caa a22 4500 44587130X CHVBK 20180317145512.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s10618-011-0212-3 doi (NATIONALLICENCE)springer-10.1007/s10618-011-0212-3 Measuring the component overlapping in the Gaussian mixture model [Elektronische Daten] [Haojun Sun, Shengrui Wang] The ability of a clustering algorithm to deal with overlapping clusters is a major indicator of its efficiency. However, the phenomenon of cluster overlapping is still not mathematically well characterized, especially in multivariate cases. In this paper, we are interested in the overlap phenomenon between Gaussian clusters, since the Gaussian mixture is a fundamental data distribution model suitable for many clustering algorithms. We introduce the novel concept of the ridge curve and establish a theory on the degree of overlap between two components. Based on this theory, we develop an algorithm for calculating the overlap rate. As an example, we use this algorithm to calculate the overlap rates between the classes in the IRIS data set and clear up some of the confusion as to the true number of classes in the data set. We investigate factors that affect the value of the overlap rate, and show how the theory can be used to generate "truthed data” as well as to measure the overlap rate between a given pair of clusters or components in a mixture. Finally, we show an example of application of the theory to evaluate the well known clustering algorithms. The Author(s), 2011 Mixture model nationallicence Ridge curve nationallicence Overlap rate nationallicence Cluster analysis nationallicence Sun Haojun College of Engineering, Shantou University, 515063, Shantou, Guangdong, China aut Wang Shengrui Départment d'informatique, Université de Sherbrooke, J1K 2R1, Sherbrooke, QC, Canada aut Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 23/3(2011-11-01), 479-502 1384-5810 23:3<479 2011 23 10618 https://doi.org/10.1007/s10618-011-0212-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10618-011-0212-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sun Haojun College of Engineering, Shantou University, 515063, Shantou, Guangdong, China aut NATIONALLICENCE 700 1- Wang Shengrui Départment d'informatique, Université de Sherbrooke, J1K 2R1, Sherbrooke, QC, Canada aut NATIONALLICENCE 773 0- Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 23/3(2011-11-01), 479-502 1384-5810 23:3<479 2011 23 10618 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer