鲁棒线性子空间学习算法与框架研究

发布时间：2018-05-21 06:39

  本文选题：线性子空间学习 + 鲁棒　； 参考：《西南交通大学》2015年博士论文

【摘要】：为了获取隐藏在高维数据中的有用信息,线性子空间学习方法往往被用来降低这些数据的维数。然而,很多现有的线性子空间学习算法对噪声、离群数据或其它扰动缺乏鲁棒性,以致相关学习算法在各种应用系统中的可靠性差。因此,该文旨在提高传统线性子空间学习算法的鲁棒性,将首先通过对线性子空间学习算法进行理论分析,然后找出影响各种学习算法鲁棒性的理论依据并对相关线性子空间方法进行改进。在此研究基础上,该文对一些关系密切的方法进行归纳总结并提出了两种一般框架,这为未来的研究工作打下了良好的基础。该文主要工作和创新包含以下五个方面：(1)为了进一步提高LPP-L1的鲁棒性,第二章提出一种基于最大相关熵标准的局部保持投影算法(LPP-MCC).LPP-MCC采用相关熵来度量数据间的相似性,形成基于最大相关熵的目标函数,并通过一个迭代的半二次优化框架轻松实现其目标函数的求解。LPP-MCC具有三个重要的优点：一是LPP-MCC在对抗离群数据方面比基于L2范数和L1范数的LPP都更具鲁棒性；二是LPP-MCC的求解过程本质上是一种简单的标准优化方法；三是LPP-MCC成功地避免了小样本问题。在人工合成数据集和从真实世界采集的数据集上的实验结果也表明LPP-MCC在对抗离群数据方面比LPP-L2和LPP-L1更具有鲁棒性。(2)虽然LDA-R1显著地提高LDA-L2对抗离群数据的鲁棒性,但是LDA-R1在面对高维输入空间时难以收敛。受PCA-L1和CSP-L1的启发,第三章提出一种基于L1范数最大化的线性鉴别分析算法(LDA-L1)。 LDA-L1是一种简单而有效的鲁棒算法,通过最大化基于L1范数的类间距与基于L1范数的类内距之比学习一系列局部最优投影向量。但是,直接求解LDA-L1的全局最优解是非常困难的。为此,一种基于迭代过程的贪婪搜索方案被用于求解其近似解。在人工合成数据集、标准分类数据集和三个高维图像数据库上的实验结果表明LDA-L1在对抗离群数据方面的鲁棒性强于LDA-L2和LDA-R1的同时,其计算开销要低于LDA-R1。(3)传统的鉴别局部保持投影算法(DLPP-L2)是一种基于子流形学习的线性维数约简技术,其目标函数采用基于L2范数的距离度量标准,所以其对离群数据非常敏感。受L1范数最大化方法的启发,第四章提出一种基于L1范数最大化的鲁棒鉴别局部保持投影算法(DLPP-L1),其通过最大化基于L1范数的局部保持类间散度与基于Ll范数的局部保持类内散度的比率学习一系列局部最优投影向量。DLPP-L1的求解过程被证明是可行的,而且克服了小样本问题。在人工合成数据集、Binary Alphadigits数据库、FERET人脸数据库子集上和PolyU掌纹数据库上的实验结果表明DLPP-L1比基于L2范数的DLPP类方法更具鲁棒性。(4)在充分分析多种鉴别分析方法的基础上,第五章提出了一种基于相似性度量的鉴别分析一般框架。该框架表明鉴别分析方法由四个方面构成：一是相似性的度量标准；二是数据的表现形式；三是相似性的计算方式；四是目标问题的形成和求解算法。在该框架下可对现有的诸多鉴别分析算法做出阐释,而且可设计出新的鲁棒鉴别分析算法。为此,第五章还根据该框架提出一种基于L2和L1范数的鲁棒鉴别分析算法-——LDA-L2L1,其类间相似性度量的标准采用基于L2范数的距离,而类内相似性度量的标准采用基于L1范数的距离。实验结果表明LDA-L2L1算法是有效的,也间接证明基于相似性度量的鉴别分析一般框架是有效的。(5)为了提高子空间学习方法在处理图像数据时的可靠性,第六章以人脸识别为例提出一种基于局部纹理模式的子空间学习一般框架,该框架是利用简单的叠加思想来形成一种有效的综合方案。在该框架的指导下,第六章提出一种基于ELDP的鲁棒子空间学习人脸识别方案。为更具鲁棒性,方案采用了鲁棒的纹理算子ELDP。ELDP是第六章在LDP的基础上提出的一种优化纹理算子,在三个人脸数据库上的实验表明ELDP在保持鉴别性的同时提高了LDP对抗轻微噪声的鲁棒性。在CAS-PEAL-R1人脸数据库上的实验结果表明推荐方案是有效的,这也说明基于局部纹理模式的子空间学习框架具有参考价值。
[Abstract]:In order to obtain useful information hidden in high dimensional data, linear subspace learning methods are often used to reduce the dimensions of these data. However, many existing linear subspace learning algorithms are not robust to noise, outlier data or other disturbances, so that the reliability of the correlation learning algorithm is poor in various application systems. The purpose of this paper is to improve the robustness of the traditional linear subspace learning algorithm. First, it will analyze the linear subspace learning algorithm, and then find out the theoretical basis which affects the robustness of various learning algorithms and improve the related linear subspace methods. On the basis of this study, this paper makes some close related methods. Two general frameworks are summarized and proposed. The main work and innovation of this paper include the following five aspects: (1) in order to further improve the robustness of LPP-L1, the second chapter proposes a local preserving projection algorithm (LPP-MCC) based on the maximum correlation entropy standard (.LPP-MCC) using the correlation entropy. The similarity between the data is measured and the objective function based on the maximum correlation entropy is formed, and.LPP-MCC has three important advantages: one is that LPP-MCC is more robust than the LPP based on the L2 norm and the L1 norm, and the two is LPP-MCC. The solution process is essentially a simple standard optimization method; the three is that LPP-MCC successfully avoids the small sample problem. Experimental results on synthetic data sets and data collected from the real world show that LPP-MCC is more robust against outlier data than LPP-L2 and LPP-L1. (2) although LDA-R1 significantly improves L DA-L2 is robust to outlier data, but LDA-R1 is difficult to converge in the face of high dimensional input space. Inspired by PCA-L1 and CSP-L1, the third chapter proposes a linear discriminant analysis algorithm (LDA-L1) based on the maximization of L1 norm. LDA-L1 is a simple and effective