Spectral Dimensionality Reduction via Maximum Entropy

Neil D. Lawrence
,  15:51-59, 2011.

Abstract

We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting probabilistic models are based on GRFs. The resulting model is a nonlinear generalization of principal component analysis. We show that parameter fitting in the locally linear embedding is approximate maximum likelihood in these models. We directly maximize the likelihood and show results that are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set.

Cite this Paper


BibTeX
@InProceedings{pmlr-v-lawrence-spectral11, title = {Spectral Dimensionality Reduction via Maximum Entropy}, author = {Neil D. Lawrence}, pages = {51--59}, year = {}, editor = {}, volume = {15}, address = {Fort Lauderdale, FL, USA}, url = {http://inverseprobability.com/publications/lawrence-spectral11.html}, abstract = {We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting probabilistic models are based on GRFs. The resulting model is a nonlinear generalization of principal component analysis. We show that parameter fitting in the locally linear embedding is approximate maximum likelihood in these models. We directly maximize the likelihood and show results that are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set.} }
Endnote
%0 Conference Paper %T Spectral Dimensionality Reduction via Maximum Entropy %A Neil D. Lawrence %B %C Proceedings of Machine Learning Research %D %E %F pmlr-v-lawrence-spectral11 %I PMLR %J Proceedings of Machine Learning Research %P 51--59 %U http://inverseprobability.com %V %W PMLR %X We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting probabilistic models are based on GRFs. The resulting model is a nonlinear generalization of principal component analysis. We show that parameter fitting in the locally linear embedding is approximate maximum likelihood in these models. We directly maximize the likelihood and show results that are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set.
RIS
TY - CPAPER TI - Spectral Dimensionality Reduction via Maximum Entropy AU - Neil D. Lawrence BT - PY - DA - ED - ID - pmlr-v-lawrence-spectral11 PB - PMLR SP - 51 DP - PMLR EP - 59 L1 - UR - http://inverseprobability.com/publications/lawrence-spectral11.html AB - We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting probabilistic models are based on GRFs. The resulting model is a nonlinear generalization of principal component analysis. We show that parameter fitting in the locally linear embedding is approximate maximum likelihood in these models. We directly maximize the likelihood and show results that are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set. ER -
APA
Lawrence, N.D.. (). Spectral Dimensionality Reduction via Maximum Entropy. , in PMLR :51-59

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