The Laplacian Eigenmaps Latent Variable Model
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:59-66, 2007.
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.