robust algorithm, by maximizing the class spacing based on L1 norm and based on L1 Learning a series of locally optimal projection vectors is the ratio of the norm of the norm. However, it is very difficult to directly solve the global optimal solution of LDA-L1. Therefore, a greedy search scheme based on the iterative process is used to solve its approximate solution. The experimental junctions on the synthetic data set, the standard classification data set and the three high dimensional image database are used. The results show that the robustness of LDA-L1 in anti outlier data is better than that of LDA-L2 and LDA-R1, and its computational cost is lower than that of LDA-R1. (3) the traditional discriminant local preserving projection algorithm (DLPP-L2) is a linear dimensionality reduction technique based on submanifold learning. The target function uses the distance metric based on the L2 norm, so it is out of order. The group data is very sensitive. Inspired by the method of maximizing the L1 norm, the fourth chapter proposes a robust discriminative local preserving projection algorithm (DLPP-L1) based on the maximization of the L1 norm, which can learn a series of locally optimal projection by maximizing the ratio of the inter class divergence based on the L1 norm and the ratio of the locally maintained class divergence based on the Ll norm based on the Ll norm. The solution process of the amount of.DLPP-L1 is proved to be feasible and overcomes the small sample problem. Experimental results on synthetic data sets, Binary Alphadigits database, FERET face database subset and PolyU palmprint database show that DLPP-L1 is more robust than DLPP based method based on L2 norm. (4) a variety of discriminant scores are fully analyzed. On the basis of the analysis method, the fifth chapter proposes a general framework of discriminant analysis based on similarity measure. The framework shows that the discriminant analysis method is composed of four aspects: one is the measurement standard of similarity; the two is the form of the data; three is the method of similarity calculation; four is the formation and solving algorithm of the target problem. Under the framework, many existing discriminant analysis algorithms can be explained and new robust discriminant analysis algorithms can be designed. For this, the fifth chapter also proposes a robust discriminant analysis algorithm based on L2 and L1 norm based on the framework - LDA-L2L1, which is based on the distance of the L2 norm based on the similarity measure between classes, and the intra class similarity The standard of measurement uses the distance based on L1 norm. The experimental results show that the LDA-L2L1 algorithm is effective and indirectly proves that the general framework of differential analysis based on similarity measure is effective. (5) in order to improve the reliability of the subspace learning method in processing the image data, the sixth chapter proposes a local texture based on face recognition. Model subspace learning general framework, which uses simple superposition ideas to form an effective comprehensive scheme. Under the guidance of this framework, the sixth chapter proposes a ELDP based Ru space learning face recognition scheme. For the more robust, the scheme adopts the Lu bar's texture operator ELDP.ELDP and the sixth chapter in LDP On the basis of an optimized texture operator, an experiment on three face databases shows that ELDP improves the robustness of LDP against slight noise while maintaining its identity. The experimental results on the CAS-PEAL-R1 face database show that the recommendation scheme is effective, which also illustrates the subspace learning framework based on local texture pattern. It is of reference value.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TP301.6
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本文编号：1918153