STOR Colloquium: Lisha Chen (Yale University)

Energy functions for Nonlinear Dimension Reduction and Graph Visualization 

Nonlinear dimension reduction concern with constructing a nonlinear low dimensional embedding of a hypothetical manifold near which the data fall. In this talk we will introduce a new family of energy functions for nonlinear dimension reduction methods called “Local Multidimensional Scaling” or LMDS. Like other methods in the area, LMDS only uses local information from user-chosen neighborhoods, but it differs from them in that it uses ideas from the area of “graph layout”. We approach the force paradigm, which is commonly used in "graph layout", by proposing a parametrized family of stress or energy functions inspired by Box-Cox power transformations. This family provides users with considerable flexibility for achieving desirable embeddings, and it comprises most energy functions proposed in the past. Facing an embarrassment of riches of energy functions, we propose a metacriterion that measures how well the sets of K-nearest neighbors agree between the original high-dimensional space and the low-dimensional embedding space. This meta-criterion has intuitive appeal, and it performs well in creating faithful embeddings.

Refreshments will be served at 3:30pm in the 3rd floor lobby of Hanes Hall