Quantum-inspired evolutionary approach for selection of optimal parameters of fuzzy clustering

Abstract

Recently, Fuzzy c-Means (FCM) algorithm is most widely used because of its efficiency and simplicity. However, FCM is sensitive to the initialization of fuzziness factor (m) and the number of clusters (c) due to which it easily trapped in local optima. A selection of these parameters is a critical issue because an adverse selection can blur the clusters in the data. In the available fuzzy clustering literature, cluster validity index is used to determine the optimal number of clusters for the dataset, but these indexes may trap into the local optima due to the random selection of m. From the perspective of handling local optima problem, we proposed a hybrid fuzzy clustering approach referred as quantum-inspired evolutionary fuzzy c-means algorithm. In the proposed approach, we integrate the concept of quantum computing with FCM to evolve the parameter m in several generations. The evolution of fuzziness factor (m) with the quantum concept aims to provide the better characteristic of population diversity and large search space to find the global optimal value of m and its corresponding value of c. Experiments using three real-world datasets are reported and discussed. The results of the proposed approach are compared to those obtained from validity indexes like $V_{CWB}$ and $V_{OS}$ and evolutionary fuzzy based clustering algorithms. The results show that proposed method achieves the global optimal value of m, c with a minimum value of fitness function and shows significant improvement in the convergence times (the number of iterations) as compared to the state-of-the-art methods.