A new approach to clustering

Estimation theory is used to derive a new approach to the clustering problem. The new method is a unification of centroid and mode estimation, achieved by considering the effect of spatial scale on the estimator. The result is a multiresolution method which spans a range of spatial scales, giving enhanced robustness both to noise in the data and to changes of scale in the data, by using comparison between scales as a test of cluster validity. Iterative and non-iterative algorithms based on the new estimator are presented and are shown to be more accurate than simple scale-space filtering in identifying and locating the cluster centres from noisy test data. Results from a wide range of applications are used to illustrate the power and versatility of the new method.