. Dai, M.J. van de Vijver, Y.D. He, A.A.M. Hart, M. Mao, H.L. Peterse, K. van der Kooy, M.J. Marton, A.T. Witteveen, G.J. Schreiber, R.M. Kerkhoven, C. Roberts, P.S. Linsley, R. Bernards, and S.H. Friend. Gene expression profiling predicts clinical outcome of breast cancer. Nature, Vol. 415, 530-536, January 2002.
[25] Singh D, Febbo PG, Ross K, Jackson DG, Manola J, Ladd C, Tamayo P, Renshaw AA, D'Amico AV, Richie JP, Lander ES, Loda M, Kantoff PW, Golub TR, Sellers WR. Gene expression correlations of clinical prostate cancer behavior. Cancer Cell, Vol.1, 203-209, 2004.
[26] Armstrong SA, Staunton JE, Silverman LB, Pieters R, den Boer ML, Minden MD, Sallan SE, Lander ES, Golub TR, Korsmeyer SJ. MLL translocations specify a distinct gene expression profile that distigushes a unique leukemia. Nature Genetics, Vol. 30, 41-47, 2001.
[27] Jason Weston, Andre Elisseeff, Bernhard Scholkopf and Mike Tipping. Use of the zero-norm with linear models and kernel methods, Journal of Machine LearningResearch, 1439-1461, 2003.
[28] Gordon GJ, Jenson RV, Hsiao L-L, Gullans SR, Blumenstock JE, Ramaswamy S, Richards WG, Sugarbaker DJ, Bueno R. Translation of microarray data into clinically relevant cancer diagnostic tests using gene expression ratios in lung cancer and mesothelima. Cancer Research, Vol. 62, 4936-4967, 2002.
[29] S. Dudoit, J. Fridlyand, and T.P. Speed. Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data. J. Am. Statistical Assoc., Vol. 97, 77-87, 2002.
[30] D. Wettschereck, D.W. Aha and T. Mohri. A review and empirical evaluation of feature weighting methods for a class of lazy learning algorithms, Artificial Intelligence Rev., Vol. 11(1-5), 273-314, 2005.
[31] 保铮,邢孟道,王彤.雷达成像技术.电子工业出版社,北京,2005.
[32] S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. Academic Press, 1998.
[33] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.
[34] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. 41(6), 2107-2119, 2008.
[35] Dai, J., Yan, S., Tang, X. and Kwok, J. T.. Locally adaptive classification piloted by uncertainty. Proceedings of the International Conference on Machine Learning, 2006, Pittsburgh, PA.
[2] 保铮,邢孟道,王彤. 雷达成像技术. 北京:电子工业出版社,2005.
[3] C.A.Wiley. Synthetic aperture radar. IEEE Trans. on AES, 1985, Vol. 21(3), 440-443.
[4] 杜兰,刘宏伟,保铮.一种基于距离-多谱勒二维联合的群目标分辨方法.电子学报.Vol.32 (6), 881-885, 2004.
[5] 杜兰,保铮,邢孟道.直升机雷达回波的分析与检测.西安电子科技大学学报, Vol.30 (5), 574-579, 2003.
[6] Moving and stationary target acquisition and recognition, Program technology review. Denver, CO. Nov. 1996. http://www.mbvlab.wpafb.af.mil/public/MBVDATA.
[7] 廖学军. 基于高分辨距离像的雷达目标识别. 博士研究生学位论文. 西安电子科技大学. 1999。
[8] 裴炳南. 高分辨雷达自动目标识别方法研究. 博士研究生学位论文. 西安电子科技大学. 2002.
[9] 刘宏伟, 杜兰, 袁莉, 保铮. 雷达高分辨距离像目标识别研究进展. 电子与信息学报. 2005 年 8 月, 27(8),1328-1334.
[10] 邢孟道. 基于实测数据的雷达成像方法研究. 博士研究生学位论文. 西安电子科技大学. 2002.
[11] 杜兰.雷达高分辨距离像目标识别方法研究. 博士研究生学位论文. 西安电子科技大学. 2007.
[12] 袁莉. 基于高分辨距离像的雷达目标识别方法研究。博士研究生学位论文. 西安电子科技大学. 2007.
[13] Jacobs S. P.. Automatic target recognition using high-resolution radar range profiles. Ph. D. Dissertation. Washington University. 1999.
[14] Li H.-J., Yang S.-H.. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. A.P., Vol. 41(3). 261-268, 1993.
[15] Anthony Zywechm and Robert E. Bogner, Radar target classification of commercial aircraft, IEEE Trans. on Aerospace and Electronic Systems, Vol. 32(2), 598-606, 1996.
[16] Anthony Zywechm and Robert E. Bogner, Coherent averaging of range profiles, in Proceedings of IEEE International Radar Conference, 456-461, 1995.
[17] Mitchell R. A., Dewall R.. Overview of high range resolution radar target identification. In Proceedings of Automatic Target Recognition Working Group,1994.
[18] Webb A. R.. Gamma Mixture Models for Target Recognition. Pattern Recognition. Vol. 33, 2045-2054, 2000.
[19] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Trans. on Signal Processing. Vol.54 (6). 2226-2238.
[20] M. Tipping and C.M. Bishop, Probabilistic Principal Component Analysis, J. Royal Statistical Soc. B, Vol. 21(3), 611-622, 1999.
[21] Rubin D., Thayer D.. EM algorithms for ML factor analysis. Psychometrika. Vol. 47(1). 69-76, 1982.
[22] Du Lan, Liu Hngwei, Bao Zheng. Radar HRRP statistical recognition: parametric model and model selection. IEEE Trans. on Signal Processing. In press.
[23] C. Cortes and V. Vapnik, Support-vector networks. Machine Learning, Vol. 20, 273-297, 1995.
[24] V. Vapnik, The nature of statistical learning theory. Springer, N. Y., 1995.
[25] C. J. C. Burges, A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, Vol. 2, 121–167, 1998.
[26] Hongwei Liu, Zheng Bao, Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel, LNCS 3174 (I) (2004) 531-536.
[27] R. Williams, J. Westerkamp, et al, Automatic target recognition of time critical moving targets using 1D high range resolution (HRR) radar, IEEE AES Magazine, April, 37-43, 2000.
[28] Xuejun Liao, Paul Runkle and Lawrence Carin, Identification of Ground Targets From Sequential High-Range-Resolution Radar Signatures, IEEE Trans. Aerospace and Electronic Systems, Vol. 38(4), 1230-1242, 2002.
