A nonlinear principal component decomposition

Florian Gunsilius and Susanne Schennach
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Florian Gunsilius: Institute for Fiscal Studies and MIT

No CWP16/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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 ef?cient 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.

Keywords: Principal Component Analysis; Nonlinear Principal Components; Factor Models (search for similar items in EconPapers)
Date: 2017-03-28
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Working Paper: A nonlinear principal component decomposition (2017)
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