A quadratically convergent proximal algorithm for nonnegative tensor decomposition

Nico Vervliet, Andreas Themelis, Panagiotis Patrinos, Lieven de Lathauwer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The decomposition of tensors into simple rank-1 terms is key in a variety of applications in signal processing, data analysis and machine learning. While this canonical polyadic decomposition (CPD) is unique under mild conditions, including prior knowledge such as nonnegativity can facilitate interpretation of the components. Inspired by the effectiveness and efficiency of Gauss-Newton (GN) for unconstrained CPD, we derive a proximal, semismooth GN type algorithm for nonnegative tensor factorization. Global convergence to local minima is achieved via backtracking on the forward-backward envelope function. If the algorithm converges to a global optimum, we show that Q-quadratic rates are obtained in the exact case. Such fast rates are verified experimentally, and we illustrate that using the GN step significantly reduces number of (expensive) gradient computations compared to proximal gradient descent.

Original languageEnglish
Title of host publication28th European Signal Processing Conference, EUSIPCO 2020 - Proceedings
PublisherEuropean Signal Processing Conference, EUSIPCO
Pages1020-1024
Number of pages5
ISBN (Electronic)9789082797053
DOIs
Publication statusPublished - Jan 24 2021
Externally publishedYes
Event28th European Signal Processing Conference, EUSIPCO 2020 - Amsterdam, Netherlands
Duration: Aug 24 2020Aug 28 2020

Publication series

NameEuropean Signal Processing Conference
Volume2021-January
ISSN (Print)2219-5491

Conference

Conference28th European Signal Processing Conference, EUSIPCO 2020
CountryNetherlands
CityAmsterdam
Period8/24/208/28/20

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'A quadratically convergent proximal algorithm for nonnegative tensor decomposition'. Together they form a unique fingerprint.

Cite this