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Supervised alternative clustering is the problem of finding a set of clusterings which are of high quality and different from a given negative clustering. The task is therefore a clear multi-objective optimization problem. Optimizing two conflicting objectives at the same time requires dealing with trade-offs. Most approaches in the literature optimize these objectives sequentially (one objective after another one) or indirectly (by some heuristic combination of the objectives). Solving a multi-objective optimization problem in these ways can result in solutions which are dominated, and not Pareto-optimal. We develop a direct algorithm, called COGNAC, which fully acknowledges the multiple objectives, optimizes them directly and simultaneously, and produces solutions approximating the Pareto front. COGNAC performs the recombination operator at the cluster level instead of at the object level, as in the traditional genetic algorithms. It can accept arbitrary clustering quality and dissimilarity objectives and provides solutions dominating those obtained by other state-of-the-art algorithms. Based on COGNAC, we propose another algorithm called SGAC for the sequential generation of alternative clusterings where each newly found alternative clustering is guaranteed to be different from all previous ones. The experimental results on widely used benchmarks demonstrate the advantages of our approach.

A flexible cluster-oriented alternative clustering algorithm for choosing from the Pareto front of solutions