支撑矢量机理论与应用研究
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摘要
统计学习理论是在有限样本下建立起来的统计学理论体系，而支撑矢量机是建立在统计学习理论的VC维理论和结构风险最小化原则上的一种非常有效的机器学习方法。支撑矢量机较好的解决了以往机器学习方法中存在的小样本、非线性、过学习、高维数、局部极小值点等实际问题，且具有很强的泛化性能。
虽然统计学习理论和支撑矢量机有比较坚实的理论基础和良好的发展前景，但是对于支撑矢量机而言，还存在着以下尚未得到很好解决的问题：核函数和核参数的构造与选择缺乏理论指导、大规模样本集快速训练算法、多类支撑矢量机优化设计以及工程应用领域的拓展等。
针对上述几个问题，本文开展了基于统计学习理论和支撑矢量机目标识别方法理论与应用的研究工作，主要包括以下几个方面的内容。
(1)特征空间线性可分性。对于两类和多类目标识别问题，本文分别给出了观测样本在特征空间中线性可分的定义和充要条件。特别地，当核函数的Gram矩阵正定时，观测样本集在由核函数导出的高维特征空间中必然线性可分。
(2)基于分类间隔的特征选择。对于两类和多类目标识别问题，本文依据各特征对分类间隔的贡献大小而定义了特征有效率，并提出了一种新的特征选择算法。该算法秉承了统计学习理论的理论基础——结构风险最小化，即要求选择出的特征子集能较好的兼顾分类能力和推广性能。
(3)核函数自适应构造。本文根据观测样本在特征空间中线性可分条件，基于函数逼近论和核函数的基本性质，提出了自适应构造核函数的两种模型，即自适应多项式核函数和自适应B—Spline核函数，并给出了模型参数估计算法。
(4)多类扩码支撑矢量机。本文通过扩展类别标示符编码，提出了一种新的多类扩码支撑矢量机——半对半算法。该多类支撑矢量机模型可以序贯求解，有效地降低了计算规模，也不存在判决“死区”。此外，本文还分析了多类目标扩码识别算法的推广性能。
(5)分片支撑矢量机。本文提出了一种新的支撑矢量机模型——分片支撑矢量机。分片支撑矢量机不仅可以有效的处理高度复杂分布区域的识别问题，提高识别率和推广能力，而且可以大幅度降低计算量和存储容量。此外，本文还探讨了其推广能力的界。
(6)基于支撑矢量机的广义相关K分布杂波检测。本文推导了广义相关K分布杂波高阶自相关矩函数，给出了杂波序列产生原理图，提出了模型参数解耦估计算法。将雷达杂波环境中信号检测问题转化为目标分类识别问题，基于支撑矢量机方法在广义K分布杂波背景下实现对目标的检测。
最后对全文的工作进行总结，指出需要进一步深入研究和解决的问题。
Statistical learning theory (SLT) is a new statistical theory framework established from small samples, and support vector machines (SVM) is a novel powerful machines learning method based on VC dimension theory and structural risk minimization (RSM) principle, which are the important foundation in SLT. SVM has good generalization capability, and also has solved some practical problems such as small samples, nonlinearity, over learning, high dimension and local minimum point etc, which exit in most of the traditional machines learning method.
Although, SLT and SVM have very stabile theory foundation and good development foreground, but there still are some problems in SVM which have not been well solved. For example, the kernel fimction adaptive construction and selection, fast training arithmetic, multi-class SVM model and expanding the application field etc.
To deal with the above-mentioned problems, this dissertation has carefully studied the pattern recognition theory and application based on SLT and SVM, the main work andnovel results in this thesis are shown as followed.
(1) To the binary and multi-class objects classification problem, the thesis differently gives out the strict definition and the distinguishable condition for separating the features by linear classification hyper surface in the feature space. Especially, when the Gram matrix of kernel function is strict positive, then the samples must be linear distinguishable in the feature space which is induced by the kernel function. The results are help to feature selection, kernel function construction and classifiers design.
(2) To the binary and multi-class pattern recognition problem, in this thesis, the efficiency rate of features are defined by the contribution to classes margin of each feature, and a novel feature selection algorithm is put forward based on the feature efficiency rate. Because the new feature selection arithmetic is foundation on the RSM, so it can make good compromise between the classification capability and generalized capability, the performance of the new feature selection method, such as classification capability and generalized capability are improved obviously in contrast to the classical Relief method.
(3) In this dissertation, a novel kernel function adaptive construction algorithm is put forward, which is based on the feature linear distinguishable condition, the function approaching theory and the properties of kernel function. This new kernel functions include the adaptive polynomial model and the B-Spline model, and the model parameters estimation method are also offered. The two kernel functions have the linear distinguishable and good generalized capability.
(4) In this thesis, a new multi-class SVM model called Half-Versus-Half (H-V-H) method is put forward, which is based on increasing the dimension of decision space through extending the classes labels binary code. The new model can be sequentially solved and effectively improve the computational velocity, and it hasn't the region which is unable to test. In a addition, this dissertation has analyzed the generalized capability of H-V-H method.
(5) A novel piecewise support vector machines (PSVM) model is provided in this thesis. The PSVM has decreased the complexity of pattern recognition, and improved the computational velocity some times by partitioning the feature space into several subspaces, and it can provide the ability to classify the samples with very complex distribution. Furthermore, this dissertation has analyzed the generalized capability of PSVM model.
(6) In the dissertation, the nonlinear curve of autocorrelation coefficients is derived, and the generalized correlated K-distributed clutter simulation principle and the flow diagram are presented in the paper, then a novel model parameters estimation algorithm is also put forward through the parameter decoupling technology. Additional, this dissertation has applied SVM to detect the objects in generalized correlated K-distributed radar clutter.
