DocumentCode :
1819394
Title :
Necessary conditions for the confidence level of the randomized algorithm of finding the true number of clusters
Author :
Granichin, Oleg ; Morozkov, Mikhail ; Volkovich, Zeev
Author_Institution :
Dept. of Math. & Mech., Sankt-Petersburg State Univ., St. Petersburg, Russia
fYear :
2011
fDate :
28-30 Sept. 2011
Firstpage :
1002
Lastpage :
1007
Abstract :
One of the most difficult problems in cluster analysis is the identification of the number of groups in a given data set. In this paper we offer the approach in the framework of the common “elbow” methodology such that the true number of clusters is recognized as the slope discontinuity of the index function. A randomized algorithm has been suggested to allocate this position. The scenario approach is used to significantly reduce the computational complexity. We present weaker necessary conditions to provide a priori chosen level of confidence. In addition, we present a number of simulation examples of unknown huge number of groups clustering to demonstrate theoretical results. Finally, we note that necessary conditions can be relaxed more and ideas considered potentially can be extended to a wide range of real-time decision-making problems in control systems.
Keywords :
computational complexity; decision making; randomised algorithms; real-time systems; statistical analysis; cluster analysis; computational complexity; confidence level; control systems; data set; elbow methodology; index function; randomized algorithm; real-time decision-making problems; Chebyshev approximation; Clustering algorithms; Control systems; Decision making; Indexes; Stability criteria;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Intelligent Control (ISIC), 2011 IEEE International Symposium on
Conference_Location :
Denver, CO
ISSN :
2158-9860
Print_ISBN :
978-1-4577-1104-6
Electronic_ISBN :
2158-9860
Type :
conf
DOI :
10.1109/ISIC.2011.6045413
Filename :
6045413
Link To Document :
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