The Laplacian Eigenmaps Latent Variable Model

Miguel A. Carreira-Perpiñan, Zhengdong Lu; JMLR W&P 2:59-66, 2007.

Abstract

We introduce the Laplacian Eigenmaps Latent Variable Model (LELVM), a probabilistic method for nonlinear dimensionality reduction that combines the advantages of spectral methods--global optimisation and ability to learn convoluted manifolds of high intrinsic dimensionality--with those of latent variable models--dimensionality reduction and reconstruction mappings and a density model. We derive LELVM by defining a natural out-of-sample mapping for Laplacian eigenmaps using a semi-supervised learning argument. LELVM is simple, nonparametric and computationally not very costly, and is shown to perform well with motion-capture data.