Integrating fitness predator optimizer with multi-objective PSO for dynamic partitional clustering

Abstract

Clustering is an unsupervised classification task in data mining, which partitions data set into certain number of clusters. Though many metaheuristics have been suggested to optimize clustering results, most of them are marred by the three key issues. First, clustering performance is devised on a single validity measure; hence, it produces a single best solution biased toward the criterion; it is unacceptable as clustering has multiple conflicting criteria. Second, they find difficulty in avoiding local optima owing to lack of balancing in exploration and exploitation in the search space. Third, they require number of clusters a priori which is difficult to decide in the real-world problems. To deal with the first issue, we follow Pareto-based approach to obtain diverse trade-off solutions by optimizing conceptually contradicting validity measures sum of squared error and connectedness. The well-known swarm intelligence-based metaheuristic particle swarm optimization (PSO) has a severe drawback that it converges prematurely owing to single directional information sharing mechanism among particles in the swarm. Therefore, for the second issue, we introduce fitness predator optimizer (FPO) to enhance diversity in the PSO in multi-objective optimization scenario; it is named as FPO-MOPSO. To address the third issue, we use dynamic clustering method to decide an optimum number of clusters (k) in the range of 2 to $\sqrt{n}$, where n is number of objects in the data set. We use eight real-world and two artificial data sets for comparison of the FPO-MOPSO results with three well-known competitive methods MOPSO, MABC, and NSGA-II using four quality measures convergence, diversity, coverage, and ONVG. The obtained results show superiority of the FPO-MOPSO over its competitors. Two external validity indices of clustering results F-measure and Rand index also establish the above finding. As the decision maker picks only a single solution from the set of trade-off solutions, we employ an additional measure silhouette index to select a final single solution from the archive and compare it with known number of clusters in the data sets.