[29] P. Bharadwaj, P. Runkle, L. Carin, et al, Multiaspect classification of airborne targets via physics-based HMMs and matching pursuits, IEEE Trans. AES, Vol.37(2), 595-606, 2001.
[30] Lan Du, Hongwei Liu, Zheng Bao and Mengdao Xing. Radar HRRP target recognition based on higher order spectra. IEEE transactions on Signal Processing, Vol. 53(7), 2359-2368, 2005.
[31] Xing M.-D., Bao Z., Pei B.. The properties of high-resolution range profiles. Optical Engineering. Vol. 41(2). 493-504, 2002.
[32] Rong Hu and Zhaoda Zhu, Research on Radar Classification based on High Resolution Range Profiles, in Proceedings of Aerospace and Electronics Conference, Vol.2, 951-955, 1997.
[33] 袁莉,刘宏伟,保铮. 雷达高分辨距离像分类器的参数自适应学习算法.电子与信息学报,已录用。
[34] Bo Chen, Hongwei Liu, Zheng Bao. Adaptively Segmenting Angular Sectors for Radar HRRP ATR. EURASIP Journal on Applied Signal Processing. In press.
[35] J.Portegies Zwart, R.van der Heiden, S.Gelsema and F.Groen. Fast translation invariant classification of HRR range profiles in a zero phase representation. IEE Proc.-Radar Sonar Navig., Vol.150(6), 411-418, 2003.
[36] 陈渤,刘宏伟,保铮. 一种基于零相位表示法的 HRRP 识别方法,西电学报,Vol. 32 (5), 657-662, 2005.
[37] 陈渤,刘宏伟,保铮. 基于三种不同绝对对齐方法的分类器的分析与研究。现代雷达, Vol. 28 (3), 58-62, 2006.
[38] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. Signal Processing. Vol. 49(9), 1875-1885, 2001.
[39] Bo Chen, Hongwei Liu, Zheng Bao. An Efficient Kernel Optimization Method for Radar High-resolution Range Profile Recognition, EURASIP Journal on Applied Signal Processing. Vol. 2007, Article ID 49597, 10 pages, 2007.
[40] 杜兰, 刘宏伟, 保铮, 张军英. 一种利用雷达高分辨距离像幅度起伏特性的特征提取新方法. 电子学报. Vol.33 (3). 411-415, 2005.
[41] 杜兰,刘宏伟,保铮,张军英.一种用于雷达 HRRP 功率谱的加权特征压缩方法. 西安电子科技大学学报. Vol. 33(2). 173-177, 2006.
[42] Bo Chen, Hongwei Liu, Zheng Bao. A Kernel Optimization Method Based on the Localized Kernel Fisher, Pattern Recognition, Vol. 41(3), 1098-1109, 2008.
[43] Bo Chen, Hongwei Liu, Zheng Bao. Large Margin Feature Weighting via Linear Programming. IEEE Transactions on Knowledge and Data Engineering. In revision.
[44] C. J. C.Burges. Simplified support vector decision rules. The Proc. of ICML’96 San Mateo, CA, 71-77, 1996.
[45] B. Sch?lkopf, S. Mika, C. J. C. Burges, P. knirsch, K. Muller, G. Ratsch, and A. J. Smola. Input space versus feature space in kernel-based methods. IEEE Trans. Neural Networks, 10, 1000-1017, 1999.
[46] DucDung Nguyen and Ho TuBao. An efficient method for simplifying support machines. The Proc. of ICML’05. Bonn, Germany, 2005.
[47] Bo Chen, Hongwei Liu, Zheng Bao. Speeding up SVM in Test Phase: Application to Radar HRRP ATR. The Proc. of ICONIP’06, Hongkong, China, 2006.
[48] John Shawe-Taylor and Nello Cristianini, Kernel Methods for Pattern Analysis, Cambridge Univerisity Press, 2004.
[49] B.E.Boser, I.M. Guyon, and V.N. Vapnik, A training algorithm for optimal margin classifiers, in Proceedings of the 5th annual ACM Workshop on Computational Learning Theory, D. Haussler, Ed., 144-152, 1992.
[50] B. Sch?lkopf, Support vector learning, Oldenbourg Verlag, Munich, 1997.
[51] V. N. Vapnik, Statistical Learning Theory, Wiley, New York, 1998.
[52] B. Sch?lkopf, C.J.C. Burges, and A.J. Smola. Advances in Kernel Methods—Support Vector Learning, MIT Press, Cambridge, MA, 1999.
[53] S. Mika, G. Ratsch, J. Weston, B. Sch?lkopf, and K.-R. Muller, Fisher discriminant analysis with kernels, in Neural Networks for Signal Precessing IX, Y.-H. Hu, J.Larsen, E. Wilson, and S. Douglas, Eds. 1999, 41-48, IEEE.
[54] V. Roth and V. Steinhage, Nonlinear discriminant analysis using kernel functions, in Advances in Neural Information Precessing Systems 12, S.A. Solla, T.K. Leen, and K.-R. Muller, Eds. 2000, 568-574, MIT Press.
[55] G. Baudat and F. Anouar, Generalized discriminant analysis using a kernel approach, Neural Computation, Vol.12 (10), 2385-2404, 2000.
[56] S. Mika, G. Ratsch, J. Weston, B. Sch?lkopf, and K.-R. Muller, Invariant feature extraction and classification in kernel spaces, in Advances in Neural Information Precessing Systems 12, S.A. Solla, T.K. Leen, and K.-R. Muller, Eds. 526-532, MIT Press, 2000.
[57] A. Smola, P. L. Bartlett, B. Scheolkopf and J. Schurmann (editors). Advances in Large Margin Classifiers. Cambridge, MA: MIT Press, 2000.
[58] B. Sch?lkopf, C.J.C. Burges, and A.J. Smola, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, Vol.10, 1299-1319, 1998.
[59] S. Mika, B. Scholkopf, A.J. Smola, K.-R. Muller, M. Scholz, and G. Ratsch, Kernel PCA and de-noising in feature spaces, in Advances in Neural Information Precessing Systems 11, M.S. Kearns, S.A. Solla, and D.A. Cohn, Eds. 536-542, MIT Press, 1999.
[60] Francis R. Bach and Michael I. Jordan, Kernel Independent Component Analysis, Journal of Machine Learning Research, Vol. 3, 1-48, 2002.
