Abstract
Fuzzy C-means problem has a broad application prospect as a branch of clustering problem. This paper deeply explores the fuzzy C-means bi-criteria problem in two different algorithms and extends the previous known \(O(k^{2}\mathrm{ln}~k)\) and \(O(k\mathrm{ln}~k)\) performance guarantee. It is shown that for any constant \(\beta \ge 1\), selecting \(\beta k\) cluster centers can achieve \(O(k^{2})\) and O(k) approximation. Preliminary numerical experiments are proposed to support the theoretical results of the paper, in which we run these algorithms on real data sets with different parameter values.
Supported by Higher Educational Science and Technology Program of Shandong Province (No. J17KA171), Natural Science Foundation of Shandong Province (Nos. ZR2019MA032, ZR2019PA004) of China.
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Zhou, Y., Liu, J., Li, M., Liu, Q. (2020). A Bi-criteria Analysis for Fuzzy C-means Problem. In: Zhang, Z., Li, W., Du, DZ. (eds) Algorithmic Aspects in Information and Management. AAIM 2020. Lecture Notes in Computer Science(), vol 12290. Springer, Cham. https://doi.org/10.1007/978-3-030-57602-8_14
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DOI: https://doi.org/10.1007/978-3-030-57602-8_14
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