CLUSTER STABILITY ESTIMATION BASED ON A MINIMAL SPANNING TREES APPROACH

2009-06-03
Volkovich, Zeev (Vladimir)
Barzily, Zeev
Weber, Gerhard Wilhelm
Toledano-Kitai, Dvora
Among the areas of data and text mining which are employed today in science, economy and technology, clustering theory serves as a preprocessing step in the data analyzing. However, there are many open questions still waiting for a theoretical and practical treatment, e.g., the problem of determining the true number of clusters has not been satisfactorily solved. In the current paper, this problem is addressed by the cluster stability approach. For several possible numbers of clusters we estimate the stability of partitions obtained from clustering of samples. Partitions are considered consistent if their clusters are stable. Clusters validity is measured as the total number of edges, in the clusters' minimal spanning trees, connecting points from different samples. Actually, we use the Friedman and Rafsky two sample test statistic. The homogeneity hypothesis, of well mingled samples within the clusters, leads to asymptotic normal distribution of the considered statistic. Resting upon this fact, the standard score of the mentioned edges quantity is set, and the partition quality is represented by the worst cluster corresponding to the minimal standard score value. It is natural to expect that the true number of clusters can be characterized by the empirical distribution having the shortest left tail. The proposed methodology sequentially creates the described value distribution and estimates its left-asymmetry. Numerical experiments, presented in the paper, demonstrate the ability of the approach to detect the true number of clusters.
2nd Global Conference on Power Control and Optimization

Suggestions

Cluster stability using minimal spanning trees
Barzily, Zeev; Volkovich, Zeev; Akteke-Oeztuerk, Basak; Weber, Gerhard Wilhelm (2008-05-23)
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 ...
An application of the minimal spanning tree approach to the cluster stability problem
Volkovich, Z.; Barzily, Z.; Weber, Gerhard Wilhelm; Toledano-Kitai, D.; Avros, R. (Springer Science and Business Media LLC, 2012-03-01)
Among the areas of data and text mining which are employed today in OR, science, economy and technology, clustering theory serves as a preprocessing step in the data analyzing. An important component of clustering theory is determination of the true number of clusters. This problem has not been satisfactorily solved. In our paper, this problem is addressed by the cluster stability approach. For several possible numbers of clusters, we estimate the stability of the partitions obtained from clustering of samp...
On a Minimal Spanning, Tree Approach in the Cluster Validation Problem
Barzily, Zeev; Volkovich, Zeev; Öztürk, Başak; Weber, Gerhard Wilhelm (2009-01-01)
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. Thus it is associated with the clusters cores. The second one, associated with file 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 obt...
Pattern extraction by using both spatial and temporal features on Turkish meteorological data
Goler, Işıl; Yazıcı, Adnan; Karagöz, Pınar; Department of Computer Engineering (2010)
With the growth in the size of datasets, data mining has been an important research topic and is receiving substantial interest from both academia and industry for many years. Especially, spatio-temporal data mining, mining knowledge from large amounts of spatio-temporal data, is a highly demanding field because huge amounts of spatio-temporal data are collected in various applications. Therefore, spatio-temporal data mining requires the development of novel data mining algorithms and computational techniqu...
Clustering of manifold-modeled data based on tangent space variations
Gökdoğan, Gökhan; Vural, Elif; Department of Electrical and Electronics Engineering (2017)
An important research topic of the recent years has been to understand and analyze data collections for clustering and classification applications. In many data analysis problems, the data sets at hand have an intrinsically low-dimensional structure and admit a manifold model. Most state-of-the-art clustering methods developed for data of non-linear and low-dimensional structure are based on local linearity assumptions. However, clustering algorithms based on locally linear representations can tolerate diff...
Citation Formats
Z. (. Volkovich, Z. Barzily, G. W. Weber, and D. Toledano-Kitai, “CLUSTER STABILITY ESTIMATION BASED ON A MINIMAL SPANNING TREES APPROACH,” Bali, INDONESIA, 2009, vol. 1159, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55487.