RECENT RESULTS IN HIERARCHICAL CLUSTERING: I–THE REDUCIBLE NEIGHBORHOODS CLUSTERING ALGORITHM

Abstract

The clustering of large data sets is of great interest in fields such as pattern recognition, numerical taxonomy, image or speech processing. The traditional Ascendant Hierarchical Algorithm (AHC) cannot be run for sets of more than a few thousand elements. The reducible neighborhoods clustering algorithm, which is presented in this paper, has overtaken the limits of the traditional hierarchical clustering algorithm by generating an exact hierarchy on a large data set. The theoretical justification of this algorithm is the so-called Bruynooghe reducibility principle, that lays down the condition under which the exact hierarchy may be constructed locally, by carrying out aggregations in restricted regions of the representation space. As for the Day and Edelsbrunner algorithm, the maximum theoretical time complexity of the reducible neighborhoods clustering algorithm is O(n2 log n), regardless of the chosen clustering strategy. But the reducible neighborhoods clustering algorithm uses the original data table and its practical performances are by far better than Day and Edelsbrunner’s algorithm, thus allowing the hierarchical clustering of large data sets, i.e. composed of more than 10 000 objects.