Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis

Andrzej Cichocki, Danilo P. Mandic, Lieven De Lathauwer, Guoxu Zhou, Qibin Zhao, César F. Caiafa, Anh Huy Phan

Abstract

This tutorial article reviews models and associated unsupervised learning algorithms for tensor decompositions (TD) and Multi-Way Component Analysis (MWCA).Our aim is to make the area of tensor decompositions approachable to a wider signal processing readership, and to show how they can be made efficient by incorporating various physically meaningful criteria, constraints and assumptions.We next briefly overview emerging models and approaches for multi-block constrained matrix/tensor decompositions in applications to group-and linkedmultiway component analysis, feature extraction, classification and clustering.The MWCA is a promising methodology for many "cause-effect" type signal processing problems due to its ability to decompose multiway data through the interaction of multiple factors or components.We illuminate that tensor decompositions are natural (non-trivial) and versatile generalizations of some most commonly used signal processing tools such correlation and component analysis and linear regressions.Following the basics of tensor multilinear algebra and decompositions models, tensor canonical correlation analysis (CCA) and higherorder partial least squares (PLS) are introduced in an intuitive way are supported by illustrative examples.

Locations

• IEEE Signal Processing Magazine - View
• arXiv (Cornell University) - View - PDF
• Americanae (AECID Library) - View - PDF
• Lirias (KU Leuven) - View - PDF
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