ISOMAP Based Metrics for Clustering

A.E. BAYÁ; P. M. GRANITTO

Mar del Plata, Argentina

Congreso; 36th International Conference of the Argentine Computer Science and Operational Research Society; 2007

Many successful clustering techniques fail to handle data with a manifold structure, i.e. data that is not shaped in the form of compact point clouds, forming arbitrary shapes or paths through a high-dimensional space. In this paper we present a new method to evaluate distances in such spaces that naturally extend the application of many clustering algorithms to these cases. Our algorithm has two stages. Following ISOMAP, it searches for sets of locally-uniform manifolds, which could be disjoint. These manifolds are then connected using two slightly different strategies. We compare these strategies between them and with a state of the art algorithm using three artificial problems, obtaining encouraging result. Both new metrics allow diverse algorithms to easily find clusters of arbitrary shape.