Abstract
Density-based clustering has the advantages for (i) allowing arbitrary shape of cluster and (ii) not requiring the number of clusters as input. However, when clusters touch each other, both the cluster centers and cluster boundaries (as the peaks and valleys of the density distribution) become fuzzy and difficult to determine. In higher dimension, the boundaries become wiggly and over-fitting often occurs. We introduce the notion of cluster intensity function (CIF) which captures the important characteristics of clusters. When clusters are well-separated, CIFs are similar to density functions. But as clusters touch each other, CIFs still clearly reveal cluster centers, cluster boundaries, and, degree of membership of each data point to the cluster that it belongs. Clustering through bump hunting and valley seeking based on these functions are more robust than that based on kernel density functions which are often oscillatory or over-smoothed. These problems of kernel density estimation are resolved using Level Set Methods and related techniques. Comparisons with two existing density-based methods, valley seeking and DBSCAN, are presented to illustrate the advantages of our approach.
This work has been partially supported by grants from DOE under contract DE-AC03-76SF00098, NSF under contracts DMS-9973341, ACI-0072112 and INT-0072863, ONR under contract N00014-03-1-0888, NIH under contract P20 MH65166, and the NIH Roadmap Initiative for Bioinformatics and Computational Biology U54 RR021813 funded by the NCRR, NCBC, and NIGMS.
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References
Ester, M., Kriegel, H., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Int. Conf. Knowledge Discovery and Data Mining, Portland, OR, pp. 226–231. AAAI Press, Menlo Park (1996)
Hinneburg, A., Keim, D.A.: An efficient approach to clustering in large multimedia databases with noise. In: Int. Conf. Knowledge Discovery and Data Mining, New York City, NY, pp. 58–65. AAAI Press, Menlo Park (1998)
Agrawal, R., Gehrke, J., Gunopulos, D., Raghavan, P.: Automatic subspace clustering of high dimensional data for data mining applications. In: Proc. ACM-SIGMOD Int. Conf. Management of Data, Seattle, WA, pp. 94–105. ACM Press, New York (1998)
Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Boston Academic Press, London (1990)
Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2003)
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Yip, A.M., Ding, C., Chan, T.F. (2005). Dynamic Cluster Formation Using Level Set Methods. In: Ho, T.B., Cheung, D., Liu, H. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2005. Lecture Notes in Computer Science(), vol 3518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11430919_46
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DOI: https://doi.org/10.1007/11430919_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26076-9
Online ISBN: 978-3-540-31935-1
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