Dynamic L1-Norm Tucker Tensor Decomposition

Dimitris G Chachlakis,Mayur Dhanaraj,Ashley Prater-Bennette,Panos P Markopoulos

doi:10.1109/jstsp.2021.3058846

Abstract

Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning and data mining, among other fields. When tensor measurements arrive in a streaming fashion or are too many to jointly decompose, incremental Tucker analysis is preferred. In addition, dynamic adaptation of bases is desired when the nominal data subspaces change. At the same time, it has been documented that outliers in the data can significantly compromise the performance of existing methods for dynamic Tucker analysis. In this work, we present Dynamic L1-Tucker: an algorithm for dynamic and outlier-resistant Tucker analysis of tensor data. Our experimental studies on both real and synthetic datasets corroborate that the proposed method (i) attains high bases estimation performance, (ii) identifies/rejects outliers, and (iii) adapts to changes of the nominal subspaces.

Highlights

Data collections across diverse sensing modalities are naturally stored and processed in the form of N -way arrays, known as tensors [1]
Tucker decomposition is a standard method for tensor analysis, with important applications in machine learning [2, 3], pattern recognition [4, 5], communications [6,7,8], and computer vision [9,10,11], among other fields
When tensor measurements arrive in a streaming fashion or are too many to jointly decompose, incremental Tucker analysis is preferred

Summary

Introduction

Data collections across diverse sensing modalities are naturally stored and processed in the form of N -way arrays, known as tensors [1]. Tucker decomposition is a standard method for tensor analysis, with important applications in machine learning [2, 3], pattern recognition [4, 5], communications [6,7,8], and computer vision [9,10,11], among other fields. Common uses of Tucker include compression, denoising, and model identification. Copyright may be transferred without notice, after which this version may no longer be accessible

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