Nonlinear principal component analysis of noisy data

Nonlinear Principal Component Analysis

A. Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call itmultiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it no...

Nonlinear principal component analysis

We study the extraction of nonlinear data models in high dimensional spaces with modi ed self organizing maps We present a general algorithm which maps low dimensional lattices into high dimensional data manifolds without violation of topology The approach is based on a new principle exploiting the speci c dynamical properties of the rst order phase tran sition induced by the noise of the data ...

Nonlinear Principal Component Analysis of Climate Data by

In traditional principal component analysis (PCA) a few significant linear combinations of the original variables are extracted to arrive at a parsimonious description of a complex. data set obtained from climate observations, analysis or from GCM ouputs. These are uncorrelated variables which are used in practice to understand the principal modes of variation in the climatological process unde...

Nonlinear Principal Component Analysis by Neural Networks

Nonlinear principal component analysis (NLPCA) can be performed by a neural network model which nonlinearly generalizes the classical principal component analysis (PCA) method. The presence of local minima in the cost function renders the NLPCA somewhat unstable, as optimizations started from different initial parameters often converge to different minima. Regularization by adding weight penalt...

Projection techniques for nonlinear principal component analysis