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ECML
2004
Springer

The Principal Components Analysis of a Graph, and Its Relationships to Spectral Clustering

11 years 10 months ago
The Principal Components Analysis of a Graph, and Its Relationships to Spectral Clustering
This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the nodes of the graph that preserves as much variance as possible, in terms of the ECTD – a principal components analysis of the graph. It is based on a Markov-chain model of random walk through the graph. The model assigns transition probabilities to the links between nodes, so that a random walker can jump from node to node. A quantity, called the average commute time, computes the average time taken by a random walker for reaching node j for the first time when starting from node i, and coming back to node i. The square root of this quantity, the ECTD, is a distance measure between any two nodes, and has the nice property of decreasing when the number of paths connecting two nodes increases and when the “length” of any path decreases. The ECTD can be computed from the pseudoinverse...
Marco Saerens, François Fouss, Luh Yen, Pie
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where ECML
Authors Marco Saerens, François Fouss, Luh Yen, Pierre Dupont
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