Nonlinear data description with Principal Polynomial Analysis

V. Laparra*, D. Tuia, S. Jimenez, G. Camps-Valls, J. Malo

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paper

4 Citations (Scopus)

Abstract

Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold learning based on the use of a sequence of Principal Polynomials that capture the eventually nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) is shown to generalize PCA. Unlike recently proposed nonlinear methods (e.g. spectral/kernel methods and projection pursuit techniques, neural networks), PPA features are easily interpretable and the method leads to a fully invertible transform, which is a desirable property to evaluate performance in dimensionality reduction. Successful performance of the proposed PPA is illustrated in dimensionality reduction, in compact representation of non-Gaussian image textures, and multispectral image classification.

Original languageEnglish
Title of host publication2012 IEEE International Workshop on Machine Learning for Signal Processing - Proceedings of MLSP 2012
ISBN (Electronic)9781467310260
DOIs
Publication statusPublished - Dec 2012
Externally publishedYes
Event2012 22nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2012 - Santander, Spain
Duration: 23 Sep 201226 Sep 2012

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing, MLSP
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Conference

Conference2012 22nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2012
CountrySpain
CitySantander
Period23/09/1226/09/12

Keywords

  • Classification
  • Coding
  • Dimensionality Reduction
  • Manifold Learning
  • Principal Polynomial Analysis

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