Spatial robust fuzzy clustering of mixed data with electoral study

A robust fuzzy clustering model for data with mixed features and spatial constraints is proposed to analyze the turnout and the preferences of the voters at the provincial level in the European elections. The 2024 European elections in Italy were held in June to elect the 76 members of the European Parliament due to Italy. The clustering model accommodates various types of variables or attributes by integrating dissimilarity measures for each one through a weighting approach. This method produces a composite distance (or dissimilarity) metric that captures multiple attribute types. The weights are determined objectively during the optimization process and indicate the importance of each attribute type. The model also incorporates robustness via the introduction of a Noise cluster, and accounts for a spatial component. The application shows consistency of the results both at the level of units’ attributes and at a spatial level.