Energy Functions for Dimension Reduction and Graph Visualization

• Activity Number: 189
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Lisha Chen*+
• Companies: Yale University
• Keywords: MDS ; nonlinear dimension reduction ; clustering

Abstract

We introduce a parametrized family of energy functions useful for proximity analysis, nonlinear dimension reduction, and graph drawing. The functions are inspired by the physics intuitions of attractive and repulsive forces common in graph drawing. Their minimization generates low-dimensional configurations (embeddings, graph drawings) whose interpoint distances match input distances as best as possible. The problem of selecting an energy/stress function is translated to a parameter selection problem which can be approached with a meta-criterion. Of particular interest is the tuning of a parameter associated with the notion of "clustering strength". Such tuning greatly helps identifying clusters.