Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data

Haiping Lu, Konstantinos N. Plataniotis, Anastasios Venetsanopoulos

December 11, 2013 by Chapman and Hall/CRC
Reference - 296 Pages - 56 B/W Illustrations
ISBN 9781439857243 - CAT# K12681
Series: Chapman & Hall/CRC Machine Learning & Pattern Recognition

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  • Introduces both MSL theories and practical considerations, including multilinear algebra fundamentals, multilinear projections, framework formulation, optimality criterion construction, and implementation tips
  • Provides a strong foundation for developing new MSL algorithms and exploring new MSL applications
  • Presents pseudocode for algorithms in a unifying format, with MATLAB code available on a supporting website
  • Offers examples of real-world applications in video surveillance, biometrics, and object recognition
  • Includes numerous figures that clarify and link concepts, enabling readers to easily grasp and visualize the main ideas
  • Covers mathematical background, data preprocessing, and software tools in the appendices


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