Nonlinear multicriteria clustering based on multiple dissimilarity matrices

• A new hard clustering multicriteria algorithm is presented.
• The algorithm is based on a more general nonlinear aggregation criterion.
• Relevance weights for dissimilarity matrices may be local (in each group) or global.
• In order to optimize the nonlinear criterion, linear programming is used.
• The linear programming approach allows the introduction of some type of constraints.

We present a new algorithm capable of partitioning sets of objects by taking simultaneously into account their relational descriptions given by multiple dissimilarity matrices. The novelty of the algorithm is that it is based on a nonlinear aggregation criterion, weighted Tchebycheff distances, more appropriate than linear combinations (such as weighted averages) for the construction of compromise solutions. We obtain a hard partition of the set of objects, the prototype of each cluster and a weight vector that indicates the relevance of each matrix in each cluster. Since this is a clustering algorithm for relational data, it is compatible with any distance function used to measure the dissimilarity between objects. Results obtained in experiments with data sets (synthetic and real) show the usefulness of the proposed algorithm.