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E-raamat: Multi-Label Dimensionality Reduction

(Arizona State University, Tempe, USA), (Arizona State University, Tempe, USA), (Arizona State University, Tempe, USA)
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Similar to other data mining and machine learning tasks, multi-label learning suffers from dimensionality. An effective way to mitigate this problem is through dimensionality reduction, which extracts a small number of features by removing irrelevant, redundant, and noisy information. The data mining and machine learning literature currently lacks a unified treatment of multi-label dimensionality reduction that incorporates both algorithmic developments and applications.

Addressing this shortfall, Multi-Label Dimensionality Reduction covers the methodological developments, theoretical properties, computational aspects, and applications of many multi-label dimensionality reduction algorithms. It explores numerous research questions, including:











How to fully exploit label correlations for effective dimensionality reduction How to scale dimensionality reduction algorithms to large-scale problems How to effectively combine dimensionality reduction with classification How to derive sparse dimensionality reduction algorithms to enhance model interpretability How to perform multi-label dimensionality reduction effectively in practical applications

The authors emphasize their extensive work on dimensionality reduction for multi-label learning. Using a case study of Drosophila gene expression pattern image annotation, they demonstrate how to apply multi-label dimensionality reduction algorithms to solve real-world problems. A supplementary website provides a MATLAB® package for implementing popular dimensionality reduction algorithms.
Preface xi
List of Symbols xiii
1 Introduction 1(28)
1.1 Introduction to Multi-Label Learning
1(1)
1.2 Applications of Multi-Label Learning
2(6)
1.2.1 Scene Classification
2(1)
1.2.2 Text Categorization
3(1)
1.2.3 Functional Genomics Analysis
4(2)
1.2.4 Gene Expression Pattern Image Annotation
6(2)
1.3 Challenges of Multi-Label Learning
8(1)
1.4 State of the Art
9(9)
1.4.1 Problem Transformation
9(3)
1.4.1.1 Copy Transformation
9(1)
1.4.1.2 Binary Relevance
10(1)
1.4.1.3 Label Power-Set
10(2)
1.4.1.4 Single-Label Classification after Transformation
12(1)
1.4.2 Algorithm Adaptation
12(6)
1.4.2.1 Decision Tree
12(1)
1.4.2.2 Algorithms Based on Probabilistic Framework
12(1)
1.4.2.3 Support Vector Machines
13(1)
1.4.2.4 Artificial Neural Networks
14(1)
1.4.2.5 k-Nearest Neighbor
15(1)
1.4.2.6 Ensemble Learning
15(1)
1.4.2.7 Other Algorithms
16(2)
1.5 Dimensionality Reduction for Multi-Label Learning
18(5)
1.5.1 Introduction to Dimensionality Reduction
18(2)
1.5.2 Linear and Nonlinear Dimensionality Reduction
20(1)
1.5.3 Multi-Label Dimensionality Reduction
20(2)
1.5.4 Related Work
22(1)
1.6 Overview of the Book
23(3)
1.6.1 Design and Analysis of Algorithms
24(1)
1.6.2 Scalable Implementations
25(1)
1.6.3 Applications
26(1)
1.7 Notations
26(1)
1.8 Organization
27(2)
2 Partial Least Squares 29(20)
2.1 Basic Models of Partial Least Squares
29(2)
2.1.1 The NIPALS Algorithm
30(1)
2.2 Partial Least Squares Variants
31(6)
2.2.1 PLS Mode A
32(1)
2.2.2 PLS 2
32(1)
2.2.3 PLS 1
33(1)
2.2.4 PLS-SB
34(1)
2.2.5 SIMPLS
34(1)
2.2.6 Orthonormalized PLS
34(2)
2.2.7 Relationship between OPLS and Other PLS Models
36(1)
2.3 PLS Regression
37(7)
2.3.1 Basics of PLS Regression
