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 facts with tremendous complex features convey new demanding situations to this "old" set of rules. This publication addresses those demanding situations and makes novel contributions in constructing theoretical frameworks for K-means distances and K-means established consensus clustering, deciding upon the "dangerous" uniform impression and zero-value problem of K-means, adapting correct measures for cluster validity, and integrating K-means with SVMs for infrequent classification research. This e-book not just enriches the clustering and optimization theories, but in addition presents solid suggestions for the sensible use of K-means, in particular for very important projects akin to community intrusion detection and credits fraud prediction. The thesis on which this e-book is predicated has received the "2010 nationwide first-class Doctoral Dissertation Award", the top honor for no more than a hundred PhD theses according to 12 months in China.

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**Sample text**

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.

As can be seen, every data set has a significant number of true clusters disappeared. 4 Entropy Percentage of Classes Disappeared (%) Fig. 7 The percentage of the disappeared true clusters in highly imbalanced data. © 2009 IEEE. Reprinted, with permission, from Ref. 4 Entropy Percentage of Classes Disappeared (%) Fig. 8 The percentage of the disappeared true clusters in relatively balanced data. © 2009 IEEE. Reprinted, with permission, from Ref. 1 0 la2 hitech ohscal pendigits letter 0 Data Sets disappear after K-means clustering!

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.