Using combinatorial optimization in model-based trimmed clustering with cardinality constraints

Abstract Statistical clustering criteria with free scale parameters and unknown cluster sizes are inclined to create small, spurious clusters. To mitigate this tendency a statistical model for cardinality–constrained clustering of data with gross outliers is established, its maximum likelihood and maximum a posteriori clustering criteria are derived, and their consistency and robustness are analyzed. The criteria lead to constrained optimization problems that can be solved by iterative, alternating trimming algorithms of k–means type. Each step in the algorithms requires the solution to a λ–assignment problem known from combinatorial optimization. The method allows to estimate the numbers of clusters and outliers. It is illustrated with a synthetic and a real data set.