By Junjie Wu

Nearly we all know K-means set of rules within the fields of information mining and enterprise intelligence. however the ever-emerging info with tremendous advanced features deliver new demanding situations to this "old" set of rules. This booklet addresses those demanding situations and makes novel contributions in setting up theoretical frameworks for K-means distances and K-means established consensus clustering, picking out the "dangerous" uniform impression and zero-value hassle of K-means, adapting correct measures for cluster validity, and integrating K-means with SVMs for infrequent classification research. This ebook not just enriches the clustering and optimization theories, but additionally offers reliable counsel for the sensible use of K-means, specially for vital initiatives equivalent to community intrusion detection and credits fraud prediction. The thesis on which this booklet is predicated has received the "2010 nationwide very good Doctoral Dissertation Award", the top honor for no more than a hundred PhD theses consistent with yr in China.

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Probability and Statistics, 3rd edn. Addison Wesley, Upper Saddle River (2001) 6. : Applied numerical linear algebra. Soc. Ind. App. Math. 32, 206–216 (1997) 7. : A new shared nearest neighbor clustering algorithm and its applications. In: Proceedings of the Workshop on Clustering High Dimensional Data and its Applications at the 2nd SIAM International Conference on Data Mining (2002) References 35 8. : A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the 2th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp.

The right hand side of Eq. 6) is also equal to d(C1 , C1 ), as there is no cross-cluster item. 1 holds. When k = 2, by Eq. 2), to prove Eq. 6) is equivalent to prove the following equation: 2d(C1 , C2 ) = n2 n1 d(C1 , C1 ) + d(C2 , C2 ) + 2n 1 n 2 m 1 − m 2 n1 n2 If we substitute m 1 = n1 i=1 xi n1 , m2 = n2 i=1 yi n2 , and 2 . 2 The Uniform Effect of K-means Clustering 21 n1 d(C1 , C1 ) = 2 xi − x j 2 = 2(n 1 − 1) 1≤i< j≤n 1 xi 2 −4 i=1 n2 d(C2 , C2 ) = 2 yi − y j 2 = 2(n 2 − 1) 1≤i< j≤n 2 yi 2 −4 i=1 xi − y j 2 = 2n 2 1≤i≤n 1 1≤ j≤n 2 2 xi i=1 −4 yi y j , 1≤i< j≤n 2 n2 n1 d(C1 , C2 ) = xi x j , 1≤i< j≤n 1 + 2n 1 2 yi i=1 xi y j 1≤i≤n 1 1≤ j≤n 2 into Eq.

6) is equivalent to prove the following equation: 2d(C1 , C2 ) = n2 n1 d(C1 , C1 ) + d(C2 , C2 ) + 2n 1 n 2 m 1 − m 2 n1 n2 If we substitute m 1 = n1 i=1 xi n1 , m2 = n2 i=1 yi n2 , and 2 . 2 The Uniform Effect of K-means Clustering 21 n1 d(C1 , C1 ) = 2 xi − x j 2 = 2(n 1 − 1) 1≤i< j≤n 1 xi 2 −4 i=1 n2 d(C2 , C2 ) = 2 yi − y j 2 = 2(n 2 − 1) 1≤i< j≤n 2 yi 2 −4 i=1 xi − y j 2 = 2n 2 1≤i≤n 1 1≤ j≤n 2 2 xi i=1 −4 yi y j , 1≤i< j≤n 2 n2 n1 d(C1 , C2 ) = xi x j , 1≤i< j≤n 1 + 2n 1 2 yi i=1 xi y j 1≤i≤n 1 1≤ j≤n 2 into Eq.

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