By Mohammed J. Zaki, Jeffrey Xu Yu, B. Ravindran, Vikram Pudi
This e-book constitutes the complaints of the 14th Pacific-Asia convention, PAKDD 2010, held in Hyderabad, India, in June 2010.
Read or Download Advances in Knowledge Discovery and Data Mining, Part II: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010, Proceedings PDF
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Extra resources for Advances in Knowledge Discovery and Data Mining, Part II: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010, Proceedings
Consequently, there is an apparent need for decentralized NLDR techniques. To the best of our knowledge, D-Isomap is the ﬁrst attempt towards this direction. 3 Distributed Non Linear Dimensionality Reduction D-Isomap capitalizes on the basic steps of Isomap and applies them in a network context, managing to successfully retrieve the underlying manifold while exhibiting tolerable network cost and computational complexity. In the rest of this section we present in details each step of the algorithm and review the cost induced by its application in a structured P2P network.
At ﬁrst, Each peer, hashes its local points and transmits the derived l1 values to the corresponding peers. This procedure yields a network cost of O(Ni L) messages per peer or a total of O(N L) messages. The process of recovering the kNNs of a point requires ck messages thus is upper bounded by O(ckN ). Time requirements on peer level 18 P. Magdalinos, M. Vazirgiannis, and D. Valsamou Algorithm 1. Data indexing and kNN retrieval Input: Local dataset in Rd (D), peers (M ), hash tables L, hash functions g, NNs (k), peer identiﬁer (id), parameter c (c) Output: The local neighbourhood graph of peer id (X) for i = 1 to Nid , j = 1 to L do hashj (pi ) = gj (pi ) - where pi is the i-th point of D l1 (hashj (pi ))−μl1 +2σl1 peerind = ( ∗ M )modM 4∗σl 1 Send message (l1 (hashj (pi )), id) to peerind and store (peerind , pi , j) end for if peer is creating its local NN graph then for i = 1 to Nid , j = 1 to L do Send message (id, hashj (pi ), boundpi ) to (peerind , pi , j) Wait for response message (host, pind , l1 (pind )) If total number of received points is over ck, request points from host nodes, sort them according to their true distance from pi and retain the k NNs of pi end for else Retrieve message (id, hashj (pi ), boundpi ) from peerid Scan local index and retrieve relevant points according to Theorem 1 Forward retrieved points’ pointers to querying node end if are O(Ni Lf + Ni klogk) induced by the hashing and ranking procedure.
On the other hand, the predecessor, is the next peer in the Distributed Knowledge Discovery with Non Linear Dimensionality Reduction 17 identiﬁer circle when moving counter-clockwise. A message in Chord may require to traverse O(logM ) hops before reaching its destination. In order to enable rapid lookup of points similar to each peer’s local data we consider locality sensitive hashing  (LSH) that hashes similar points to the same bucket with high probability. L. f , randomly chosen from the same family of LSH functions H.
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