Agreement-based fuzzy C-means for clustering data with blocks of features

In real-world problems we encounter situations where patterns are described by blocks (families) of features where each of these groups comes with a well-expressed semantics. For instance, in spatiotemporal data we are dealing with spatial coordinates of the objects (say, x-y coordinates) while the temporal part of the objects forms another collection of features. It is apparent that when clustering objects being described by families of features, it becomes intuitively justifiable to anticipate their different role and contribution to the clustering process of the data whereas the clustering is sought to be reflective of an overall structure in the data set. To address this issue, we introduce an agreement based fuzzy clustering-a fuzzy clustering with blocks of features. The detailed investigations are carried out for the well-known algorithm of fuzzy clustering that is fuzzy C-means (FCM). We propose an extended version of the FCM where a composite distance function is endowed with adjustable weights (parameters) quantifying an impact coming from the blocks of features. A global evaluation criterion is used to assess the quality of the obtained results. It is treated as a fitness function in the optimization of the weights through the use of particle swarm optimization (PSO). The behavior of the proposed method is investigated in application to synthetic and real-world data as well as a certain case study.