Rank Priors for Continuous Non-Linear Dimensionality Reduction

Non-linear dimensionality reductionmethods are powerful techniques to deal with high-dimensional datasets. However, they often are susceptible to local minima and perform poorly when initialized far from the global optimum, even when the intrinsic dimensionality is known a priori. In this work we introduce a prior over the dimensionality of the latent space, and simultaneously optimize both the latent space and its intrinsic dimensionality. Ad-hoc initialization schemes are unnecessary with our approach; we initialize the latent space to the observation space and automatically infer the latent dimensionality using an optimization scheme that drops dimensions in a continuous fashion. We report results applying our prior to various tasks involving probabilistic non-linear dimensionality reduction, and show that our method can outperform graph-based dimensionality reduction techniques as well as previously suggested ad-hoc initialization strategies.

• Type: Conference
• Year: 2009
• Where: CVPR
• Authors: Andreas Geiger (Karlsruhe Institute of Technology), Raquel Urtasun (University of California, Berkeley), Trevor Darrell (University of California, Berkeley)
• Keywords: Computer Vision, CVPR 2009, Non-Linear Dimensionality Reduction, Rank Priors