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Multiobjective graph clustering with variable neighbourhood descent Naverniouk, Igor

Abstract

Graph clustering is a well-known combinatorial problem that appears in many different incarnations. The task is to partition the vertex set of a graph in order to minimize a given cost function. Clustering has applications in VLSI design, protein-protein interaction networks, data mining and many other areas. In the context of multiobjective optimization, we have more than one cost function, and instead of finding a single optimal solution, we are interested in a set of Pareto-optimal solutions. We present a multiobjective variable neighbourhood descent algorithm for this problem and its results on a collection of synthetic and real world data. On data sets that have a known "correct" clustering, our algorithm consistently finds interesting unsupported solutions (those that can not be found by any linear single-objective restriction of the problem), demonstrating a clear advantage of the multiobjective approach. Additionally, the shape of the Pareto front generated by the algorithm can give clues for the areas of the cost function space that contain non-trivial solutions. We compare our method to a single-objective clustering algorithm (RNSC, [41]) and a multiobjective algorithm (MOCK, [27]). On all data sets, our algorithm requires substantially longer CPU time, but produces higher quality results.

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