37(1)
2.3.2 Shrinkage in Regression
38(3)
2.3.3 Principal Component Regression
41(1)
2.3.4 Ridge Regression
41(2)
2.3.5 Shrinkage Properties of PLS Regression
43(1)
2.4 Partial Least Squares Classification
44(5)
3 Canonical Correlation Analysis 49(20)
3.1 Classical Canonical Correlation Analysis
49(7)
3.1.1 Linear Correlation Coefficient
49(1)
3.1.2 The Maximum Correlation Formulation of CCA
50(4)
3.1.3 The Distance Minimization Formulation of CCA
54(1)
3.1.4 Regularized CCA
55(1)
3.1.5 CCA for Multiple Sets of Variables
55(1)
3.2 Sparse CCA
56(3)
3.2.1 Sparse CCA via Linear Regression
57(1)
3.2.2 Sparse CCA via Iterative Greedy Algorithms
57(1)
3.2.3 Sparse CCA via Bayesian Learning
58(1)
3.3 Relationship between CCA and Partial Least Squares
59(5)
3.3.1 A Unified Framework for PLS and CCA
59(1)
3.3.2 The Equivalence without Regularization
60(1)
3.3.3 The Equivalence with Regularization
61(2)
3.3.3.1 Regularization on X
62(1)
3.3.3.2 Regularization on Y
62(1)
3.3.4 Analysis of Regularization on CCA
63(1)
3.4 The Generalized Eigenvalue Problem
64(5)
3.4.1 The Generalized Rayleigh Quotient Cost Function
64(1)
3.4.2 Properties of the Generalized Eigenvalue Problem
65(1)
3.4.3 Algorithms for the Generalized Eigenvalue Problem ..
66(3)
4 Hypergraph Spectral Learning 69(22)
4.1 Hypergraph Basics
69(5)
4.1.1 Clique Expansion
71(1)
4.1.2 Star Expansion
72(1)
4.1.3 Hypergraph Laplacian
73(1)
4.2 Multi-Label Learning with a Hypergraph
74(1)
4.3 A Class of Generalized Eigenvalue Problems
75(3)
4.3.1 Canonical Correlation Analysis
76(1)
4.3.2 Orthonormalized Partial Least Squares
76(1)
4.3.3 Hypergraph Spectral Learning
77(1)
4.3.4 Linear Discriminant Analysis
77(1)
4.4 The Generalized Eigenvalue Problem versus the Least Squares Problem
78(6)
4.4.1 Multivariate Linear Regression and Least Squares
78(1)
4.4.2 Matrix Orthonormality Property
79(2)
4.4.3 The Equivalence Relationship
81(1)
4.4.4 Regularized Least Squares
82(1)
4.4.5 Efficient Implementation via LSQR
83(1)
4.5 Empirical Evaluation
84(7)
4.5.1 Empirical Evaluation Setup
84(1)
4.5.2 Performance of Hypergraph Spectral Learning
85(1)
4.5.3 Evaluation of the Equivalence Relationship
86(2)
4.5.4 Evaluation of Scalability
88(3)
5 A Scalable Two-Stage Approach for Dimensionality Reduction 91(14)
5.1 The Two-Stage Approach without Regularization
91(4)
5.1.1 The Algorithm
92(1)
5.1.2 Time Complexity Analysis
92(1)
5.1.3 The Equivalence Relationship
93(2)
5.2 The Two-Stage Approach with Regularization
95(4)
5.2.1 The Algorithm
96(1)
5.2.2 Time Complexity Analysis
96(1)
5.2.3 The Equivalence Relationship
96(3)
5.3 Empirical Evaluation
99(6)
5.3.1 Empirical Evaluation Setup
99(1)
5.3.2 Performance Comparison
100(1)
5.3.3 Scalability Comparison
101(4)
6 A Shared-Subspace Learning Framework 105(18)
6.1 The Framework
105(4)
6.1.1 Problem Formulation
105(2)
6.1.2 A Trace Ratio Formulation
107(2)
6.2 An Efficient Implementation
109(2)
6.2.1 Reformulation
109(1)
6.2.2 Eigendecomposition
110(1)
6.2.3 The Main Algorithm
111(1)
6.3 Related Work
111(1)
6.4 Connections with Existing Formulations
112(1)
6.5 A Feature Space Formulation
113(1)
6.6 Empirical Evaluation
114(9)
6.6.1 Empirical Evaluation Setup
115(1)
6.6.2 Web Page Categorization
116(5)
6.6.2.1 Performance Evaluation
116(2)
6.6.2.2 Scalability Evaluation
118(3)
6.6.2.3 Sensitivity Analysis
121(1)
6.6.3 Discussion
121(2)
7 Joint Dimensionality Reduction and Classification 123(10)
7.1 Background
123(2)
7.1.1 Squared Loss
124(1)
7.1.2 Hinge Loss
124(1)