[61] Bo Chen, Hongwei Liu, Zheng Bao. Kernel Subclass Discriminant Analysis. Neurocomputing, Vol. 71, 455-458, 2007.
[62] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. Vol. 41(6), 2107-2119, 2008.
[63] Bo Chen, Hongwei Liu, Zheng Bao. PCA and Kernel PCA for Radar High Range Resolution Profiles Recognition. IEEE International Radar Conference in Arlington, Virginia USA, 528-533, 2005.
[64] T. Joachims, Text categorization with support vector machines: Learning with many relevant features, in Proc. Europ. Conf. Machine Learning. Berlin, Germany: Springer-Verlag, 137–142, 1998.
[65] S. Dumais, J. Platt, D. Heckerman, and M. Sahami, Inductive learning algorithms and representations for text categorization, in Proc. 7th Int. Conf. Inform. Knowledge Management, 1998.
[66] H. Drucker, D.Wu, and V. N. Vapnik, Support vector machines for span categorization, IEEE Trans. Neural Networks, Vol. 10, 1048–1054, 1999.
[67] K.-R. Müller, A. J. Smola, G. R?tsch, B. Sch?lkopf, J. Kohlmorgen, and V. N. Vapnik, Predicting time series with support vector machines, in Artificial Neural Networks—ICANN’97. Springer Lecture Notes in Computer Science, W. Gerstner, A. Germond, M. Hasler, and J.-D. Nicoud, Eds. Berlin, Germany: Springer-Verlag, Vol. 1327, 999–1004, 1997.
[68] D. Mattera and S. Haykin, Support vector machines for dynamic reconstructionof a chaotic system, in Advances in Kernel Methods—Support Vector Learning, B. Sch?lkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 211–242, 1999.
[69] M. P. S. Brown, W. N. Grundy, D. Lin, N. Cristianini, C. Sugnet, T.S. Furey, M. Ares, and D. Haussler, Knowledge-based analysis of microarray gene expression data using support vector machines, Proc. Nat. Academy Sci., Vol. 97(1), 262–267, 2000.
[70] T. Furey, N. Cristianini, N. Duffy, D. Bednarski, M. Schummer, and D. Haussler, Support vector machine classification and validation of cancer tissue samples using microarray expression data, Bioinformatics, Vol. 16, 906–914, 2000.
[71] A. Zien, G. R?tsch, S. Mika, B. Sch?lkopf, T. Lengauer, and K.-R. Müller, Engineering support vector machine kernels that recognize translation initiation sites in DNA, Bioinformatics, Vol. 16, 799–807, 2000.
[72] T. S. Jaakkola, M. Diekhans, and D. Haussler, A discriminative framework for detecting remote protein homologies. [online] http://www.cse.ucsc.edu/~research/compbio/research.html, Oct. 1999.
[73] D. Haussler, Convolution kernels on discrete structures, UC Santa Cruz, Tech. Rep. UCSC-CRL-99-10, July 1999.
[74] O. Chapelle, V. Vapnik, O. Bousquet, S. Mukherjee, Choosing multiple parameters for support vector machines, Machine Learning, Vol.46(1), 131-159, 2002.
[75] J. T. Kwok, The evidence framework applied to support vector machines, IEEE Trans. Neural Networks, Vol. 11(5), 1162–1173, 2000.
[76] P. Sollich, Bayesian methods for support vector machines: Evidence and predictive class probabilities, Machine Learning, Vol. 46(1-3), 21–52, 2002.
[77] M. M. S. Lee, S. S. Keerthi, C. J. Ong, and D. DeCoste, An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels, IEEE Trans. Neural Networks, Vol. 15(3), 750–757, 2004.
[78] Daoqiang Zhang, Songcan Chen and Zhi-Hua Zhou, Learning the kernel parameters in kernel minimum distance classifier, Pattern Recognition, Vol. 39(1), 133-135, 2006.
[79] N. Cristianini, J. Kandola, A. Elisseeff, J. Shawe-Taylor, On kernel target alignment, in: Advances in Neural Information Processing Systems (NIPS’01), MIT Press, Cambridge, MA, 367-373, 2001.
[80] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, M. I. Jordan, Learning the kernel matrix with semidefinte programming, J. Mach. Learn. Res. 5, 27-72, 2004.
[81] O. Bousquet and D. Herrmann. On the complexity of learning the kernel matrix, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[82] C. S. Ong, A. J. Smola, R. C.Williamson, Learning the kernel with hyperkernels, J. Mach. Learn. Res., Vol. 3, 1001-1030, 2003.
[83] K. Crammer, J. Keshet, Y. Singer, Kernel design using boosting, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[84] T. Hertz, A. B. Hillel, D. Weinshall, Learning a kernel function for classification with small training samples, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, 2006.
[85] H. L. Xiong, M. N. S. Swamy, M. Omair Ahmad, Optimizing the kernel in the empirical feature space, IEEE Trans. Neural Networks, Vol. 16(2), 460-474, 2005.
[86] S. Amari, S. Wu, Improving support vector machine classifiers by modifying kernel functions, Neural Networks, Vol. 12(6), 783–789, 1999.
[87] K. Fukunaga, Introduction to statistical pattern recognition. Boston, Academic Press Inc., 1990.
[88] M. Zhu and A. M. Martinez, Subclass discriminant analysis. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 28(8), 1274-1286, 2006.
[89] A. M. Martinez and M. Zhu, Where are linear feature extraction methods applicable?, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(12), 1934-1944, 2005.
[1] John Shawe-Taylor and Nello Cristianini, Kernel Methods for Pattern Analysis, Cambridge Univerisity Press, 2004.
[2] V. Vapnik, The nature of statistical learning theory. Springer, N. Y., 1995.
[3] Richard O. Duda, Peter E. Hart, and David G. Stork. Pattern Classification, Second Edition, John Wiley & Sons, 2001.
[4] G. S. Kimeldorf and G.Wahba. Some results on Tchebycheffian spline functions, J. Math. Anal. Applicat., Vol. 33, 82–95, 1971.
[5] A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Washington, D.C.: Winston, 1977.
[6] T. Poggio and F. Girosi. Regularization algorithms for learning that are equivalent to multilayer networks, Science, Vol. 247, 978–982, 1990.
[7] D. D. Cox and F. O’Sullivan. Asymptotic analysis of penalized likelihood and related estimates, Ann. Statist., Vol. 18(4), 1676–1695, 1990.
