Some theoretical results on nonlinear principal components analysis

E. C. Malthouse*, R. S.H. Mah, A. C. Tamhane

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations

Abstract

We present some results on the NonLinear Principal Components Analysis (NLPCA) method of doing nonlinear feature extraction and discuss its relation to the principal curve/surface method. Both methods attempt to reduce the dimension of a set of multivariate observations by fitting a curve or surface through the middle of the observations and projecting the observations onto this curve/surface. The two methods fit their models under a similar objective function, with one important difference: NLPCA defines the function which maps observed variables to scores (projection index) to be continuous. We show that the effects of this constraint are (1) NLPCA is unable to model curves and surfaces which intersect themselves and (2) the NLPCA 'projections' are suboptimal producing larger approximation error. We show how NLPCA score values can be interpreted and give the results of a small simulation study comparing the two methods.

Original languageEnglish (US)
Pages (from-to)744-748
Number of pages5
JournalProceedings of the American Control Conference
Volume1
StatePublished - Jan 1 1995
EventProceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA
Duration: Jun 21 1995Jun 23 1995

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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