基于图的半监督学习和维数约简方法及其应用研究
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摘要
半监督学习和维数约简已经成为当前机器学习领域的研究热点。半监督学习研究的目的是在整个数据集中只有一部分样本有标记的情况下,如何对数据进行分类。本文主要研究的是基于图的半监督学习方法与应用。维数约简是在尽可能多地保持数据集结构的前提下,将数据集转换成一个新的数据集,新数据集的维数是原始数据集的本征维数。本文对基于图的半监督学习和维数约简方法与应用进行了系统的研究,具体来说,全文的主要工作概括如下：
(1)提出了一种新的多步骤降维方法对基因表达谱数据进行降维。首先采用秩和检验方法来进行差异表达的基因选择,然后将排在前面的一定数量的基因再进行离散余弦变换,并采用主成分分析对变换后的系数进行主成分提取。我们首先将基于图的半监督方法引入到肿瘤分类中,采用基于图的半监督学习算法对抽取的主成分特征进行分类性能评估。
(2)针对基于图的半监督学习方法提出了一种新的自适应权值学习方法。传统的基于图的半监督学习算法大都采用高斯函数来计算图的边权。我们提出一种新颖的针对基于图的半监督学习方法的边权设计方法。该方法添加了标签信息,并且采用测地距离而不是欧氏距离来计算两个样本点之间的距离。此外,我们还添加了类的先验信息,并针对基于局部和全局一致性的学习方法来改进边权。实验结果表明,我们所提出的方法要优于原算法。
(3)提出了一种基于局部保持投影的监督特征提取方法,即局部保持判别投影算法。局部保持投影(LPP)没有加入判别信息,仅仅考虑局部信息。我们将类内散度矩阵和类间散度矩阵加入到LPP的目标函数中,从而提出局部保持判别投影(LPDP)方法。该方法的优点是能够最大化类间距离和最小化类内距离,同时保持LPP的局部保持特性。LPDP可被看作是一种组合了流形准则和Fisher准则的新方法。因此,与LPP相比,LPDP能够成功地找到具有更好判别性能的子空间,因而更适合于做分类,从而能有效地提高识别率。
(4)提出了基于谱回归的判别分析(Spectral Regression Discriminant Analysis, SRDA)和基于谱回归的核化判别分析(Spectral Regression Kernel DiscriminantAnalysis, SRXDA)的正则化参数估计方法。SRDA的正则化参数的估计在以往的研究中没有得到很好的解决。我们基于扰动的线性判别分析(Perturbation Linear Discriminant Analysis, PLDA)准则提出一种新的方法,来估计SRDA的正则化参数。在另一方面,SRKDA的正则化参数估计在以前的研究中也没有解决。我们提出两种方法来估计SRKDA的正则化参数,在不同数据集上的实验结果显示我们的方法是有效可行的。
Recently, semi-supervised learning and dimensionality reduction have become hot topics in the field of machine learning. The goal of semi-supervised learning is to learn from partially labeled data. In this thesis, I focused on graph-based semi-supervised learning. Dimensionality reduction techniques can transform dataset X with dimensionality D into a new dataset Y with dimensionality d, while retaining the geometry of the data as much as possible. The dimensionality of the new data set, i.e., d is the intrinsic dimensionality. I make a through study on graph-based semi-supervised learning and dimensionality reduction methods. More concretely, the main work for this thesis can be summarized as follows:
(1) Both supervised methods and unsupervised methods have been widely used to solve the tumor classification problem based on gene expression profiles. This paper introduces a semi-supervised graph-based method for tumor classification. Feature extraction plays a key role in tumor classification based on gene expression profiles, and can greatly improve the performance of a classifier. In this paper we proposed a novel feature extraction method for extracting tumor-related features. First the Wilcoxon rank-sum test was used for gene selection. Then gene ranking and discrete cosine transform are combined with principal component analysis for feature extraction. Finally, the performance was evaluated by semi-supervised learning algorithms.
(2) A modified version for semi-supervised learning algorithm with local and global consistency was proposed in this paper. The new method adds the label information, and adopts the geodesic distance rather than Euclidean distance as the measure of the difference between two data points when conducting calculation. In addition, we add class prior knowledge into the cost function. It was found that the effect of class prior knowledge was different between under high label rate and low label rate. The experimental results show that the changes attain the satisfying classification performance better than the original algorithms.
(3) A new subspace learning algorithm called locality preserving discriminant projections (LPDP) was proposed by adding the maximum margin criterion (MMC) into the objective function of locality preserving projections (LPP). LPDP remains the locality preserving characteristic of LPP and utilizes label information in MMC, which can maximize the between-class distance and minimize the within-class distance. Thus our proposed LPDP is a new method that combines manifold criterion and Fisher criterion and has more discriminant power and more suitable for recognition tasks than LPP which considers only the local information for clustering or classification tasks. Moreover, two kinds of tensorized (multilinear) forms of LPDP are also derived in this paper. One is iterative while the other is non-iterative. Finally, the proposed LPDP method is applied to face and palmprint biometrics and is examined using the Yale, ORL face image databases and the PolyU palmprint database. Experimental results show the effectiveness of the proposed LPDP and demonstrate that LPDP is a good choice for real-world biometrics applications.
(4) Spectral regression discriminant analysis (SRDA) and its kernel version SRKDA are important subspace learning methods proposed recently, both of which have a free parameter, i.e., the regularization parameter. However, how to set this parameter automatically has not been well solved before. In SRDA, this regularization parameter was only set as a constant, which is obviously suboptimal. In this paper, we developed a new algorithm to automatically estimate the regularization parameter of SRDA based on the perturbation linear discriminant analysis (PLDA). We also proposed two methods for regularization parameter estimation of SRKDA. One is derived from the method of optimal regularization parameter estimation for SRDA (OR-SRDA). The other is to utilize the kernel version of PLDA. Experiments on different data sets demonstrate the effectiveness and feasisblity of proposed methods.
