The Laplacian Eigenmaps Latent Variable Model

Miguel A. Carreira-Perpiñán, Zhengdong Lu
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-carreira-perpinan07a, title = {The Laplacian Eigenmaps Latent Variable Model}, author = {Carreira-Perpiñán, Miguel A. and Lu, Zhengdong}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {59--66}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/carreira-perpinan07a/carreira-perpinan07a.pdf}, url = {https://proceedings.mlr.press/v2/carreira-perpinan07a.html}, 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.} }
Endnote
%0 Conference Paper %T The Laplacian Eigenmaps Latent Variable Model %A Miguel A. Carreira-Perpiñán %A Zhengdong Lu %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-carreira-perpinan07a %I PMLR %P 59--66 %U https://proceedings.mlr.press/v2/carreira-perpinan07a.html %V 2 %X 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.
RIS
TY - CPAPER TI - The Laplacian Eigenmaps Latent Variable Model AU - Miguel A. Carreira-Perpiñán AU - Zhengdong Lu BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-carreira-perpinan07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 59 EP - 66 L1 - http://proceedings.mlr.press/v2/carreira-perpinan07a/carreira-perpinan07a.pdf UR - https://proceedings.mlr.press/v2/carreira-perpinan07a.html AB - 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. ER -
APA
Carreira-Perpiñán, M.A. & Lu, Z.. (2007). The Laplacian Eigenmaps Latent Variable Model. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:59-66 Available from https://proceedings.mlr.press/v2/carreira-perpinan07a.html.

Related Material