Deriving Meaningful Biological Structure from Spectral Embedding and Clustering

• Activity Number: 129
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statisticians in Defense and National Security
• Author(s): Brandon Higgs*+ and Jeffrey L. Solka and Jennifer Weller
• Companies: George Mason University and Naval Surface Warfare Center, Dahlgren Division and George Mason University
• Keywords: microarray ; gene expression ; spectral clustering

Abstract

The reduction of high-dimensional data into meaningful low-dimensional representations often is necessary to clarify important relationships and reveal inherent structure. Nonlinear data structures in high-dimensional space are not represented accurately by strict Euclidean distances, and as such, not optimal for conventional methods of dimension reduction. Such methods generally seek to minimize a global cost function, which tends to distort local associations and inaccurately represent the inherent connections between points. The spectrum of the Laplacian operator preserves these neighborhood geometries as it learns the data on a low-dimensional manifold. We extend previous results on image data types with an investigation of the outcome when applying the graph Laplacian and Laplace-Beltrami operators on biological data. We find the spectral properties of the weighted graph Laplacian have particular applicability to gene expression data as judged by the ability to classify and cluster points of known disease type and biological function and provide a meaningful projection map.