Robust clustering methods: a unified view

TLDR

Clustering methods must be robust to be useful in practice. The paper analyzes commonalities among popular robust clustering methods and proposes generic concepts, algorithms, and guidelines for clustering noisy data. The authors connect fuzzy set theory to robust statistics, compare robust clustering to statistical techniques such as weighted least squares, M‑estimators, and minimum volume ellipsoid, and explain why the generalized Hough transform is suboptimal. These insights yield a unified view of robust clustering methods.

Abstract

Clustering methods need to be robust if they are to be useful in practice. In this paper, we analyze several popular robust clustering methods and show that they have much in common. We also establish a connection between fuzzy set theory and robust statistics, and point out the similarities between robust clustering methods and statistical methods such as the weighted least-squares technique, the M estimator, the minimum volume ellipsoid algorithm, cooperative robust estimation, minimization of probability of randomness, and the epsilon contamination model. By gleaning the common principles upon which the methods proposed in the literature are based, we arrive at a unified view of robust clustering methods. We define several general concepts that are useful in robust clustering, state the robust clustering problem in terms of the defined concepts, and propose generic algorithms and guidelines for clustering noisy data. We also discuss why the generalized Hough transform is a suboptimal solution to the robust clustering problem.