Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization

Abstract

An ant-based approach to heuristic centroid searching is introduced. The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek's partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.