Just compress and relax: Handling missing values in big tensor analysis

J. H. Marcos, Nikolaos Sidiropoulos

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

1 Scopus citations

Abstract

In applications of tensor analysis, missing data is an important issue that is usually handled via weighted least-squares fitting, imputation, or iterative expectation-maximization. The resulting algorithms are often cumbersome, and tend to fail when the percentage of missing samples is large. This paper proposes a novel and refreshingly simple approach for handling randomly missing values in big tensor analysis. The stepping stone is random multi-way tensor compression, which enables indirect tensor factorization via analysis of compressed 'replicas' of the big tensor. A Bernoulli model for the misses, and two opposite ends of the tensor modeling spectrum are considered: independent and identically distributed (i.i.d.) tensor elements, and low-rank (and in particular rank-one) tensors whose latent factors are i.i.d. In both cases, analytical results are established, showing that the tensor approximation error variance is inversely proportional to the number of available elements. Coupled with recent developments in robust CP decomposition, these results show that it is possible to ignore missing values without losing the ability to identify the underlying model.

Original languageEnglish (US)
Title of host publicationISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings
PublisherIEEE Computer Society
Pages218-221
Number of pages4
ISBN (Print)9781479928903
DOIs
StatePublished - Jan 1 2014
Event6th International Symposium on Communications, Control and Signal Processing, ISCCSP 2014 - Athens, Greece
Duration: May 21 2014May 23 2014

Publication series

NameISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings

Other

Other6th International Symposium on Communications, Control and Signal Processing, ISCCSP 2014
CountryGreece
CityAthens
Period5/21/145/23/14

Keywords

  • CANDECOMP / PARAFAC
  • Tensor decomposition
  • big data
  • imputation
  • missing elements
  • missing values
  • multi-way arrays
  • tensor completion

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