By Mohammed J. Zaki, Jeffrey Xu Yu, B. Ravindran, Vikram Pudi
This ebook constitutes the complaints of the 14th Pacific-Asia convention, PAKDD 2010, held in Hyderabad, India, in June 2010.
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Extra info for Advances in Knowledge Discovery and Data Mining, Part II: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010, Proceedings
Example text
Valsamou Incremental Isomap [20] (I-Isomap) which guarantees the construction of a fully connected graph and is able to update the embedding when data is inserted or deleted. DDR algorithms assume data distributed across a set of nodes and the existence of some kind of network organization scheme. The simplest case, where organization exists by construction, are structured P2P networks. In such networks, a protocol (usually based on distributed hast tables - DHT) ensures that any peer can efficiently route a search to a peer that has a specific file.
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. Throughout the analysis we assume that N points, residing in Rd , are distributed in a P2P network of M M peers. Each peer stores Ni points ( i=1 Ni = N ). The objective is to recover the manifold residing in Rn using a graph defined by the k NNs of each point. 1 Data Indexing and Nearest Neighbours Retrieval The first step of Isomap necessitates the definition of a kNN graph for each point.
In order to guarantee the Distributed Knowledge Discovery with Non Linear Dimensionality Reduction 19 Algorithm 2. Definition of geodesic distances Input: peer id (id), local dataset (D), distances from NNs (DIST ), time (t) Output: SP distances of local points to the rest of the dataset (DIST ) for i = 1 to Ni do Send (DIST [i], i, id) to peers hosting NNs of pi end for while Time to receive a message < t do Receive message (DIST [n], p, peerj ) - distances of pp ’s NN n residing in peerj if d(p, j) > d(p, n) + d(n, j) for any j ∈ DIST [n] then DIST [p][j] = d(p, n) + d(n, j) end if if update took place then Send (DIST [p], p, id) to peers hosting NNs of pp end if end while Substitute ∞ with 5 ∗ max(DIST ) creation of a connected SP graph we substitute in the end all remaining ∞ values with five times the largest local geodesic distance.