[8] H. Akaike. A new look at the statistical model identification, IEEE Trans. Automat. Control, Vol. AC-19, 716–723, 1974.
[9] J. Moody. The effective number of parameters: An analysis of generalization and regularization in nonlinear learning systems, in Advances in Neural Information Processings Systems 4, S. J. Hanson, J. Moody, and R. P. Lippman Eds., 847–854, San Mateo CA: Morgan Kaufman, 1992.
[10] N. Murata, S. Amari, and S. Yoshizawa. Network information criterion— determining the number of hidden units for an artificial neural network model, IEEE Trans. Neural Networks, Vol. 5, 865–872, 1994.
[11] V. N. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
[12] V. N. Vapnik and A. Y. Chervonenkis. Theory of Pattern Recognition (in Russian). Moscow, Russia: Nauka, 1974.
[13] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning 20, 273-297, 1995.
[14] K. P. Bennett and O. L. Mangasarian. Robust linear programming discrimination of two linearly inseparable sets, Optimization Methods Software, Vol. 1, 23–34, 1992.
[15] B.E.Boser, I.M. Guyon, and V.N. Vapnik. A training algorithm for optimal margin classifiers, in Proceedings of the 5th annual ACM Workshop on Computational Learning Theory, D. Haussler, Ed., 144-152, 1992.
[16] M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning, Automat. Remote Contr., Vol. 25, 821–837, 1964.
[17] S. Saitoh. Theory of Reproducing Kernels and Its Applications. Harlow, U.K.: Longman, 1988.
[18] J. Mercer. Functions of positive and negative type and their connection with the theory of integral equations, Philos. Trans. Roy. Soc. London, Vol. A 209,415–446, 1909.
[19] N. Aronszajn. Theory of reproducing kernels. Transactions of the American Mathe-matical Society, 68: 337-404, 1950.
[20] B. Sch?lkopf. Support vector learning, Oldenbourg Verlag, Munich, 1997.
[21] G. Wahba. Spline models for observational data, Vol. 59 of CBMS-NSF Regional conference series in applied mathematics, SIAM, Philadephia, 1990.
[22] F. Girosi. An equivalence between sparse approximation and support vector machines, Neural Computation, 10(6), 1455-1480, 1998.
[23] Roman Rosipal. Kernel-Based regression and objective nonlinear measures to assess brain functioning. PhD Thesis, 2001.
[24] G. Kimeldorf and G. Wahba. Some results on Tchebucheffian spline functions. Journal of Machematical Analysis and Applications, Vol.33, 82-95, 1971.
[25] G. Wahba. Support vector machines, Reproducing Kernel Hilbert Spaces, and Randomized GACV. In B. Sch?lkopf, C.J.C Burges, and A.J. Smola, editor, Advances in Kernel Methods-Support Vector Learning, 69-88. MIT press, Cambridge, MA, 1999.
[26] B. Sch?lkopf, C.J.C. Burges, and A.J. Smola. Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, Vol.10, 1299-1319, 1998.
[27] S. Mika, B. Scholkopf, A.J. Smola, K.-R. Muller, M. Scholz, and G. Ratsch. Kernel PCA and de-noising in feature spaces, in Advances in Neural Information Precessing Systems 11, M.S. Kearns, S.A. Solla, and D.A. Cohn, Eds. 1999, 536-542, MIT Press.
[28] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. 41(6): 2107-2119, 2008.
[29] Bo Chen, Hongwei Liu, Zheng Bao. A Kernel Optimization Method Based on the Localized Kernel Fisher, Pattern Recognition, Vol.41 (3), 1098-1109, 2008.
[30] Bo Chen, Hongwei Liu, Zheng Bao. An Efficient Kernel Optimization Method for Radar High-resolution Range Profile Recognition, EURASIP Journal on Applied Signal Processing. Vol. 2007, Article ID 49597, 10 pages, 2007.
[31] J. T. Kwok, The evidence framework applied to support vector machines, IEEE Trans. Neural Networks, Vol. 11(5), 1162–1173, 2000.
[32] P. Sollich, Bayesian methods for support vector machines: Evidence and predictive class probabilities, Machine Learning, Vol. 46(1-3), 21–52, 2002.
[33] M. M. S. Lee, S. S. Keerthi, C. J. Ong, and D. DeCoste. An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels, IEEE Trans. Neural Networks, Vol. 15(3), 750–757, 2004.
[34] Daoqiang Zhang, Songcan Chen and Zhi-Hua Zhou. Learning the kernel parameters in kernel minimum distance classifier. Pattern Recognition, Vol. 39(1), 133-135, 2006.
[35] N. Cristianini, J. Kandola, A. Elisseeff, J. Shawe-Taylor. On kernel target alignment, in: Advances in Neural Information Processing Systems (NIPS’01), MIT Press, Cambridge, MA, 367-373, 2001.
[36] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, M. I. Jordan, Learning the kernel matrix with semidefinte programming, J. Mach. Learn. Res., Vol. 5, 27-72, 2004.
[37] O. Bousquet and D. Herrmann. On the complexity of learning the kernel matrix, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[38] C. S. Ong, A. J. Smola, R. C.Williamson. Learning the kernel with hyperkernels, J. Mach. Learn. Res., Vol. 3, 1001-1030, 2003.
[39] K. Crammer, J. Keshet, Y. Singer. Kernel design using boosting, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[40] T. Hertz, A. B. Hillel, D. Weinshall. Learning a kernel function for classification with small training samples, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, 2006.
[41] James T. Kwok, Ivor W. Tsang. Learning with idealized kernels, in: Proceedings of the International Conference on Machine Learning, Washington DC, USA, 2003.
[42] H. L. Xiong, M. N. S. Swamy, M. Omair Ahmad. Optimizing the kernel in the empirical feature space, IEEE Trans. Neural Networks, Vol. 16(2), 460-474, 2005.
[43] Bo Chen, Hongwei Liu, Zheng Bao. PCA and Kernel PCA for Radar High Range Resolution Profiles Recognition. 2005 IEEE International Radar Conference in Arlington, Virginia USA: 528-533.
[44] I. T. Jolliffe. Principle Component analysis. New York: Springer-Verlag, 1986.
[45] Y.Linde, A.Buzo and R.M.Gray. An algorithm for vector quantizer design. IEEE Trans. Communications, Vol. 28(1), 84-95, 1988.