The problems needed further research and some personal ideas for developing SVM are pointed out in conclusion part.
虽然统计学习理论和支撑矢量机有比较坚实的理论基础和良好的发展前景，但是对于支撑矢量机而言，还存在着以下尚未得到很好解决的问题：核函数和核参数的构造与选择缺乏理论指导、大规模样本集快速训练算法、多类支撑矢量机优化设计以及工程应用领域的拓展等。
针对上述几个问题，本文开展了基于统计学习理论和支撑矢量机目标识别方法理论与应用的研究工作，主要包括以下几个方面的内容。
(1)特征空间线性可分性。对于两类和多类目标识别问题，本文分别给出了观测样本在特征空间中线性可分的定义和充要条件。特别地，当核函数的Gram矩阵正定时，观测样本集在由核函数导出的高维特征空间中必然线性可分。
(2)基于分类间隔的特征选择。对于两类和多类目标识别问题，本文依据各特征对分类间隔的贡献大小而定义了特征有效率，并提出了一种新的特征选择算法。该算法秉承了统计学习理论的理论基础——结构风险最小化，即要求选择出的特征子集能较好的兼顾分类能力和推广性能。
(3)核函数自适应构造。本文根据观测样本在特征空间中线性可分条件，基于函数逼近论和核函数的基本性质，提出了自适应构造核函数的两种模型，即自适应多项式核函数和自适应B—Spline核函数，并给出了模型参数估计算法。
(4)多类扩码支撑矢量机。本文通过扩展类别标示符编码，提出了一种新的多类扩码支撑矢量机——半对半算法。该多类支撑矢量机模型可以序贯求解，有效地降低了计算规模，也不存在判决“死区”。此外，本文还分析了多类目标扩码识别算法的推广性能。
(5)分片支撑矢量机。本文提出了一种新的支撑矢量机模型——分片支撑矢量机。分片支撑矢量机不仅可以有效的处理高度复杂分布区域的识别问题，提高识别率和推广能力，而且可以大幅度降低计算量和存储容量。此外，本文还探讨了其推广能力的界。
(6)基于支撑矢量机的广义相关K分布杂波检测。本文推导了广义相关K分布杂波高阶自相关矩函数，给出了杂波序列产生原理图，提出了模型参数解耦估计算法。将雷达杂波环境中信号检测问题转化为目标分类识别问题，基于支撑矢量机方法在广义K分布杂波背景下实现对目标的检测。
最后对全文的工作进行总结，指出需要进一步深入研究和解决的问题。
Statistical learning theory (SLT) is a new statistical theory framework established from small samples, and support vector machines (SVM) is a novel powerful machines learning method based on VC dimension theory and structural risk minimization (RSM) principle, which are the important foundation in SLT. SVM has good generalization capability, and also has solved some practical problems such as small samples, nonlinearity, over learning, high dimension and local minimum point etc, which exit in most of the traditional machines learning method.
Although, SLT and SVM have very stabile theory foundation and good development foreground, but there still are some problems in SVM which have not been well solved. For example, the kernel fimction adaptive construction and selection, fast training arithmetic, multi-class SVM model and expanding the application field etc.
To deal with the above-mentioned problems, this dissertation has carefully studied the pattern recognition theory and application based on SLT and SVM, the main work andnovel results in this thesis are shown as followed.
(1) To the binary and multi-class objects classification problem, the thesis differently gives out the strict definition and the distinguishable condition for separating the features by linear classification hyper surface in the feature space. Especially, when the Gram matrix of kernel function is strict positive, then the samples must be linear distinguishable in the feature space which is induced by the kernel function. The results are help to feature selection, kernel function construction and classifiers design.
(2) To the binary and multi-class pattern recognition problem, in this thesis, the efficiency rate of features are defined by the contribution to classes margin of each feature, and a novel feature selection algorithm is put forward based on the feature efficiency rate. Because the new feature selection arithmetic is foundation on the RSM, so it can make good compromise between the classification capability and generalized capability, the performance of the new feature selection method, such as classification capability and generalized capability are improved obviously in contrast to the classical Relief method.
(3) In this dissertation, a novel kernel function adaptive construction algorithm is put forward, which is based on the feature linear distinguishable condition, the function approaching theory and the properties of kernel function. This new kernel functions include the adaptive polynomial model and the B-Spline model, and the model parameters estimation method are also offered. The two kernel functions have the linear distinguishable and good generalized capability.
(4) In this thesis, a new multi-class SVM model called Half-Versus-Half (H-V-H) method is put forward, which is based on increasing the dimension of decision space through extending the classes labels binary code. The new model can be sequentially solved and effectively improve the computational velocity, and it hasn't the region which is unable to test. In a addition, this dissertation has analyzed the generalized capability of H-V-H method.
(5) A novel piecewise support vector machines (PSVM) model is provided in this thesis. The PSVM has decreased the complexity of pattern recognition, and improved the computational velocity some times by partitioning the feature space into several subspaces, and it can provide the ability to classify the samples with very complex distribution. Furthermore, this dissertation has analyzed the generalized capability of PSVM model.
(6) In the dissertation, the nonlinear curve of autocorrelation coefficients is derived, and the generalized correlated K-distributed clutter simulation principle and the flow diagram are presented in the paper, then a novel model parameters estimation algorithm is also put forward through the parameter decoupling technology. Additional, this dissertation has applied SVM to detect the objects in generalized correlated K-distributed radar clutter.
The problems needed further research and some personal ideas for developing SVM are pointed out in conclusion part.
引文
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