A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances

This work introduces a new family of link-based dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortest-path (RSP) dissimilarity, depends on a parameter and has the interesting property of reducing, on one end, to the standard shortest-path distance when is large and, on the other end, to the commute-time (or resistance) distance when is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy (related to ) spread in the graph. The parameter is therefore biasing gradually the simple random walk on the graph towards the shortest-path policy. By adopting a statistical physics approach and computing a sum over all the possible paths (discrete path integral), it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear syst...

• Type: Conference
• Year: 2008
• Where: KDD
• Authors: Luh Yen, Marco Saerens, Amin Mantrach, Masashi Shimbo
• Keywords: Data Mining, Destination Node, Graph Mining Tasks, KDD 2008, Weighted Directed Graph