[46] András Kocsor and László Tóth. Kernel-Based feature extraction with a speech technology application. IEEE Trans on Signal Processing. 2004. 52(8): 2250-2263.
[47] Hongwei Liu and Zheng Bao. Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel. Springer Lecture Notes in Computer Science. Editors: Fuliang Yin, Jun Wang, Chengan Guo. Berlin: Springer-Verlag, 2004. 3174(I), 531-536.
[48] Anthony Zywechm, et al. Radar target classification of commercial aircraft. IEEE Trans. on Aerospace and Electronic Systems, 1996, Vol.32(2): 598-606.
[49] Xing mengdao and Bao zheng. The properties of range profile of aircraft. Optical Engineering. 2002. Vol.41(2): 493-504
[50] Anthony Zywechm and Robert E. Bogner. Coherent averaging of range profiles. Proceedings of IEEE International Radar Conference. Alexandria, VA, USA: IEEE, 456-461, 1995.
[51] 刘宏伟,马建华,保铮 . BOX-COX 变换提高雷达高分辨距离像识别性能的物理机理分析. 烟台:海军航空工程学院,2004. 254-357.
[52] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, Vol. 20, 273-297, 1995.
[1] K. Fukunaga, Introduction to statistical pattern recognition. Boston, Academic Press Inc., 1990.
[2] T.K., Kim and J. Kittler, Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(3), 318-327, 2005.
[3] Bo Chen, Hongwei Liu and Zheng Bao, A Kernel Optimization Method Based on the Localized Kernel Fisher Criterion, Pattern Recognition. In press.
[4] M. Zhu and A. M. Martinez, Subclass discriminant analysis. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 28(8), 1274-1286, 2006.
[5] A. M. Martinez and M. Zhu, Where are linear feature extraction methods applicable?, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(12), 1934-1944, 2005.
[6] G. Baudat and F. Anouar, Generalized discriminant analysis using a kernel approach, Neural Comput., 12, 2385-2404, 2000.
[7] S. Mika, G. Ratsch, J. Weston, B. Scholkopf, A. Smola and K.-R. Muller. Invariance feature extraction and classification in kernel spaces, Advances in neural information processing systems, 12, 526-532, 2000.
[8] B. Scholkopf and A. J. Smola. Learning with kernels. The MIT Press, Cambridge, MA, 2002.
[9] Sugiyama, M., Local Fisher discriminant analysis for supervised dimensionality reduction, In: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, 2006.
[10] J. Shawe-Taylor and N. Cristianini, Kernel methods for pattern analysis, Cambridge University Press, 2004.
[11] Sam Roweis. Finding the first few eigenvectors in a large space. Available from< http://www.cs.toronto.edu/~roweis/ >.
[12] B. Scholkopf, A. Smola and K.-R. Muller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, Vol. 10, 1299-1319, 1998.
[13] J., Lu, K. N. Plataniotis and A. N. Venetsanopoulos, Face recognition using kernel discriminant analysis algorithms, IEEE Trans. Neural Networks, Vol. 14(1), 117-126, 2003.
[14] J., Yang, A.F. Frangi, J. Yang, D. Zhang and Z. Jin. KPCA plus LDA: a complete kernel fisher discriminant framework for feature extraction and recognition, IEEE Trans. PAMI 27(2), 230-244, 2005.
[15] C., Blake, E., Keogh and C. J., Merz., UCI Repository of Machine Learning Databases. Dept. Inform. Comput. Sci., Univ. California, Irvine, CA, 1998. Available from< http://www.ics.uci.edu/mlearn>.
[16] B. Leibe and B. Schiele, Analyzing Appearance and Contour Based Methods for Object Categorization, Proc. IEEE Conf. Computer Vision and Pattern Recognition, June 2003.
[17] Bo Chen, Hongwei Liu, Zheng Bao. Kernel Subclass Discriminant Analysis. Neurocomputing, Vol. 71, 455-458, 2007.
[18] 刘宏伟,马建华,保铮 . BOX-COX 变换提高雷达高分辨距离像识别性能的物理机理分析. 烟台:海军航空工程学院. 254-357,2004.
[1] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, Vol. 20, 273-297, 1995.
[2] B. Schoelkopf, C. Burges, and A. Smola (editors). Advances in kernel methods: Support Vector Machines. Cambridge, MA: MIT Press, 1998.
[3] A. Smola, P. L. Bartlett, B. Scheolkopf and J. Schurmann (editors). Advances in Large Margin Classifiers. Cambridge, MA: MIT Press, 2000.
[4] V. Vapnik. The nature of statistical learning theory. N. Y.: Springer, 1995.
[5] C. J. C.Burges. Simplified support vector decision rules. The Proc. of ICML’96. San Mateo, CA, 71-77, 1996.
[6] B. Schoelkopf, S. Mika, C. J. C. Burges, P. knirsch, K. Muller, G. Ratsch, and A. J. Smola. Input space versus feature space in kernel-based methods. IEEE Trans. Neural Networks, Vol. 10, 1000-1017, 1999.
[7] DucDung Nguyen and Ho TuBao. An efficient method for simplifying support machines. The Proc. of ICML’05. Bonn, Germany, 2005.
[8] G. Baudat and F. Anouar. Feature vector selection and projection using kernels. Neurocomputing, Vol.5, 20-38, 2003.
[9] Bo Chen, Hongwei Liu and Zheng Bao. Speeding Up SVM In Test Phase: Application To Radar HRRP ATR. The Proc. of ICONIP’06. Hongkong, China, 2006.
[10] S. Theodoridis and K. Koutroumbas. Pattern Recognition, second edition. USA: Elsevier Science.
[11] A. J. Smola and B. Scheolkopf. Sparse greedy matrix approximation for machine learning. The Proc. of ICML’00. 2000: 911-918.
[12] Antoine Bordes, Seyda Ertekin, Jason Weston and Leon Bottou. Fast kernel classifiers with online and active learning. Journal of Machine Learning Research, Vol. 6, 1579-1619, 2005.
[13] C. Domingo and O.Watanabe. MadaBoost: a modification of AdaBoost. The Proc. of COLT’00. Berlin: Springer, 180–189, 2000.
[14] S. Sathiya Keerthi, Olivier Chapelle and Dennis DeCoste. Building Support Vector Machine with Reduced Classifier Complexity. Journal of Machine LearningResearch, Vol. 8, 1-22, 2006.
