1st Edition

Multilinear Subspace Learning Dimensionality Reduction of Multidimensional Data

    296 Pages 56 B/W Illustrations
    by Chapman & Hall

    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

    Tensor Representation of Multidimensional Data
    Dimensionality Reduction via Subspace Learning
    Multilinear Mapping for Subspace Learning

    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
    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




    Haiping Lu, Konstantinos N. Plataniotis, Anastasios Venetsanopoulos

    "…this book is built to be read as a rich and yet accessible introduction… artfully structured for a specialized audience of new researchers and bleeding-edge practitioners. …The treatment builds an overarching framework and provides an analytical reader with a well-expressed taxonomy on the foundations of historical developments and similarity in content and goals. Thus, packaged, current research is endowed with instant meaning and purpose, the derivation of which would initially elude a newcomer to this complex and articulated branch of machine learning."
    —Computing Reviews, November 2014

    "Experimentally inclined readers will probably like this book … . Practitioners will appreciate that the presentation of the subject matter is goal oriented … The structure that this book builds can allow a neophyte to avoid much of the initial confusion and wasted effort necessary to classify unfamiliar work and distinguish between what may be useful or not to one’s intents and interests. … an exquisitely enriched literature review that is almost good enough to use as an auxiliary graduate textbook … a rich yet accessible introduction …"
    Computing Reviews, October 2014