Dirichlet Aggregation: Unsupervised Learning towards an Optimal Metric for Proportional Data
published: June 23, 2007, recorded: June 2007, views: 6043
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Proportional data (normalized histograms) have been frequently occurring in various areas, and they could be mathematically abstracted as points residing in a geometric simplex. A proper distance metric on this simplex is of importance in many applications including classification and information retrieval. In this paper, we develop a novel framework to learn an optimal metric on the simplex. Ma jor features of our approach include: 1) its flexibility to handle correlations among bins/dimensions; 2) widespread applicability without being limited to ad hoc backgrounds; and 3) a "real" global solution in contrast to existing traditional local approaches. The technical essence of our approach is to fit a parametric distribution to the observed empirical data in the simplex. The distribution is parameterized by affinities between simplex vertices, which is learned via maximizing likelihood of observed data. Then, these affinities induce a metric on the simplex, defined as the earth mover's distance equipped with ground distances derived from simplex vertex affinities.
Download slides: icml07_corvallis_wang_hua_yan.pdf (524.7 KB)
Download slides: icml07_corvallis_wang_hua_yan.ppt (556.0 KB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !
Write your own review or comment: