Computer Science – Artificial Intelligence
Scientific paper
2010-10-22
Computer Science
Artificial Intelligence
26 pages,11 figures
Scientific paper
We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian Markov random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting model, which we call maximum entropy unfolding (MEU) is a nonlinear generalization of principal component analysis. We relate the model to Laplacian eigenmaps and isomap. We show that parameter fitting in the locally linear embedding (LLE) is approximate maximum likelihood MEU. We introduce a variant of LLE that performs maximum likelihood exactly: Acyclic LLE (ALLE). We show that MEU and ALLE are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set. Finally the maximum likelihood perspective allows us to introduce a new approach to dimensionality reduction based on L1 regularization of the Gaussian random field via the graphical lasso.
No associations
LandOfFree
A Unifying Probabilistic Perspective for Spectral Dimensionality Reduction: Insights and New Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Unifying Probabilistic Perspective for Spectral Dimensionality Reduction: Insights and New Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Unifying Probabilistic Perspective for Spectral Dimensionality Reduction: Insights and New Models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-115507