K-means algorithm is one of the most popular and widely used clustering method because it is easy to implement and very efficient. However, this method has the limitation to be used with fixed number of clusters because of only considering the intra-cluster distance to evaluate the data clustering solutions. Silhouette is useful and stable valid index to decide the data clustering solution with number of clusters to consider the intra and inter cluster distance for unsupervised data. However, this valid index has high computational burden because of considering quality measure for each data object. The objective of this paper is to propose the fast and simple speed-up method to overcome this limitation to use silhouette for the effective large-scale data clustering. In the first step, the proposed method calculates and saves the distance for each data once. In the second step, this distance matrix is used to calculate the relative distance rate (Vｊ) of each data j and this rate is used to choose the suitable number of clusters without much computation time. In the third step, the proposed efficient heuristic algorithm (Group search optimization, GSO, in this paper) can search the global optimum with saving computational capacity with good initial solutions using Vｊ probabilistically for the data clustering. The performance of our proposed method is validated to save significantly computation time against the original silhouette only using Ruspini, Iris, Wine and Breast cancer in UCI machine learning repository datasets by experiment and analysis. Especially, the performance of our proposed method is much better than previous method for the larger size of data.

Data clustering is one of the most difficult and challenging problems and can be formally considered as a particular kind of NP-hard grouping problems. The K-means algorithm is one of the most popular and widely used clustering method because it is easy to implement and very efficient. However, it has high possibility to trap in local optimum and high variation of solutions with different initials for the large data set. Therefore, we need study efficient computational intelligence method to find the global optimal solution in data clustering problem within limited computational time. The objective of this paper is to propose a combined artificial bee colony (CABC) with K-means for initialization and finalization to find optimal solution that is effective on data clustering optimization problem. The artificial bee colony (ABC) is an algorithm motivated by the intelligent behavior exhibited by honeybees when searching for food. The performance of ABC is better than or similar to other population-based algorithms with the added advantage of employing fewer control parameters. Our proposed CABC method is able to provide near optimal solution within reasonable time to balance the converged and diversified searches. In this paper, the experiment and analysis of clustering problems demonstrate that CABC is a competitive approach comparing to previous partitioning approaches in satisfactory results with respect to solution quality. We validate the performance of CABC using Iris, Wine, Glass, Vowel, and Cloud UCI machine learning repository datasets comparing to previous studies by experiment and analysis. Our proposed KABCK (K-means+ABC+K-means) is better than ABCK (ABC+K-means), KABC (K-means+ABC), ABC, and K-means in our simulations.