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 (R) 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