Abstract
Data clustering is an important theoretical topic and a sharp tool for various applications. Its main objective is to partition a given data set into clusters such that the data within the same cluster are “more” similar to each other with respect to certain measures. In this paper, we study the pairwise data clustering problem with pairwise similarity/ dissimilarity measures that need not satisfy the triangle inequality. By using a criterion, called the minimum normalized cut, we model the pairwise data clustering problem as a graph partition problem. The graph partition problem based on minimizing the normalized cut is known to be NP-hard. We present a ((4 + o(1)) ln n)-approximation polynomial time algorithm for the minimum normalized cut problem. We also give a more efficient algorithm for this problem by sacrificing the approximation ratio slightly. Further, our scheme achieves a ((2 + o(1)) ln n)-approximation polynomial time algorithm for computing the sparsest cuts in edge-weighted and vertex-weighted undirected graphs, improving the previously best known approximation ratio by a constant factor.
This research was supported in part by the 21st Century Research and Technology Fund from the State of Indiana.
The work of this author was supported in part by the Computing and Information Technology Center, and by the Faculty Research Council, University of Texas-Pan American, Edinburg, Texas, USA.
The work of this author was supported in part by the National Science Foundation under Grants CCR-9623585 and CCR-9988468.
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Wu, X., Chen, D.Z., Mason, J.J., Schmid, S.R. (2003). Pairwise Data Clustering and Applications. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_46
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DOI: https://doi.org/10.1007/3-540-45071-8_46
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