Tensor canonical correlation analysis

Eun Jeong Min, Eric C. Chi, Hua Zhou

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Canonical correlation analysis (CCA) is a multivariate analysis technique for estimating a linear relationship between two sets of measurements. Modern acquisition technologies, for example, those arising in neuroimaging and remote sensing, produce data in the form of multidimensional arrays or tensors. Classic CCA is not appropriate for dealing with tensor data due to the multidimensional structure and ultrahigh dimensionality of such modern data. In this paper, we present tensor CCA (TCCA) to discover relationships between two tensors while simultaneously preserving multidimensional structure of the tensors and utilizing substantially fewer parameters. Furthermore, we show how to employ a parsimonious covariance structure to gain additional stability and efficiency. We delineate population and sample problems for each model and propose efficient estimation algorithms with global convergence guarantees. Also we describe a probabilistic model for TCCA that enables the generation of synthetic data with desired canonical variates and correlations. Simulation studies illustrate the performance of our methods.

Original languageEnglish
Article numbere253
JournalStat
Volume8
Issue number1
DOIs
StatePublished - Jan 2019

Bibliographical note

Publisher Copyright:
© 2019 John Wiley & Sons, Ltd.

Keywords

  • CP decomposition
  • block coordinate ascent
  • multidimensional array data

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