A Novel Two-Level Entropy-Weighted Fuzzy C-Means Algorithm and Its Application for Classifying Urban Patterns by Residential Building Characteristics

In this work, a novel entropy-weighted fuzzy c-means variation, referred to as Group-based Entropy Weighted Fuzzy C-Means (GEWFCM), is proposed. This variation introduces a semantic level of partitioning of features into groups. This approach enables the provision of optimal semantic meaning to the clusters, thereby capturing the intrinsic structure of the features, which are naturally grouped into homogeneous semantic sets; the weights are independent of the clusters. The cluster weights provide a direct measure of the importance of each group, determining which dimensions of the phenomenon are relevant, and the intragroup weights determine the most relevant features within a group. Additionally, GEWFCM is computationally more efficient than other cluster-specific weighted fuzzy clustering algorithms, due to the independence of the weights from the clusters. The efficacy of the method was assessed by evaluating census data from 16 Italian cities, with the objective of partitioning urban settlements based on characteristics of residential buildings, including construction technique, period, number of floors, and state of conservation. The findings suggest that the proposed algorithm effectively captures the semantic meaning of clusters. In addition, a comparative analysis between GEWFCM and the well-known Entropy Weighted Fuzzy C-Means (EWFCM) algorithm showed that, although both algorithms provide high similarity of results for all case studies, GEWFCM is significantly faster.