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研究生:普蒂雅
研究生(外文):Diyah Utami Kusumaning Putri
論文名稱:臉部辨識和臉部表情辨識中實域和複域的約束矩陣分解
論文名稱(外文):Constrained Matrix Factorization in Real and Complex Domain for Face and Facial Expression Recognition
指導教授:王家慶
學位類別:碩士
校院名稱:國立中央大學
系所名稱:資訊工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2019
畢業學年度:107
語文別:英文
論文頁數:105
中文關鍵詞:特徵提取非負矩陣分解複矩陣分解投影梯度下降臉部辨識臉部表情辨識
外文關鍵詞:feature extractionnon-negative matrix factorizationcomplex matrix factorizationprojected gradient descentface recognitionfacial expression recognition
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本研究提出了複雜域上的矩陣分解的新方法,以獲得提取的特徵和係數矩陣,在臉部辨識和臉部表情辨識問題中具有高識別結果。基於複數的歐拉表示將實數據矩陣變換為複數。

基礎複雜矩陣分解(CMF)使用幾個約束進行修改並在本研究中進行了研究。使用嶺項(SCMF-L2)將基本 CMF修改為稀疏複矩陣分解,其在係數中添加稀疏 L2 範數約束。本研究也開發了新穎的約束,它在稱為空間約束複雜矩陣分解(SpatialCMF)的基礎矩陣上實施像素色散懲罰。本研究構建了新的約束,它使用像素圖像表示和類註釋約束的組合來訓練稱為耦合複矩陣分解(CoupledCMF)的數據。本研究所提出的方
法與普遍大家所使用的 NMF方法和 CMF方法的擴張相比較,包括稀疏複矩陣分解(SCMF)和分別添加稀疏 L1 範數和圖形約束的圖複雜矩陣分解(GCMF)。梯度下降法則是用於解決優化問題。

臉部表情辨識場景的實驗包含整個臉部和遮蔽臉部的識別,本研究提出的方法比較普遍大家使用的 NMF和 CMF方法提升了更好的識別結果。此方法也達到停止條件,並且比 NMF和 CMF方法的擴張快得許多。
This work proposes novel methods of matrix factorization on the complex domain to obtain both extracted features and coefficient matrix with high recognition results in a face recognition and facial expression recognition problems. The real data matrix is transformed into a complex number based on the Euler representation of complex numbers.
The basic complex matrix factorization (CMF) is modified using several constraints and is investigated in this study. The basic CMF is modified into Sparse Complex Matrix Factorization using Ridge Term (SCMF-L2) which adds sparse L2-norm constraint in the coefficient. This study also develops novel constraint which enforces pixel dispersion penalty on the basis matrix called Spatial Constrained Complex Matrix Factorization (SpatialCMF). This study also builds novel constraint which uses the combination of pixel images representation and class annotation constraints for training data named as Coupled Complex Matrix Factorization (CoupledCMF). The proposed methods compare with prevalent NMF methods and extensions of CMF methods, including sparse complex matrix factorization (SCMF) and graph complex matrix factorization (GCMF) which adds sparse L1-norm and graph constraints, respectively. The gradient descent method is used to solve optimization problems.
Experiments on face recognition and facial expression recognition scenarios that involve a whole face and an occluded face reveal that the proposed methods provide better recognition results that common NMF and CMF methods. The proposed methods also reach the stopping condition and converge much faster than the extensions of NMF and CMF methods.
摘要 i
Abstract ii
Acknowledgements iii
Contents iv
List of Symbols and Abbreviations vii
List of Figures ix
List of Tables x
CHAPTER 1 1
1.1 Motivation 1
1.2 Research Problem 3
1.3 Research Objective 4
1.3.1 General Objective 4
1.3.2 Specific Objectives 4
1.4 Thesis Overview 5
1.4.1 Chapter 2 Related Work 5
1.4.2 Chapter 3 Theoretical Basis 5
1.4.3 Chapter 4 Experiments 5
1.4.4 Chapter 5 Results and Analysis 5
1.4.5 Chapter 6 Conclusion and Future Work 5
CHAPTER 2 6
CHAPTER 3 20
3.1 Matrix Theory 20
3.1.1 Matrix Manipulation 20
3.1.2 Vector Spaces 23
3.1.3 Norm 24
3.2 Lagrangian Duality and the Karush-Kuhn-Tucker (KKT Conditions) 24
3.3 Complex Analysis and Optimization in the Complex Domain 26
3.3.1 Wirtinger Calculus and Differentials of Real-Valued Functions 26
3.3.2 Optimization in Complex Domain 27
3.4 Nonnegative Matrix Factorization 30
3.4.1 Introductions of Nonnegative Matrix Factorization 30
3.4.2 Nonnegative Matrix Factorization 31
3.4.3 Selected Applications of NMF 35
3.4.4 Extensions of Nonnegative Matrix Factorization Methods 35
3.5 Complex Matrix Factorization 42
3.5.1 Extensions of Complex Matrix Factorization Methods 45
3.6 Recognition Workflow 47
3.6 Performance Measure 49
CHAPTER 4 51
4.1 Datasets 51
4.2 Proposed Methods 52
A. Sparse Complex Matrix Factorization using Ridge Term (SCMF-L2) 52
B. Spatial Complex Matrix Factorization (SpatialCMF) 53
C. Coupled Complex Matrix Factorization (CoupledCMF) 54
4.3 Comparison of Methods and Experimental Settings 56
4.4 Experimental Methods 59
A. Different Subspace Dimensions 59
B. Different K-Fold Cross-Validation 60
C. Recognition of Occluded Faces 60
D. Reconstructed Images 60
E. Convergence Time 61
CHAPTER 5 62
5.1 Face Recognition on Un-occluded ORL Dataset with Different Subspace Dimensions 62
5.2 Facial Expression Recognition on Un-Occluded JAFFE Dataset with Different Subspace Dimensions 65
5.3 Face Recognition on Un-occluded ORL Dataset with Different K-Fold Cross-Validation 68
5.4 Facial Expression Recognition on Un-occluded JAFFE dataset with Different K-Fold Cross-Validation 69
5.5 Learned Basis Images on ORL dataset 70
5.6 Learned Basis Images on JAFFE dataset 71
5.7 Face Recognition on Occluded ORL Dataset 72
5.8 Facial Expression Recognition on Occluded JAFFE dataset 73
5.9 Reconstructed Images on ORL dataset 75
5.10 Reconstructed Images on JAFFE dataset 76
5.11 Convergence Time on ORL Dataset 77
5.12 Convergence Time on JAFFE Dataset 80
CHAPTER 6 84
6.1 Result Summary 84
6.2 Limitation 85
6.3 Future Research 85
Bibliographies 86
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