聯合具有約束非負矩陣分解的支持向量機及其應用

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研究生：	林梅 Mai Lam
論文名稱：	聯合具有約束非負矩陣分解的支持向量機及其應用 Joint Support Vector Machine with Constrained Nonnegative Matrix Factorization and Its Applications
指導教授：	王家慶 Wang Jia-Ching
口試委員:
學位類別：	碩士 Master
系所名稱：	資訊電機學院 - 資訊工程學系 Department of Computer Science & Information Engineering
論文出版年：	2017
畢業學年度：	105
語文別：	英文
論文頁數：	63
中文關鍵詞：	非負矩陣分解、支持向量機、空間約束、圖形正則化、面部識別
外文關鍵詞：	nonnegative matrix factorization, support vector machine, spatial constrain, graph regularization, face recognition
相關次數：	點閱：8 下載：0
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本研究的目的是研究最大邊際分類限制對於約束非負矩陣分解目標函數的影響。
非負矩陣分解（NMF）是基於特徵空間的降維技術。不幸的是，大多數現有NMF的方法並不足以編碼高階數據信息，且忽略了數據集中的局部幾何結構。此外，在以往的方法中分類步驟和矩陣分解步驟為獨立分開進行。第一個執行數據轉換，第二個利用支持向量機（SVM）分類那些轉換後的數據。
因此，在這項研究中，我們使用統一最大化邊際分類限制於限制型NMF的最佳化以結合SVM與限制型NMF。所提出的演算法是從NMF算法通過利用空間屬性和保護圖型結構屬性所推導出來的。還提出了一種乘法演算法來更新，並解決對應的最佳化問題。
基準圖像數據集的實驗結果證明了該方法的有效性。結果說明，我們提出的算法提供了更好的臉部表示，並且比標準非負矩陣分解及其變體獲得更高的識別率。

The purpose of this study is to investigate the effects of merging maximum margin classification constraints on the constrained non-negative matrix factorization objective function.
Non-negative matrix factorization (NMF) is a dimension-reduction technique based on a low-rank approximation of the feature space. Unfortunately, most existing NMF based methods are not ready for encoding higher-order data information and ignore the local geometric structure contained in the data set. Furthermore, the previous classification approaches which the classification and matrix factorization steps are separated independently. The first one performs data transformation and the second one classifies the transformed data using classification methods as support vector machine (SVM).
In this research, therefore, we joint SVM and constrained NMF into one by uniting maximum margin classification constraints into the constrained NMF optimization. The proposed algorithm is derived from NMF algorithm by exploiting both spatial and graph-preserving properties. A multiplicative updating algorithm is also proposed to solve the corresponding optimization problem.
Experimental results on benchmark image data sets demonstrate the effectiveness of the proposed method. The results show that our proposed algorithm provides better facial representations and achieves higher recognition rates than standard non-negative matrix factorization and its variants.

Abstract    ii
Acknowledgement    iii
Contents    iv
List of Tables    vi
List of Figures    vii
Chapter 1 Introduction    1
1 Motivation    1
2 Research Objective    2
3 Research Methodology    3
4 Contribution    4
5 Outline of Thesis    5
Chapter 2 Related Works    6
1 Non-negative Matrix Factorization    6
2 Non-negative Matrix Factorization and Variants    8
2.1 Spatial NMF    8
2.2 Graph NMF    10
2.3 Max-margin Semi-NMF    12
3 Support Vector machine    14
3.1 SVM for Linearly Separable Data    15
3.2 SVM for Non-linearly Separable Data    16
3.3 Types of kernel    17
3.4 Advantages and Disadvantages of SVM    18
Chapter 3 Proposed Method    19
1 Introduction    19
2 Objective Function    19
3 Update the Projection Vector and Slack Variables    20
4 Update the Coefficient Matrix    20
5 Update the Basis Matrix    21
6 Classification    23
Chapter 4 MNMFSGR  for Face Recognition    24
1 Face Recognition    24
1.1 Problem Definition    24
1.2 Approaches    25
1.3 Structure and Procedure    26
1.4 Applications    26
2 Experiments    27
2.1 Data Preparation    28
2.2 Experimental Design    29
2.3 Experimental Setup    30
2.4 Experimental Results    30
Chapter 5 Other Applications    36
1 Facial Expression Recognition    36
1.1 Introduction    36
1.2 Approaches    38
1.3 Experimental Results    41
2 Action Recognition    45
2.1 Introduction    45
2.2 Histogram of Oriented Gradients (HoG)    45
2.3 Experimental Results    46
Chapter 6 Conclusion    48
List of References    49

                                

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