Due to advances in sensor, storage, and networking technologies, data is being generated on a daily basis at an ever-increasing pace in a wide range of applications, including cloud computing, mobile Internet, and medical imaging. This large multidimensional data requires more efficient dimensionality reduction schemes than the traditional techniques. Addressing this need, multilinear subspace learning (MSL) reduces the dimensionality of big data directly from its natural multidimensional representation, a tensor.
Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data gives a comprehensive introduction to both theoretical and practical aspects of MSL for the dimensionality reduction of multidimensional data based on tensors. It covers the fundamentals, algorithms, and applications of MSL.
Emphasizing essential concepts and system-level perspectives, the authors provide a foundation for solving many of today’s most interesting and challenging problems in big multidimensional data processing. They trace the history of MSL, detail recent advances, and explore future developments and emerging applications.
The book follows a unifying MSL framework formulation to systematically derive representative MSL algorithms. It describes various applications of the algorithms, along with their pseudocode. Implementation tips help practitioners in further development, evaluation, and application. The book also provides researchers with useful theoretical information on big multidimensional data in machine learning and pattern recognition. MATLAB® source code, data, and other materials are available at www.comp.hkbu.edu.hk/~haiping/MSL.html
Introduction
Tensor Representation of Multidimensional Data
Dimensionality Reduction via Subspace Learning
Multilinear Mapping for Subspace Learning
Roadmap
Fundamentals and Foundations
Linear Subspace Learning for Dimensionality Reduction
Principal Component Analysis
Independent Component Analysis
Linear Discriminant Analysis
Canonical Correlation Analysis
Partial Least Squares Analysis
Unified View of PCA, LDA, CCA, and PLS
Regularization and Model Selection
Ensemble Learning
Fundamentals of Multilinear Subspace Learning
Multilinear Algebra Preliminaries
Tensor Decompositions
Multilinear Projections
Relationships among Multilinear Projections
Scatter Measures for Tensors and Scalars
Overview of Multilinear Subspace Learning
Multilinear Subspace Learning Framework
PCA-Based MSL Algorithms
LDA-Based MSL Algorithms
History and Related Works
Future Research on MSL
Algorithmic and Computational Aspects
Alternating Partial Projections for MSL
Initialization
Projection Order, Termination, and Convergence
Synthetic Data for Analysis of MSL Algorithms
Feature Selection for TTP-Based MSL
Computational Aspects
(A Summary and Further Reading appear at the end of each chapter in this section.)
Algorithms and Applications
Multilinear Principal Component Analysis
Generalized PCA
Multilinear PCA
Tensor Rank-One Decomposition
Uncorrelated Multilinear PCA
Boosting with MPCA
Other Multilinear PCA Extensions
Multilinear Discriminant Analysis
Two-Dimensional LDA
Discriminant Analysis with Tensor Representation
General Tensor Discriminant Analysis
Tensor Rank-One Discriminant Analysis
Uncorrelated Multilinear Discriminant Analysis
Other Multilinear Extensions of LDA
Multilinear ICA, CCA, and PLS
Overview of Multilinear ICA Algorithms
Multilinear Modewise ICA
Overview of Multilinear CCA Algorithms
Two-Dimensional CCA
Multilinear CCA
Multilinear PLS Algorithms
Applications of Multilinear Subspace Learning
Pattern Recognition System
Face Recognition
Gait Recognition
Visual Content Analysis in Computer Vision
Brain Signal/Image Processing in Neuroscience
DNA Sequence Discovery in Bioinformatics
Music Genre Classification in Audio Signal Processing
Data Stream Monitoring in Data Mining
Other MSL Applications
Appendix A: Mathematical Background
Appendix B: Data and Preprocessing
Appendix C: Software
Bibliography
Index
Overview
Due to advances in sensor, storage, and networking technologies, data is being generated on a daily basis at an ever-increasing pace in a wide range of applications, including cloud computing, mobile Internet, and medical imaging. This large multidimensional data requires more efficient dimensionality reduction schemes than the traditional techniques. Addressing this need, multilinear subspace learning (MSL) reduces the dimensionality of big data directly from its natural ...