Multilinear Subspace Learning
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Multilinear Subspace Learning
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
Multilinear Subspace Learning
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 techniqu
Multilinear Subspace Learning Via Linear Tansforms and Grassmannian Manifold Analysis
Furthermore, in general, the number of observations is relatively small compared to the feature vector dimension potentially resulting in poor conditioning (referred to as the small sample size problem). Due to these issues, particularly when dealing with higher-order data with high dimensionality, there has been a growing interest in multilinear subspace learning (MSL) to maintain the natural representation of multidimensional arrays (commonly referred to as tensors). To best explore, analyze, and provide insights from such data, new mathematical tools are required in an effort to bridge the gap between traditional machine learning models and their multilinear counterparts. In this dissertation, we present new approaches and formulate mathematical theories to deal with such data using a multilinear (tensor-tensor) perspective. In particular, we provide insights into several different application areas within the machine learning community and illustrate how multilinear extensions can be achieved.