7.2 Joint Dimensionality Reduction and Multi-Label Classification
125(4)
7.2.1 Joint Learning with Squared Loss
125(1)
7.2.2 Joint Learning with Hinge Loss
126(4)
7.2.2.1 A Convex-Concave Formulation
127(1)
7.2.2.2 Solving the Min-Max Problem
128(1)
7.2.2.3 Learning Orthonormal Features
128(1)
7.2.2.4 Joint Learning with Squared Hinge Loss
128(1)
7.2.2.5 Related Work
129(1)
7.3 Dimensionality Reduction with Different Input Data
129(1)
7.4 Empirical Evaluation
130(3)
7.4.1 Evaluation on Multi-Label Data Sets
130(1)
7.4.2 Evaluation on Data with Different Inputs
131(2)
8 Nonlinear Dimensionality Reduction: Algorithms and Applications 133(22)
8.1 Background on Kernel Methods
133(1)
8.2 Kernel Centering and Projection
134(2)
8.2.1 Kernel Centering
135(1)
8.2.2 Kernel Projection
135(1)
8.3 Kernel Canonical Correlation Analysis
136(2)
8.4 Kernel Hypergraph Spectral Learning
138(1)
8.5 The Generalized Eigenvalue Problem in the Kernel-Induced Feature Space
139(1)
8.6 Kernel Least Squares Regression
140(1)
8.7 Dimensionality Reduction and Least Squares Regression in the Feature Space
140(3)
8.7.1 Matrix Orthonormality Property
140(2)
8.7.2 The Equivalence Relationship
142(1)
8.8 Gene Expression Pattern Image Annotation
143(12)
8.8.1 Problem Description
143(2)
8.8.2 Feature Generation and Kernel Construction
145(2)
8.8.3 Multi-Label Multiple Kernel Learning
147(2)
8.8.4 Empirical Evaluation Setup
149(1)
8.8.5 Annotation Results
150(5)
Appendix Proofs 155(12)
A.1 Proofs for
Chapter 2
155(4)
A.2 Proofs for
Chapter 3
159(2)
A.3 Proofs for
Chapter 4
161(1)
A.4 Proofs for
Chapter 6
162(2)
A.5 Proofs for
Chapter 8
164(3)
References 167(24)
Index 191
Liang Sun is a scientist in the R&D of Opera Solutions, a leading company in big data science and predictive analytics. He received a PhD in computer science from Arizona State University. His research interests lie broadly in the areas of data mining and machine learning. His team won second place in the KDD Cup 2012 Track 2 and fifth place in the Heritage Health Prize. In 2010, he won the ACM SIGKDD best research paper honorable mention for his work on an efficient implementation for a class of dimensionality reduction algorithms.

Shuiwang Ji is an assistant professor of computer science at Old Dominion University. He received a PhD in computer science from Arizona State University. His research interests include machine learning, data mining, computational neuroscience, and bioinformatics. He received the Outstanding PhD Student Award from Arizona State University in 2010 and the Early Career Distinguished Research Award from Old Dominion Universitys College of Sciences in 2012.

Jieping Ye is an associate professor of computer science and engineering at Arizona State University, where he is also the associate director for big data informatics in the Center for Evolutionary Medicine and Informatics and a core faculty member of the Biodesign Institute. He received a PhD in computer science from the University of Minnesota, Twin Cities. His research interests include machine learning, data mining, and biomedical informatics. He is an associate editor of IEEE Transactions on Pattern Analysis and Machine Intelligence. He has won numerous awards from Arizona State University and was a recipient of an NSF CAREER Award. His papers have also been recognized at the International Conference on Machine Learning, KDD, and the SIAM International Conference on Data Mining (SDM).
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