Abstract
In the field of clustering, non-spherical data clustering is a relatively complex case. To satisfy the practical application, the solution should be able to capture non-convex patterns in data sets with high performance. At present, the multi-prototype method can meet the former requirement, but the time cost is still high. This paper proposes a new multi-prototype extension of the K-multiple-means type algorithm, which aims to further reduce the computation time in processing non-spherical data sets with a concise principle while maintaining close performance. Compared with other methods, the method still adopts the idea of multiple prototypes and uses agglomerative strategies in the phase of class cluster connection. However, to reduce the amount of data involved in the computation and the interference of incorrect partition, the subclass data of the first partition is filtered. In addition, the agglomeration is divided into two stages: the agglomeration between prototypes and the agglomeration between clusters, and two agglomeration modes are provided to deal with different clustering tasks. Before updating the means, the filtered data needs a quadratic partition. Experimental results show that compared with the state-of-the-art approaches, the proposed method is still effective with lower time complexity in both synthetic and real-world data sets.
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References
Dhillon, I.S.: Co-clustering documents and words using bipartite spectral graph partitioning. In: ACM SIGKDD (2001)
Jain, A.K., Narasimha Murty, M., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999)
Nie, F., Tian, L., Li, X.: Multiview clustering via adaptively weighted procrustes. In: ACM SIGKDD(2018)
Nie, F., Wang, X., Huang, H.: Clustering and projected clustering with adaptive neighbors. In: ACM SIGKDD (2014)
Von Luxburg, U.: A tutorial on spectral clustering. Statist. Comput. 17(4), 395–416 (2007)
Von Luxburg, U.: Clustering stability: an overview. Found. Trends Mach. Learn. 2(3) (2010)
Ben-Hur, A., Elisseeff, A., Guyon, I.: A stability based method for discovering structure in clustered data. Pac. Symp. Biocomput. 6–17 (2002)
Arthur, D., Vassilvitskii, S.: k-means++: the advantages of careful seeding. In: 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1027–1035. Society for Industrial and Applied Mathematics (2007)
Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. J. Mach. Learn. Res. 6, 1705–1749 (2005)
Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy C-means clustering algorithm. Comput. Geosci. 2(3), 191–203 (1984)
Cannon, R.L., Dave, J.V., Bezdek, J.C.: Efficient implementation of the fuzzy C-means clustering algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 2, 248–255 (1986)
Ding, C., He, X.: K-means clustering via principal component analysis. In: Twenty-First International Conference on Machine Learning, vol. 29. ACM (2004)
Hamerly, G., Elkan, C.: Learning the K in k-means. Adv. Neural Inf. Process. Syst. 281–288 (2004)
Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy C-means model. IEEE Trans. Fuzzy Syst. 3(3), 370–379 (1995)
Wagstaff, K., Cardie, C., Rogers, S., Schrödl, S., et. al.: Constrained k-means clustering with background knowledge. In: ICML, vol. 1, pp. 577–584 (2001)
MacQueen, J., et. al.: Some methods for classification and analysis of multivariate observations. In: Fifth Berkeley Symposium on Mathematical Statistics and Probability, Oakland, vol. 1, pp. 281–297 (1967)
Ruspini, E.H.: A new approach to clustering. Inf. Control 15(1), 22–32 (1969)
Karypis, G., Han, E.-H., Kumar, V.: Chameleon: a hierarchical clustering using dynamic modeling. Computer 32(8), 68–75 (1999). https://doi.org/10.1109/2.781637
Tao, C.-W.: Unsupervised fuzzy clustering with multi-center clusters. Fuzzy Sets Syst. 128(3), 305–322 (2002)
Liu, M., Jiang, X., Kot, A.C.: A multi-prototype clustering algorithm. Pattern Recogn. 42(5), 689–698 (2009)
Luo, T., Zhong, C., Li, H., Sun, X.: A multi-prototype clustering algorithm based on minimum spanning tree. In: Fuzzy Systems and Knowledge Discovery (FSKD), 2010 Seventh International Conference on, vol. 4, pp. 1602–1607. IEEE (2010)
Ben, S., Jin, Z., Yang, J.: Guided fuzzy clustering with multi-prototypes. In: IJCNN (2011)
Liang, J., Bai, L., Dang, C., Cao, F.: The K-means-type algorithms versus imbalanced data distributions. IEEE Trans. Fuzzy Syst. 20(4), 728–745 (2012)
Nie, F., Wang, C.-L., Li, X.: K-multiple-means: a multiple-means clustering method with specified K clusters. In: ACM SIGKDD (2019)
Nie, F., Wang, X., Jordan, M.I., Huang, H.: The constrained Laplacian rank algorithm for graph-based clustering. In: AAAI (2016)
Dhillon, I.S., Guan, Y., Kulis, B.: Kernel k-means: spectral clustering and normalized cuts. In: ACM SIGKDD (2004)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS (2001)
Zha, H., He, X., Ding, C., Gu, M., Simon, H.D.: Spectral relaxation for k-means clustering. Adv. Neural Inf. Process. Syst. 1057–1064 (2002)
Bai, L., Liang, J.: A three-level optimization model for nonlinearly separable clustering. In: AAAI(2020)
Wang, C.D., Lai, J.H., Zhu, J.Y.: Graph-based multiprototype competitive learning and its applications. IEEE Trans. Syst. Man Cybern. C Appl. 42(6), 934–946 (2012)
Wang, C.-D., Lai, J.-H., Suen, C.Y., Zhu, J.-Y.: Multi-exemplar affinity propagation. IEEE Trans. Pattern Anal. Mach. Intell. 35(9), 2223–2237 (2013)
Wang, Y., Chen, L.: K-MEAP: multiple exemplars affinity propagation with specified K clusters. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2670–2682 (2016)
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Zhang, J. (2022). A New K-Multiple-Means Clustering Method. In: Memmi, G., Yang, B., Kong, L., Zhang, T., Qiu, M. (eds) Knowledge Science, Engineering and Management. KSEM 2022. Lecture Notes in Computer Science(), vol 13369. Springer, Cham. https://doi.org/10.1007/978-3-031-10986-7_50
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DOI: https://doi.org/10.1007/978-3-031-10986-7_50
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