Fuzzy clustering Algorithm based on Adaptive City-block distance and Entropy Regularization
Sara Inés Rizo Rodríguez, Francisco de A.T. de Carvalho · 2018
The Euclidean distance is traditionally used to compare the objects and the prototypes in the Fuzzy C-Means algorithms, but theoretical studies indicate that methods based on City-Block distances are more robust concerning the presence of outliers in the dataset than those based on Euclidean distances. Moreover, most often conventional Fuzzy C-Means clustering algorithms consider that all variables are equally important for the clustering task. However, in real situations, some variables may be more or less relevant or even irrelevant for clustering. This paper proposes a partitioning fuzzy clustering algorithm based on Adaptive City-block distances and entropy regularization. The proposed method optimizes an objective function by alternating three steps aiming to compute the fuzzy cluster representatives, the fuzzy partition, as well as relevance weights for the variables. Several experiments on synthetic and real-world datasets including its application to noisy image texture segmentation are presented to corroborate both clustering and robustness capabilities of the proposed algorithm over conventional approaches.