Matrix Product State for Feature Extraction of Higher-Order Tensors

Bengua, JA; Phien, HN; Tuan, HD; Do, MN

Matrix Product State for Feature Extraction of Higher-Order Tensors

Bengua, JA Phien, HN Tuan, HD Do, MN

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Field	Value	Language
dc.contributor.author	Bengua, JA	en_US
dc.contributor.author	Phien, HN	en_US
dc.contributor.author	Tuan, HD	en_US
dc.contributor.author	Do, MN	en_US
dc.identifier.uri	http://hdl.handle.net/10453/41664
dc.description.abstract	This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to the so-called core tensor of maximum order three which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement without any recursive procedure needed for optimizing local tensors. Thus, it leads to substantial computational savings compared to other tensor feature extraction methods such as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition (TD). Benchmark results show that MPS can reduce significantly the feature space of data while achieving better classification performance compared to HOOI.	en_US
dc.title	Matrix Product State for Feature Extraction of Higher-Order Tensors	en_US
dc.type	Journal Article
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	open_access

Abstract:

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to the so-called core tensor of maximum order three which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement without any recursive procedure needed for optimizing local tensors. Thus, it leads to substantial computational savings compared to other tensor feature extraction methods such as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition (TD). Benchmark results show that MPS can reduce significantly the feature space of data while achieving better classification performance compared to HOOI.

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http://hdl.handle.net/10453/41664