Fuzzy clustering of mixed data with spatial regularization

A fuzzy clustering model for data with mixed features and spatial constraints is proposed. The clustering model allows different types of variables, or attributes, to be taken into account. This result is achieved by combining the dissimilarity measures for each attribute employing a weighting scheme, to obtain a distance measure for multiple attributes. The weights are objectively computed during the optimization process. The weights reflect the relevance of each attribute type in the clustering results. A spatial term is taken into account, considering a wide definition of contiguity, either physical contiguity or the adjacency matrix in a network. Simulation studies and two empirical applications, including both physical and abstract definitions of contiguity are presented that show the effectiveness of the proposed clustering model.