On Measure Transformed Canonical Correlation Analysis

Abstract

In this paper linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability measure defined on their joint observation space. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the data after transformation of the joint probability measure. We show that judicious choice of the transform leads to a modified canonical correlation analysis, which, in contrast to LCCA, is capable of detecting non-linear relationships between the considered pair of random vectors. Unlike kernel canonical correlation analysis, where the transformation is applied to the random vectors, in MTCCA the transformation is applied to their joint probability distribution. This results in performance advantages and reduced implementation complexity. The proposed approach is illustrated for graphical model selection in simulated data having non-linear dependencies, and for measuring long-term associations between companies traded in the NASDAQ and NYSE stock markets.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2012
Accession Number
ADA578246

Entities

People

  • Alfred O. Hero
  • Koby Todros

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Algorithms
  • Computational Complexity
  • Computer Science
  • Correlation Analysis
  • Data Analysis
  • Data Science
  • Databases
  • Eigenvalues
  • Electrical Engineering
  • Estimators
  • Information Science
  • Monte Carlo Method
  • Probability
  • Probability Distributions
  • Random Variables
  • Simulations
  • Standards

Readers

  • Cardiovascular Physiology
  • Statistical inference.

Technology Areas

  • Space