Density-Weighted Fuzzy c-Means Clustering

In this short paper, a unified framework for performing density-weighted fuzzy $c$-means (FCM) clustering of feature and relational datasets is presented. The proposed approach consists of reducing the original dataset to a smaller one, assigning each selected datum a weight reflecting the number of nearby data, clustering the weighted reduced dataset using a weighted version of the feature or relational data FCM algorithm, and if desired, extending the reduced data results back to the original dataset. Several methods are given for each of the tasks of data subset selection, weight assignment, and extension of the weighted clustering results. The newly proposed weighted version of the non-Euclidean relational FCM algorithm is proved to produce the identical results as its feature data analog for a certain type of relational data. Artificial and real data examples are used to demonstrate and contrast various instances of this general approach.