By Mohammed J. Zaki, Jeffrey Xu Yu, B. Ravindran, Vikram Pudi
This publication constitutes the lawsuits of the 14th Pacific-Asia convention, PAKDD 2010, held in Hyderabad, India, in June 2010.
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Additional resources for Advances in Knowledge Discovery and Data Mining, Part II: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010, Proceedings
Theorem 1. f , the diﬀerence δ of the l1 norms of the T projections xf ,y f of two points x, y ∈ Rn is upper bounded by where x − y is the points’ euclidean distace. f i=1 |ri | w x−y Proof: Since |a| − |b| ≤ |a − b| ≤ |a + b| ≤ |a| + |b| we derive l1 (xf ) ≤ f f f f 1 1 1 T T i=1 (|ri x |+|bi |) ≤ w ( i=1 |ri |)|x| + w i=1 |bi |. We assume A=( i=1 |ri |) w 1 f f and employ the inequality in order to derive δ = |l1 (x ) − l1 (y )| ≤ | w A(|x|T − |y|T )| ≤ | w1 A||(|x|T − |y|T )| ≤ | w1 A||(xT − y T )| = | w1 A||x − y|T = w1 A|x − y|T since w and |ri | are positive.
The experimental results show that DPSP can ﬁnd progressive sequential patterns eﬃciently and DPSP possesses great scalability. The distributed scheme not only improves the eﬃciency but also consequently increases the practicability. The rest of this work is organized as follows. We will derive some preliminaries in Section 2. The proposed algorithm DPSP will be introduced in Section 3. Some experiments to evaluate the performance will be shown in Section 4. Finally, the conclusion is given in Section 5.
Network cost reported as a fraction of the worst case bound RequiredM essages W orstCaseBound D-Isomap deployed with LMDS. We used MATLAB R2008a for the implementation of the algorithms and E2LSH  for LSH. Due to space limitations, we report only a subset of the experiments1 . 3. First we validated the bound of Theorem 1 with the Swiss Roll. The results (Figures 2(a), 2(b)) indicate a reduction in the number of messages; consequently we employed the bounded version of the algorithm for all experiments.
Advances in Knowledge Discovery and Data Mining, Part II: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010, Proceedings by Mohammed J. Zaki, Jeffrey Xu Yu, B. Ravindran, Vikram Pudi