(1)提出了一种新的多步骤降维方法对基因表达谱数据进行降维。首先采用秩和检验方法来进行差异表达的基因选择,然后将排在前面的一定数量的基因再进行离散余弦变换,并采用主成分分析对变换后的系数进行主成分提取。我们首先将基于图的半监督方法引入到肿瘤分类中,采用基于图的半监督学习算法对抽取的主成分特征进行分类性能评估。
(2)针对基于图的半监督学习方法提出了一种新的自适应权值学习方法。传统的基于图的半监督学习算法大都采用高斯函数来计算图的边权。我们提出一种新颖的针对基于图的半监督学习方法的边权设计方法。该方法添加了标签信息,并且采用测地距离而不是欧氏距离来计算两个样本点之间的距离。此外,我们还添加了类的先验信息,并针对基于局部和全局一致性的学习方法来改进边权。实验结果表明,我们所提出的方法要优于原算法。
(3)提出了一种基于局部保持投影的监督特征提取方法,即局部保持判别投影算法。局部保持投影(LPP)没有加入判别信息,仅仅考虑局部信息。我们将类内散度矩阵和类间散度矩阵加入到LPP的目标函数中,从而提出局部保持判别投影(LPDP)方法。该方法的优点是能够最大化类间距离和最小化类内距离,同时保持LPP的局部保持特性。LPDP可被看作是一种组合了流形准则和Fisher准则的新方法。因此,与LPP相比,LPDP能够成功地找到具有更好判别性能的子空间,因而更适合于做分类,从而能有效地提高识别率。
(4)提出了基于谱回归的判别分析(Spectral Regression Discriminant Analysis, SRDA)和基于谱回归的核化判别分析(Spectral Regression Kernel DiscriminantAnalysis, SRXDA)的正则化参数估计方法。SRDA的正则化参数的估计在以往的研究中没有得到很好的解决。我们基于扰动的线性判别分析(Perturbation Linear Discriminant Analysis, PLDA)准则提出一种新的方法,来估计SRDA的正则化参数。在另一方面,SRKDA的正则化参数估计在以前的研究中也没有解决。我们提出两种方法来估计SRKDA的正则化参数,在不同数据集上的实验结果显示我们的方法是有效可行的。
Recently, semi-supervised learning and dimensionality reduction have become hot topics in the field of machine learning. The goal of semi-supervised learning is to learn from partially labeled data. In this thesis, I focused on graph-based semi-supervised learning. Dimensionality reduction techniques can transform dataset X with dimensionality D into a new dataset Y with dimensionality d, while retaining the geometry of the data as much as possible. The dimensionality of the new data set, i.e., d is the intrinsic dimensionality. I make a through study on graph-based semi-supervised learning and dimensionality reduction methods. More concretely, the main work for this thesis can be summarized as follows:
(1) Both supervised methods and unsupervised methods have been widely used to solve the tumor classification problem based on gene expression profiles. This paper introduces a semi-supervised graph-based method for tumor classification. Feature extraction plays a key role in tumor classification based on gene expression profiles, and can greatly improve the performance of a classifier. In this paper we proposed a novel feature extraction method for extracting tumor-related features. First the Wilcoxon rank-sum test was used for gene selection. Then gene ranking and discrete cosine transform are combined with principal component analysis for feature extraction. Finally, the performance was evaluated by semi-supervised learning algorithms.
(2) A modified version for semi-supervised learning algorithm with local and global consistency was proposed in this paper. The new method adds the label information, and adopts the geodesic distance rather than Euclidean distance as the measure of the difference between two data points when conducting calculation. In addition, we add class prior knowledge into the cost function. It was found that the effect of class prior knowledge was different between under high label rate and low label rate. The experimental results show that the changes attain the satisfying classification performance better than the original algorithms.
(3) A new subspace learning algorithm called locality preserving discriminant projections (LPDP) was proposed by adding the maximum margin criterion (MMC) into the objective function of locality preserving projections (LPP). LPDP remains the locality preserving characteristic of LPP and utilizes label information in MMC, which can maximize the between-class distance and minimize the within-class distance. Thus our proposed LPDP is a new method that combines manifold criterion and Fisher criterion and has more discriminant power and more suitable for recognition tasks than LPP which considers only the local information for clustering or classification tasks. Moreover, two kinds of tensorized (multilinear) forms of LPDP are also derived in this paper. One is iterative while the other is non-iterative. Finally, the proposed LPDP method is applied to face and palmprint biometrics and is examined using the Yale, ORL face image databases and the PolyU palmprint database. Experimental results show the effectiveness of the proposed LPDP and demonstrate that LPDP is a good choice for real-world biometrics applications.
(4) Spectral regression discriminant analysis (SRDA) and its kernel version SRKDA are important subspace learning methods proposed recently, both of which have a free parameter, i.e., the regularization parameter. However, how to set this parameter automatically has not been well solved before. In SRDA, this regularization parameter was only set as a constant, which is obviously suboptimal. In this paper, we developed a new algorithm to automatically estimate the regularization parameter of SRDA based on the perturbation linear discriminant analysis (PLDA). We also proposed two methods for regularization parameter estimation of SRKDA. One is derived from the method of optimal regularization parameter estimation for SRDA (OR-SRDA). The other is to utilize the kernel version of PLDA. Experiments on different data sets demonstrate the effectiveness and feasisblity of proposed methods.
引文
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