Download Advances in K-means Clustering: a Data Mining Thinking by Junjie Wu PDF

By Junjie Wu

Nearly we all know K-means set of rules within the fields of information mining and company intelligence. however the ever-emerging facts with super advanced features carry new demanding situations to this "old" set of rules. This e-book addresses those demanding situations and makes novel contributions in constructing theoretical frameworks for K-means distances and K-means dependent consensus clustering, picking the "dangerous" uniform impression and zero-value challenge of K-means, adapting correct measures for cluster validity, and integrating K-means with SVMs for infrequent type research. This publication not just enriches the clustering and optimization theories, but additionally offers strong tips for the sensible use of K-means, specially for vital projects similar to community intrusion detection and credits fraud prediction. The thesis on which this booklet is predicated has received the "2010 nationwide first-class Doctoral Dissertation Award", the top honor for no more than a hundred PhD theses in line with yr in China.

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6) holds for the case that the cluster number is k − 1, we have ( p) Dk−1 = 1≤l≤k,l = p n − np d(Cl , Cl ) + 2 nl i, j = p [n i n j m i − m j 2 ]. 1≤i< j≤k So the first part of the right hand side of Eq. 9) is k ⎛ ( p) Dk−1 = (k − 2) ⎝ p=1 k l=1 ⎞ n d(Cl , Cl ) + 2 nl ni n j m i − m j 2⎠ 1≤i< j≤k k d(Cl , Cl ). 10) 22 2 The Uniform Effect of K-means Clustering Accordingly, we can further transform Eq. 9) into ⎛ k k Dk = (k − 2) ⎝ l=1 ⎡ ⎞ n d(Cl , Cl ) + 2 nl k +2⎣ 1≤i< j≤k 2 ]⎠ ⎤ d(Ci , C j )⎦ .

Vc )T ∈ Rcd such that Jm can be minimized. In [3], the author gave the necessary conditions for a minimizer (U ∗ , V ∗ ) as follows. 2 ([3]) Let X = {x k }nk=1 contain n > c distinct points and m ∈ (1, +∞). Let dik = x k − vi 2 , 1 ≤ k ≤ n, 1 ≤ i ≤ c. ∀ k, define the sets Ik = {i|dik = 0, 1 ≤ i ≤ c} and I˜k = {1, . . , c} \ Ik . 2 Preliminaries and Problem Definition 41 Fig. 4b) i∈Ik ∗ = x − v∗ 2 , 1 ≤ k ≤ n, 1 ≤ i ≤ c. 2 can be found in pages 67–69 of [3]. Note that the computations of U ∗ and V ∗ in Eqs.

Vc )T ∈ Rcd such that Jm can be minimized. In [3], the author gave the necessary conditions for a minimizer (U ∗ , V ∗ ) as follows. 2 ([3]) Let X = {x k }nk=1 contain n > c distinct points and m ∈ (1, +∞). Let dik = x k − vi 2 , 1 ≤ k ≤ n, 1 ≤ i ≤ c. ∀ k, define the sets Ik = {i|dik = 0, 1 ≤ i ≤ c} and I˜k = {1, . . , c} \ Ik . 2 Preliminaries and Problem Definition 41 Fig. 4b) i∈Ik ∗ = x − v∗ 2 , 1 ≤ k ≤ n, 1 ≤ i ≤ c. 2 can be found in pages 67–69 of [3]. Note that the computations of U ∗ and V ∗ in Eqs.

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