Standard Article

Independent Component Analysis

Statistical Theory and Methods

  1. Hannu Oja,
  2. Klaus Nordhausen

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn086

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Oja, H. and Nordhausen, K. 2013. Independent Component Analysis. Encyclopedia of Environmetrics. 3.

Author Information

  1. University of Tampere, Finland

Publication History

  1. Published Online: 15 JAN 2013

Abstract

Independent component models have gained increasing interest in various fields of applications in recent years. The basic independent component model is a semiparametric model assuming that a p-variate observed random vector is a linear transformation of an unobserved vector of p independent latent variables. This linear transformation is given by an unknown mixing matrix, and one of the main objectives of independent component analysis (ICA) is to estimate an unmixing matrix by means of which the latent variables can be recovered. In this article, we discuss the basic independent component model in detail, define the concepts and analysis tools carefully, and consider two families of ICA estimates. The statistical properties (consistency, asymptotic normality, efficiency, robustness) of the estimates can be analyzed and compared via the so called gain matrices. Some extensions of the basic independent component model, such as models with additive noise or models with dependent observations, are briefly discussed. The article ends with a short example.

Keywords:

  • blind source separation;
  • fastICA;
  • independent component model;
  • independent subspace analysis;
  • mixing matrix;
  • overcomplete ICA;
  • undercomplete ICA;
  • unmixing matrix