Scale-space unsupervised cluster analysis

Most scientific disciplines generate experimental data from an observed system about which we have may have little understanding of the data generating function. It is attractive, therefore, for an analysis system to break a complex data set into a series of piecewise similar groups or structures, each of which may then be regarded as a separate data state, for example, thus reducing overall data complexity. Cluster analysis has a long and rich history and excellent reviews of many methods may be found in Jain-Dubes (1988), Jain (1982), Hartigan (1975) and Everitt (1974). This paper presents a scale-space method of unsupervised clustering (the `optimal´ number of partitions is unknown a priori). Its performance is compared to that of a Gaussian-mixture model (GMM) approach using both maximum-likelihood and K-means algorithms. The multi-scale method may be seen as falling within the hierarchical clustering genre or as a method of scale-space (multiresolution) parameter estimation. We show that the GMM fails for data sets which are not multivariate Gaussian whilst the scale-space method is considerably more robust