Abstract
k-means clustering (KM) algorithm, also called hard c-means clustering (HCM) algorithm, is a very powerful clustering algorithm [1, 2], but it has a serious problem of strong initial value dependence. To decrease the dependence, Arthur and Vassilvitskii proposed an algorithm of k-means++ clustering (KM++) algorithm on 2007 [3]. By the way, there are many case that each object is allocated on an unit sphere, e.g. text clustering. Dhillon and Modha proposed the primitive spherical k-means clustering algorithm to classify such objects on 2007 [4] and Honik, Kober, and Buchta proposed new spherical k-means clustering (SKM) algorithm on 2012 [5]. However, both of the algorithms also have the same problem of initial value dependence as KM. Therefore, the paper discuss the following points: (1) the dissimilarity of SKM is extended to satisfy the triangle inequality, and (2) spherical k-means++ clustering (SKM++) algorithm which works well for the problem is proposed. The paper shows that the effectiveness of SKM++ is theoretically guaranteed.
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References
Steinhaus, H.: Sur la division des corps matériels en parties. Bulletin de l’Académie Polonaise des Sci. 4(12), 801–804 (1957)
MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Statistics, vol. 1, pp. 281–297. University of California Press (1967)
Arthur, D., Vassilvitskii, S.: \(k\)-means++: the advantages of careful seeding, In: Proceedings of the Eighteenth Annual ACM-SIAM symposium on Discrete algorithms, pp. 1027–1035. Society for Industrial and Applied Mathematics, Philadelphia (2007)
Dhillon, I.S., Modha, D.S.: Concept decompositions for large sparse text data using clustering. Mach. Learn. 42, 143–175 (2001)
Hornik, K., Feinerer, I., Kober, M., Buchta, C.: Spherical \(k\)-Means Clustering, vol. 50(10), September 2012
Dasgupta, S.: Lecture 3 – Algorithms for \(k\)-means clustering (2013). http://cseweb.ucsd.edu/dasgupta/291-geom/kmeans.pdf
Acknowledgment
This work has partly been supported by JSPS KAKENHI Grant Numbers 26330270 and 26330271.
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Endo, Y., Miyamoto, S. (2015). Spherical k-Means++ Clustering. In: Torra, V., Narukawa, T. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2015. Lecture Notes in Computer Science(), vol 9321. Springer, Cham. https://doi.org/10.1007/978-3-319-23240-9_9
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DOI: https://doi.org/10.1007/978-3-319-23240-9_9
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