[15] A. J. Smola and P. L. Bartlett. Sparse greedy Gaussian process regression. The Proc. of NIPS’01, Cambridge, MA, 619-625, 2001.
[16] I. W. Tsang, J. T. Kwok, and P.-M Cheung. Core vector machines: Fast SVM training on very large data sets. Journal of Machine Learning Research, Vol. 6, 363-392, 2005.
[17] S. V. N. Vishwanathan, A. J. Smola, and M. Narasimha Murty. SimpleSVM. The Proc. of ICML’03, 760–767, 2003.
[18] Lan Du, Hongwei Liu, Zheng Bao and Mengdao Xing. Radar HRRP target recognition based on higher order spectra. IEEE Transactions on Signal Processing , Vol. 54(6): 2359-2368, 2006.
[19] Lan Du, Hongwei Liu, Zheng Bao and Junying Zhang. A two-distribution compounded statistical modelfor radar HRRP target recognition. IEEE Transactions on Signal Processing, Vol. 53(7), 2226-2238, 2005.
[20] 陈渤,刘宏伟,保铮. 一种针对高分辨距离像识别的融合核优化算法.电子学报, Vol.34 (6), 1146-1151,2006.
[21] Yoshua Bengio, Olivier Delalleau and Nicolas Le Roux. The curse of dimensionality for local kernel machines. Technical Report 1258, Dept. IRO, University of Montreal, Canada, 2005.
[22] C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, Vol. 2, 121–167, 1998.
[23] W J Duncan. Some devices for the solution of large sets of simultaneous linear equations, The London, Edinburgh, anf Dublin Philosophical Magazine and Journal of Science 1944, Series 7, 35, 660-670.
[24] M A Woodbury. Inverting modified matrices. Memorandum Report 42, Statistical Research Group, NJ: Princeton, 1950.
[1] N. Cristianini and J. Shawe-Taylor, An Introduction to support vector machines. Cambridge: Cambridge Univ. Press, 2000.
[2] B. Scholkopf and A. J. Smola, Learning with kernels, MIT Press, Cambridge, MA, 2002.
[3] V. Vapnik, Statistical learning theory. New York: Wiley, 1998.
[4] O. Chapelle, V. Vapnik, O. Bousquet and S. Mukherjee. Choosing multiple parameters for support vector machines, Machine Learning, Vol. 46(1), 131-159, 2002.
[5] J. T. Kwok. The evidence framework applied to support vector machines, IEEE Trans. Neural Networks, Vol.11(5), 1162–1173, 2000.
[6] P. Sollich. Bayesian methods for support vector machines: Evidence and predictive class probabilities, Machine Learning, Vol. 46(1-3), 21–52, 2002.
[7] M. M. S. Lee, S. S. Keerthi, C. J. Ong, and D. DeCoste. An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels, IEEE Trans. Neural Networks, Vol. 15(3), 750–757, 2004.
[8] Daoqiang Zhang, Songcan Chen and Zhi-Hua Zhou. Learning the kernel parameters in kernel minimum distance classifier, Pattern Recognition, Vol. 39(1), 133-135, 2006.
[9] N. Cristianini, J. Kandola, A. Elisseeff and J. Shawe-Taylor. On kernel target alignment, in: Advances in Neural Information Processing Systems (NIPS’01), MIT Press, Cambridge, MA, 2001, 367-373.
[10] G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui and M. I. Jordan. Learning the kernel matrix with semidefinte programming, J. Mach. Learn. Res., Vol. 5, 27-72, 2004.
[11] O. Bousquet and D. Herrmann. On the complexity of learning the kernel matrix, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press,Cambridge, MA, 2003.
[12] C. S. Ong, A. J. Smola, R. C.Williamson. Learning the kernel with hyperkernels, J. Mach. Learn. Res., Vol. 3, 1001-1030, 2003.
[13] K. Crammer, J. Keshet, Y. Singer. Kernel design using boosting, in: Advances in Neural Information Processing Systems (NIPS’03), MIT Press, Cambridge, MA, 2003.
[14] T. Hertz, A. B. Hillel and D. Weinshall. Learning a kernel function for classification with small training samples, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, 2006.
[15] James T. Kwok and Ivor W. Tsang. Learning with idealized kernels, in: Proceedings of the International Conference on Machine Learning, Washington DC, USA, 2003.
[16] S. Amari and S. Wu. Improving support vector machine classifiers by modifying kernel functions, Neural Networks, Vol. 12(6), 783–789, 1999.
[17] H. L. Xiong, M. N. S. Swamy and M. Omair Ahmad, Optimizing the kernel in the empirical feature space, IEEE Trans. Neural Networks, Vol. 16(2), 460-474, 2005.
[18] Bo Chen, Hongwei Liu, Zheng Bao. A Kernel Optimization Method Based on the Localized Kernel Fisher, Pattern Recognition, Vol. 41(3), 1098-1109, 2008.
[19] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. Vol. 41(6): 2107-2119, 2008.
[20] Bo Chen, Hongwei Liu, Zheng Bao. An Efficient Kernel Optimization Method for Radar High-resolution Range Profile Recognition, EURASIP Journal on Applied Signal Processing. Vol. 2007, Article ID 49597, 10 pages, 2007.
[21] Bo Chen, Hongwei Liu, Zheng Bao. PCA and kernel PCA for radar high range resolution profiles recognition. The Proc of 2005 IEEE International Radar Conference. USA, 528-533, 2005.
[22] 保铮,邢孟道,王彤.雷达成像技术.电子工业出版社,北京,2005.
[23] Hongwei Liu and Zheng Bao. Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel. 2004 LNCS, 3174(I), 531-536.
[24] Shaohua Kevin Zhou and Rama Chellappa. From Sample Similarity to Ensemble Similarity: Probabilistic Distance Measures in Reproducing Kernel Hilbert Space. IEEE Trans. Pattern Analysis Machine Intelligence, Vol. 28(6), 917-929, 2006.
[25] C. Blake, E., Keogh and C. J., Merz, UCI Repository of Machine Learning Databases. Dept. Inform. Comput. Sci., Univ. California, Irvine, CA, 1998.[Online]. Available from< http://www.ics.uci.edu/mlearn>.
[26] S. Roweis and L. Saul. Nonlinear dimensionality reduction by locally linear embedding, Science, Vol. 290(22), 2323- 2326, 2000.
[27] T.K., Kim, J. Kittler. Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image. IEEE Trans. Pattern Anal. Mach. Intell., Vol. 27(3), 318-327, 2005.
