本文選題：線性子空間學習 + 魯棒��； 參考：《西南交通大學》2015年博士論文

【摘要】：為了獲取隱藏在高維數(shù)據(jù)中的有用信息,線性子空間學習方法往往被用來降低這些數(shù)據(jù)的維數(shù)。然而,很多現(xiàn)有的線性子空間學習算法對噪聲、離群數(shù)據(jù)或其它擾動缺乏魯棒性,以致相關學習算法在各種應用系統(tǒng)中的可靠性差。因此,該文旨在提高傳統(tǒng)線性子空間學習算法的魯棒性,將首先通過對線性子空間學習算法進行理論分析,然后找出影響各種學習算法魯棒性的理論依據(jù)并對相關線性子空間方法進行改進。在此研究基礎上,該文對一些關系密切的方法進行歸納總結并提出了兩種一般框架,這為未來的研究工作打下了良好的基礎。該文主要工作和創(chuàng)新包含以下五個方面：(1)為了進一步提高LPP-L1的魯棒性,第二章提出一種基于最大相關熵標準的局部保持投影算法(LPP-MCC).LPP-MCC采用相關熵來度量數(shù)據(jù)間的相似性,形成基于最大相關熵的目標函數(shù),并通過一個迭代的半二次優(yōu)化框架輕松實現(xiàn)其目標函數(shù)的求解。LPP-MCC具有三個重要的優(yōu)點：一是LPP-MCC在對抗離群數(shù)據(jù)方面比基于L2范數(shù)和L1范數(shù)的LPP都更具魯棒性；二是LPP-MCC的求解過程本質(zhì)上是一種簡單的標準優(yōu)化方法；三是LPP-MCC成功地避免了小樣本問題。在人工合成數(shù)據(jù)集和從真實世界采集的數(shù)據(jù)集上的實驗結果也表明LPP-MCC在對抗離群數(shù)據(jù)方面比LPP-L2和LPP-L1更具有魯棒性。(2)雖然LDA-R1顯著地提高LDA-L2對抗離群數(shù)據(jù)的魯棒性,但是LDA-R1在面對高維輸入空間時難以收斂。受PCA-L1和CSP-L1的啟發(fā),第三章提出一種基于L1范數(shù)最大化的線性鑒別分析算法(LDA-L1)。 LDA-L1是一種簡單而有效的魯棒算法,通過最大化基于L1范數(shù)的類間距與基于L1范數(shù)的類內(nèi)距之比學習一系列局部最優(yōu)投影向量。但是,直接求解LDA-L1的全局最優(yōu)解是非常困難的。為此,一種基于迭代過程的貪婪搜索方案被用于求解其近似解。在人工合成數(shù)據(jù)集、標準分類數(shù)據(jù)集和三個高維圖像數(shù)據(jù)庫上的實驗結果表明LDA-L1在對抗離群數(shù)據(jù)方面的魯棒性強于LDA-L2和LDA-R1的同時,其計算開銷要低于LDA-R1。(3)傳統(tǒng)的鑒別局部保持投影算法(DLPP-L2)是一種基于子流形學習的線性維數(shù)約簡技術,其目標函數(shù)采用基于L2范數(shù)的距離度量標準,所以其對離群數(shù)據(jù)非常敏感。受L1范數(shù)最大化方法的啟發(fā),第四章提出一種基于L1范數(shù)最大化的魯棒鑒別局部保持投影算法(DLPP-L1),其通過最大化基于L1范數(shù)的局部保持類間散度與基于Ll范數(shù)的局部保持類內(nèi)散度的比率學習一系列局部最優(yōu)投影向量。DLPP-L1的求解過程被證明是可行的,而且克服了小樣本問題。在人工合成數(shù)據(jù)集、Binary Alphadigits數(shù)據(jù)庫、FERET人臉數(shù)據(jù)庫子集上和PolyU掌紋數(shù)據(jù)庫上的實驗結果表明DLPP-L1比基于L2范數(shù)的DLPP類方法更具魯棒性。(4)在充分分析多種鑒別分析方法的基礎上,第五章提出了一種基于相似性度量的鑒別分析一般框架。該框架表明鑒別分析方法由四個方面構成：一是相似性的度量標準；二是數(shù)據(jù)的表現(xiàn)形式；三是相似性的計算方式；四是目標問題的形成和求解算法。在該框架下可對現(xiàn)有的諸多鑒別分析算法做出闡釋,而且可設計出新的魯棒鑒別分析算法。為此,第五章還根據(jù)該框架提出一種基于L2和L1范數(shù)的魯棒鑒別分析算法-——LDA-L2L1,其類間相似性度量的標準采用基于L2范數(shù)的距離,而類內(nèi)相似性度量的標準采用基于L1范數(shù)的距離。實驗結果表明LDA-L2L1算法是有效的,也間接證明基于相似性度量的鑒別分析一般框架是有效的。(5)為了提高子空間學習方法在處理圖像數(shù)據(jù)時的可靠性,第六章以人臉識別為例提出一種基于局部紋理模式的子空間學習一般框架,該框架是利用簡單的疊加思想來形成一種有效的綜合方案。在該框架的指導下,第六章提出一種基于ELDP的魯棒子空間學習人臉識別方案。為更具魯棒性,方案采用了魯棒的紋理算子ELDP。ELDP是第六章在LDP的基礎上提出的一種優(yōu)化紋理算子,在三個人臉數(shù)據(jù)庫上的實驗表明ELDP在保持鑒別性的同時提高了LDP對抗輕微噪聲的魯棒性。在CAS-PEAL-R1人臉數(shù)據(jù)庫上的實驗結果表明推薦方案是有效的,這也說明基于局部紋理模式的子空間學習框架具有參考價值。
[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.
【學位授予單位】：西南交通大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：TP301.6
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本文編號：1918153