Bayesian Graph Cutting

• Activity Number: 497
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2007 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Bani Mallick*+
• Companies: Texas A&M University
• Keywords: Microarray ; gene networks ; graph cutting ; Dirichlet process ; kernel k-mean

Abstract

Graph cutting techniques prevail in the non-statistical community for identifying meaningful subgraphs or significantly interacting subset of vertices in a large graph. We explore the nonparametric Bayesian partitioning of graphical structures representing the dependency between different responses in a dataset. We propose a nonparametric Bayesian alternative to graph cutting by approaching it as a clustering problem. For clustering, we use nonparametric Dirichlet process priors . It is shown that loss functions similar to the kernel $k$-means naturally arises in this model and the minimization of associated posterior risk comprises an effective graph cutting strategy. The method has been applied to two microarray datasets namely, the melanoma dataset (Bittner et al., 2000) and the sarcoma dataset (Nykter et al., 2006). Some preliminary results are reported.