Proximity-Graph-Based Tools for DNA Clustering

Abstract

Clustering is considered the most important aspect of unsupervised learning in data mining. It deals with finding structure in a collection of unlabeled data. One simple way of defining clustering is as follows: the process of organizing data elements into groups, called clusters, whose members are similar to each other in some way. Several algorithms for clustering exist (Gan, Ma, & Wu, 2007); proximity-graph-based ones, which are untraditional from the point of view of statisticians, emanate from the field of computational geometry and are powerful and often elegant (Bhattacharya, Mukherjee, & Toussaint, 2005). A proximity graph is a graph formed from a collection of elements, or points, by connecting with an edge those pairs of points that satisfy a particular neighbor relationship with each other. One key aspect of proximity-graph-based clustering techniques is that they may allow for an easy and clear visualization of data clusters, given their geometric nature. Proximity graphs have been shown to improve typical instance-based learning algorithms such as the k-nearest neighbor classifiers in the typical nonparametric approach to classification (Bhattacharya, Mukherjee, & Toussaint, 2005). Furthermore, the most powerful and robust methods for clustering turn out to be those based on proximity graphs (Koren, North, & Volinsky, 2006). Many examples have been shown where proximity-graph-based methods perform very well when traditional methods fail miserably (Zahn, 1971; Choo, Jiamthapthaksin, Chen, Celepcikay, Giusti, & Eick, 2007).