By Bi-Ru Dai, Shu-Ming Hsu (auth.), Joshua Zhexue Huang, Longbing Cao, Jaideep Srivastava (eds.)

The two-volume set LNAI 6634 and 6635 constitutes the refereed court cases of the fifteenth Pacific-Asia convention on wisdom Discovery and information Mining, PAKDD 2011, held in Shenzhen, China in may perhaps 2011.

The overall of 32 revised complete papers and fifty eight revised brief papers have been conscientiously reviewed and chosen from 331 submissions. The papers current new rules, unique learn effects, and sensible improvement reviews from all KDD-related components together with facts mining, laptop studying, synthetic intelligence and trend popularity, facts warehousing and databases, records, knoweldge engineering, habit sciences, visualization, and rising parts resembling social community analysis.

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Extra resources for Advances in Knowledge Discovery and Data Mining: 15th Pacific-Asia Conference, PAKDD 2011, Shenzhen, China, May 24-27, 2011, Proceedings, Part I

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K}. 2 Because of the AS and symmetric preferences, we have ui (C) = j∈C vij for any coalition C, and hence the cut capacity of this newly formed k-cut after the switching is given by cap(new cut) = cap(C1 , . . , Ck ) + ui (Ct ) − ui (Cz ). Because ui (Cz ) > ui (Ct ), we have cap(new cut) < cap(C1 , C2 , . . , Ck ) which is a contradiction to the assumption that {C1 , C2 , . . e. Cz = ∅) because in that case ui (Cz ) = vii = 0 and 0 > ui (Ct ) which is a contradiction because v is non-negative.

Given a graph G, a k-cut {C1 , C2 , . . , Ck } is said to be an -Regret k-cut iff cap∗ (k) ≤ cap(C1 , C2 , . . , Ck ) ≤ cap∗ (k) + , where cap∗ (k) is the capacity of the minimum k-cut. Theorem 3. 2 -Regret k-cut having s > 1 ⇒ -Regret k-NSP Hierarchical Feature Clustering From Theorem 3, it is apparent that any scheme that efficiently computes an Regret k-cut of a graph would be an efficient scheme for computing the -Regret k-NSP also. Therefore, we propose a simple hierarchical scheme (without any theoretical bounds on the value of ) for computing an -Regret k-cut and hence an -Regret k-NSP.

A Game Theoretic Approach for Feature Clustering and Its Application 21 In the above proof, s > 1 is required to ensure that even after node i switches, the resulting partition is a k-way cut. Theorem 2 gives a sufficiency condition for the existence of a k-NSP and hence becomes useful in the case when computing a minimum k-cut of a graph is an easy problem. However, it is a well known fact that computing a minimum k-cut of a graph is NP-hard for k > 2 [20]. Therefore, this theorem would not help much for computing a k-NSP of a given game if k > 2.

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