Application of local linear embedding to nonlinear exploratory latent structure analysis

In this paper we discuss the use of a recent dimension reduction technique called Locally Linear Embedding, introduced by Roweis and Saul, for performing an exploratory latent structure analysis. The coordinate variables from the locally linear embedding describing the manifold on which the data reside serve as the latent variable scores. We propose the use of semiparametric penalized spline methods for reconstruction of the manifold equations that approximate the data space. We also discuss a crossvalidation strategy that can guide in selecting an appropriate number of latent variables. Synthetic as well as real data sets are used to illustrate the proposed approach. A nonlinear latent structure representation of a data set also serves as a data visualization tool.