[28] M., Sugiyama, Local Fisher discriminant analysis for supervised dimensionality reduction, Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, 2006.
[29] M., Zhu and Martinez, A. M., Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell., Vol. 28(8), 1274-1286, 2006.
[30] Yan, S., Xu, D., Zhang, B., Zhang, H., Yang, Q. and Lin, S., Graph embedding and extensions: a general framework for dimensionality reduction, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 29(1), 40-51, 2007.
[31] Huilin Xiong and Xue-wen Chen, Kernel-based distance metric learning for microarray data classification, BMC Bioinformatics, 2006, 7:299.
[32] Machine Learning, Neural and Statistical Classification, D. Michie, D.J. Spiegelhalter, C.C. Taylor, eds, Ellis Horwood, 1994, data sets available from
[33] Sam Roweis, Finding the first few eigenvectors in a large space. Individual research note. Available from< http://www.cs.toronto.edu/~roweis/ >.
[34] Dai, J., Yan, S., Tang, X. and Kwok, J. T., Locally adaptive classification piloted by uncertainty. Proceedings of the International Conference on Machine Learning, 2006, Pittsburgh, PA.
[35] M. Loog and R.P.W. Duin. Linear dimensionality reduction via a heteroscedastic extension of LDA: the Chernoff criterion. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26(6), 32–739, 2004.
[36] Guang Dai, Dit-Yan Yeung, and Hong Chang, Extending kernel Fisher discriminant analysis with the weighted pairwise Chernoff criterion, in: Proceedings of ECCV 2006, 308-320, Springer-Verlag Berlin Heidelberg.
[37] I. Joliffe, Principal Component Analysis. Springer-Verlag, 1986.
[38] X. He, S. Yan, Y. Hu, P. Niyogi, and H. Zhang, Face recognition using laplacianfaces, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 27(3), 328-340, 2005.
[39] J. Tenenbaum, V. Silva, and J. Langford, A global geometric framework fornonlinear dimensionality reduction, Science, Vol. 290(22), 2319-2323, 2000.
[40] J., Yang, David Zhang, Jing-yu Yang and Ben Niu, Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 29(4), 650-664, 2007.
[1] Hudson S, Psaltis D. Correlation filters for aircraft identification from radar range profile. IEEE Trans. AES, Vol. 29(3), 741-748, 1993.
[2] Li H J, Yang S H. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. AP, Vol. 41(3), 261-268, 1993.
[3] Jacobs S P, O’sollivan J A. Automatic target recognition using sequences of high resolution radar-profiles. IEEE Trans. AES, Vol. 36(2), 364-380, 2000.
[4] Xing M D, Bao Z, Pei B N.The properties of high-resolution range profiles. Optical Engineering, Vol. 41(2), 493-504, 2002.
[5] 刘宏伟,杜兰,袁莉. 雷达高分辨距离像目标识别研究进展.电子与信息学报. 27(8), 1328-1334,2005.
[6] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition, IEEE Trans. on Signal Processing, Vol. 54(6), 2226- 2238, 2006.
[7] Anthony Zywechm and Robert E. Bogner, Radar target classification of commercial aircraft, IEEE Trans. on Aerospace and Electronic Systems, Vol. 32(2): 598-606, 1996.
[8] Anthony Zywechm and Robert E. Bogner, Coherent averaging of range profiles, Proc. IEEE International Radar Conference, 456-461, 1995.
[9] Lan Du, Hongwei Liu, Zheng Bao and Mengdao Xing, Radar HRRP target recognition based on higher order spectra. IEEE transactions on signal processing 53(7): 2359-2368. 2005.
[10] Rong Hu and Zhaoda Zhu, Research on Radar Classification based on High Resolution Range Profiles, in Proceedings of Aerospace and Electronics Conference, Vol. 2, 951-955, 1997.
[11] Xuejun Liao, Paul Runkle and Lawrence Carin, Identification of Ground Targets From Sequential High-Range-Resolution Radar Signatures, IEEE Trans. Aerospace and Electronic Systems, Vol. 38(4), 1230-1242, 2002.
[12] Yoshua Bengio and Martin Monperrus. Discovering shared structure in manifold learning. Technical Report 1250, Dept. IRO, University of Montreal, July 6, 2004.
[13] J. Tenenbaum, V. De Silva and J. Langford. A global geometric framework for nonlinear dimension reduction. Science, Vol. 290, 2319–2323, 2000.
[14] S. T. Roweis and L. K. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science, Vol. 290, 2323–2326, 2000.
[15] Z. Zhang and H. Zha. Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment. SIAM J. Scientific Computing, Vol. 26, 313–338, 2004.
[16] S. A. Gorshkov, S. P. Leschenko, V. M. Orlenko, S. Y. Sedyshev, and Y. D. Shirman, Radar Target Backscattering Simulation Software and User’s Manual. Artech House, Boston, MA, 2002.
[17] Li Q, Iiavarasan P, et al. Radar target identification using a combined early-time/late-time e-pulse technique, IEEE Trans. AP, 1998, Vol. 46(9), 1272-1278.
[18] J. Wang, Z. Zhang and H. Zha. Adaptive Manifold Learning. Technical Report CSE-04-21, Dept. CSE, Pennsylvania State University, 2004.
[19] Hongwei Liu and Zheng Bao. Radar HRR profiles recognition based on SVM with power-transformed-correlation kernel, Springer Lecture Notes in Computer Science, 3174 (I), 531-536, 2004.
[1] A.K. Jain, R.P.W. Duin and J. Mao. Statistical pattern recognition: a review, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 22(1), 4–37, 2000.
[2] Fix, E. and Hodges, j.. Discriminatory analysis nonparametric discrimination: Consistency properties (Technical Report 4). USAF school of Aviation Medicine, 1951.
[3] Y. Yang and J.O. Pedersen. A comparative study on feature selection, in: Proceedings of ACM International Conference on Research and Development in Information Retrieval, 42–49, 1999.
[4] J. Mao and A.K. Jain. Artificial neural networks for feature selection and multivariate data projection, IEEE Trans. Neural Networks, Vol. 6(2), 296–317, 1995.
[5] R. Kohavi and G.H. John. Wrappers for feature subset selection, Artificial Intelligence, 273–324, 1997.
[6] I. Guyon and A. Elisseeff. An Introduction to Variable and Feature Selection, Journal of Machine Learning Research, Vol. 3, 1157-1182, 2003.
