LLp metric based robust clustering

This paper introduces the generalized Cauchy distribution derived LLp metric. We analyze the properties of the metric from the point of view of robust statistics and relate the metric to the Lp metric, comparing the robustness of the metrics according to their influence functions. The derived metric is employed in robust clustering. To implement the proposed robust clustering method, a robust centroid updating algorithm based on maximum likelihood estimation theory is introduced. Simulations are performed to evaluate the validity of the algorithm and demonstrate its robustness compared with classical robust clustering methods.