Optimal Clustering with Twofold Memberships
This paper proposes two clustering algorithms of twofold memberships for each cluster. One uses a membership similar to that in K-means, while another membership is defined for a core of a cluster, which is compared to the lower approximation of a cluster in rough K-means. Two ideas for the lower approximation are proposed in this paper: one uses a neighborhood of a cluster boundary and another uses a simple circle from a cluster center. By using the two memberships, two alternate optimization algorithms are proposed. Numerical examples show the effectiveness of the proposed algorithms.
KeywordsNeighborhood Clustering K-means Rough K-means Twofold memberships
This paper is based upon work supported in part by the Air Force Office of Scientific Research/Asian Office of Aerospace Research and Development (AFOSR/AOARD) under award number FA2386-17-1-4046.
- 4.Kinoshita, N., Endo, Y., Miyamoto, S.: On some models of objective-based rough clustering. In: Proceedings of 2014 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technologies, 11–14 August 2014, Warsaw, Poland (2014)Google Scholar
- 7.MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press (1967)Google Scholar
- 11.Ubukata, S., Notsu, A., Honda, K.: The rough set \(k\)-means clustering. In: Proceedings of SCIS-ISIS, pp. 189–193 (2016)Google Scholar