[7] Kononenko, I.. Estimating attributes: analysis and extensions of RELIEF. in: Proceedings of the European conference on machine learning on Machine Learning, 171–182, 1994.
[8] Gilad-Bachrach, R., Navot, A. and Tishby, N.. Margin based feature selection - theory and algorithms. ICML'04, 43-50, 2004.
[9] Yijun Sun. Iterative RELIEF for feeature weighting: algorithms, theories, and applications, IEEE Trans. on Pattern analysis and Machine Intelligence, vol. 29(6), 1-17, 2007.
[10] Kira, K. and Rendell, L. A.. A practical approach to feature selection. ICML'92, 249–256, 1992.
[11] Cor J. Veenman and David M.J. Tax. LESS: a Model-Based Classifier for Sparse Subspaces, IEEE Trans. on Pattern analysis and Machine Intelligence, Vol. 27(9), 1496-1500, 2005.
[12] Kilian Q. Weinberger, John Blitzer and Lawrence K. Saul. Distance metric learning for large margin nearest neighbor classification, NIPS 2006.
[13] L. Vandenberghe and S. P. Boyd. Semidefinite programming. SIAM Review, Vol. 38(1), 49–95, March 1996.
[14] C. Cortes and V. Vapnik, Support-vector networks. Machine Learning 20, 273-297, 1995.
[15] C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery 2, 121–167, 1998.
[16] Lerenzo Torresani and Kuang-chih Lee. Large margin component analysis, NIPS, 2006.
[17] Blake, C., Keogh, E. and Merz. C. J., UCI Repository of Machine Learning Databases. Dept. Inform. Comput Sci., Univ. California, Irvine, CA. [Online]. Available from< http://www.ics.uci.edu/mlearn>.
[18] J. Weston, S. Mukherjee, O. Chapelle, M. Pontil, T. Poggio and V. Vapnik. Feature selection for svms. In Neural Information Processing Systems, Cambridge, MA, 2001b. MIT Press.
[19] E.-J. Yeoh, M.E. Ross, S.A. Shurtleff, W.K. Williams, D. Patel, R. Mahrouz, F.G. Behm, S.C. Raimondi, M.V. Relling, A. Patel, C. Cheng, D. Campana, D. Wilkins,X. Zhou, J. Li, H. Liu, C.-H. Pui, W.E. Evans, C. Naeve, L. Wong, and J.R. Downing. Classification, Subtype Discovery, and Prediction of Outcome in Pediatric Lymphoblastic Leukemia by Gene Expression Profiling, Cancer Cell, Vol. 1, 133-143, 2002.
[20] Golub TR, Slonim DK, Tamayo P, Huard C, Gassenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA, Bloomfield CD, Lander ES. Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science, 286, 531-537, October 1999
[21] A.A. Alizadeh. Distinct types of diffuse large b-cell lymphoma identified by gene expression profiling. Nature, 403, 503–511, 2000.
[22] Pomeroy SL, Tamayo P, Gaasenbeek M, Sturla LM, Angelo M, McLaughlin ME, Kim JYH, Goumnerova LC, Black PM, Lau C, Allen JC, Zagzag D, Olson JM, Curran T, Wetmore C, Biegel JA, Poggio T, Mukherjee S, Rifkin R, Califano A, Stolovitzky G, Louis DN, Mesirov JP, Lander ES, Golub TR. Prediction of central nervous system embryonal tumor outcome based on gene expression. Nature, Vol. 415, 436-442, 2002.
[23] U. Alon, N. Barkai, D. Notterman, K. Gish, S. Ybarra, D. Mack, and A. Levine. Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon cancer tissues probed by oligonucleotide arrays. Cell Biology, Vol. 96, 6745–6750, 1999.
[24] L.J. van 't Veer, H. Dai, M.J. van de Vijver, Y.D. He, A.A.M. Hart, M. Mao, H.L. Peterse, K. van der Kooy, M.J. Marton, A.T. Witteveen, G.J. Schreiber, R.M. Kerkhoven, C. Roberts, P.S. Linsley, R. Bernards, and S.H. Friend. Gene expression profiling predicts clinical outcome of breast cancer. Nature, Vol. 415, 530-536, January 2002.
[25] Singh D, Febbo PG, Ross K, Jackson DG, Manola J, Ladd C, Tamayo P, Renshaw AA, D'Amico AV, Richie JP, Lander ES, Loda M, Kantoff PW, Golub TR, Sellers WR. Gene expression correlations of clinical prostate cancer behavior. Cancer Cell, Vol.1, 203-209, 2004.
[26] Armstrong SA, Staunton JE, Silverman LB, Pieters R, den Boer ML, Minden MD, Sallan SE, Lander ES, Golub TR, Korsmeyer SJ. MLL translocations specify a distinct gene expression profile that distigushes a unique leukemia. Nature Genetics, Vol. 30, 41-47, 2001.
[27] Jason Weston, Andre Elisseeff, Bernhard Scholkopf and Mike Tipping. Use of the zero-norm with linear models and kernel methods, Journal of Machine LearningResearch, 1439-1461, 2003.
[28] Gordon GJ, Jenson RV, Hsiao L-L, Gullans SR, Blumenstock JE, Ramaswamy S, Richards WG, Sugarbaker DJ, Bueno R. Translation of microarray data into clinically relevant cancer diagnostic tests using gene expression ratios in lung cancer and mesothelima. Cancer Research, Vol. 62, 4936-4967, 2002.
[29] S. Dudoit, J. Fridlyand, and T.P. Speed. Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data. J. Am. Statistical Assoc., Vol. 97, 77-87, 2002.
[30] D. Wettschereck, D.W. Aha and T. Mohri. A review and empirical evaluation of feature weighting methods for a class of lazy learning algorithms, Artificial Intelligence Rev., Vol. 11(1-5), 273-314, 2005.
[31] 保铮,邢孟道,王彤.雷达成像技术.电子工业出版社,北京,2005.
[32] S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. Academic Press, 1998.
[33] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.
[34] Bo Chen, Hongwei Liu, Zheng Bao. Optimizing the Data-dependent Kernel under a Unified Kernel Optimization Framework. Pattern Recognition. 41(6), 2107-2119, 2008.
[35] Dai, J., Yan, S., Tang, X. and Kwok, J. T.. Locally adaptive classification piloted by uncertainty. Proceedings of the International Conference on Machine Learning, 2006, Pittsburgh, PA.