Abstract

In this paper, a systematic optimization approach for clustering proximity or similarity data is developed. Starting from fundamental invariance and robustness properties, a set of axioms is proposed and discussed to distinguish different cluster compactness and separation criteria. The approach covers the case of sparse proximity matrices, and is extended to nested partitionings for hierarchical data clustering. To solve the associated optimization problems, a rigorous mathematical framework for deterministic annealing and mean--field approximation is presented. Efficient optimization heuristics are derived in a canonical way, which also clarifies the relation to stochastic optimization by Gibbs sampling. Similarity-based clustering techniques have a broad range of possible applications in computer vision, pattern recognition, and data analysis. As a major practical application we present a novel approach to the problem of unsupervised texture segmentation, which relies on statistical...

Citations