Cluster stability using minimal spanning trees

Date

2008-05-23

Author

Barzily, Zeev
Volkovich, Zeev
Akteke-Oeztuerk, Basak
Weber, Gerhard Wilhelm

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In this paper, a method for the study of cluster stability is purposed. We draw pairs of samples from the data, according to two sampling distributions. The first distribution corresponds to the high density zones of data-elements distribution. It is associated with the clusters cores. The second one, associated with the cluster margins, is related to the low density zones. The samples are clustered and the two obtained partitions are compared. The partitions are considered to be consistent if the obtained clusters are similar. The resemblance is measured by the total number of edges, in the clusters minimal spanning trees, connecting points from different samples. We use the Friedman and Rafsky two sample test statistic. Under the homogeneity hypothesis, this statistic is normally distributed. Thus, it can expected that the true number of clusters corresponds to the statistic empirical distribution which is the closest to normal. Numerical experiments demonstrate the ability of the approach to detect the true number of clusters.

Subject Keywords

Clustering, Cluster validation, Minimal Spanning Tree two sample test

URI

https://hdl.handle.net/11511/55891

Conference Name

20th International Conference/Euro Mini Conference on Continuous Optimization and Knowledge-Based Technologies (EurOPT 2008)

Collections

Graduate School of Applied Mathematics, Conference / Seminar

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Citation Formats

Z. Barzily, Z. Volkovich, B. Akteke-Oeztuerk, and G. W. Weber, “Cluster stability using minimal spanning trees,” presented at the 20th International Conference/Euro Mini Conference on Continuous Optimization and Knowledge-Based Technologies (EurOPT 2008), Neringa, LITHUANIA, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55891.