Geometric biclustering and its applications to cancer tissue classification based on DNA microarray gene expression data

Biclustering is an important tool in microarray data analysis when only a subset of genes coregulates under a subset of conditions. It is a useful technique for cancer tissue classification based on gene expression data. Unlike standard clustering analysis, biclustering methodology can perform simultaneous classification on the two dimensions of genes and conditions in a data matrix. However, the biclustering problem is inherently intractable and computationally complex. In this chapter, we present a novel geometric perspective of a biclustering problem and the related geometric algorithms. In the view of geometrical interpretation, different types of biclusters can be mapped to the linear geometric structures, such as points, lines, or hyperplanes in a high-dimensional data space. Such a perspective makes it possible to unify the formulation of biclusters and thus the biclustering process can be interpreted as a search for linear geometries in spatial space. Based on the linear geometry formulation, we develop Hough transform-based biclustering algorithms. Considering the computational complexity in searching the existence of noise in microarray data, and the biological meanings of biclusters, we propose several methods to improve the geometric biclustering algorithms. Simulation studies show that the algorithms can discover significant biclusters despite the increased noise level and regulatory complexity. Furthermore, the algorithms are also effective in extracting biologically meaningful biclusters from real microarray gene expression data.