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A nonlinear principal component decomposition

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  • Florian Gunsilius
  • Susanne M. Schennach

Abstract

The idea of summarizing the information contained in a large number of variables by a small number of "factors" or "principal components" has been widely adopted in economics and statistics. This paper introduces a generalization of the widely used principal component analysis (PCA) to nonlinear settings, thus providing a new tool for dimension reduction and exploratory data analysis or representation. The distinguishing features of the method include (i) the ability to always deliver truly independent factors (as opposed to the merely uncorrelated factors of PCA); (ii) the reliance on the theory of optimal transport and Brenier maps to obtain a robust and efficient computational algorithm and (iii) the use of a new multivariate additive entropy decomposition to determine the principal nonlinear components that capture most of the information content of the data.

Suggested Citation

  • Florian Gunsilius & Susanne M. Schennach, 2017. "A nonlinear principal component decomposition," CeMMAP working papers 16/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:16/17
    DOI: 10.1920/wp.cem.2017.1617
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