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Multiscale analysis for higher-order tensors
Author(s): Alp Ozdemir; Ali Zare; Mark A. Iwen; Selin Aviyente
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Paper Abstract

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches focused on matrix- and vector-based methods to represent these higher-order data, more recently it has been shown that tensor decomposition methods are better equipped to capture couplings across their different modes. For these reasons, tensor decomposition methods have found applications in many different signal processing problems including dimensionality reduction, signal separation, linear regression, feature extraction, and classification. However, most of the existing tensor decomposition methods are based on the principle of finding a low-rank approximation in a linear subspace structure, where the definition of rank may change depending on the particular decomposition. Since many datasets are not necessarily low-rank in a linear subspace, this often results in high approximation errors or low compression rates. In this paper, we introduce a new adaptive, multi-scale tensor decomposition method for higher-order data inspired by hybrid linear modeling and subspace clustering techniques. In particular, we develop a multi-scale higher-order singular value decomposition (MS-HoSVD) approach where a given tensor is first permuted and then partitioned into several sub-tensors each of which can be represented as a low-rank tensor with increased representational efficiency. The proposed approach is evaluated for dimensionality reduction and classification for several different real-life tensor signals with promising results.

Paper Details

Date Published: 9 September 2019
PDF: 20 pages
Proc. SPIE 11138, Wavelets and Sparsity XVIII, 1113808 (9 September 2019); doi: 10.1117/12.2525530
Show Author Affiliations
Alp Ozdemir, Michigan State Univ. (United States)
Ali Zare, Michigan State Univ. (United States)
Mark A. Iwen, Michigan State Univ. (United States)
Selin Aviyente, Michigan State Univ. (United States)


Published in SPIE Proceedings Vol. 11138:
Wavelets and Sparsity XVIII
Dimitri Van De Ville; Manos Papadakis; Yue M. Lu, Editor(s)

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