Affinity measures based on the graph Laplacian

Several language processing tasks can be inherently represented by a weighted graph where the weights are interpreted as a measure of relatedness between two vertices. Measuring similarity between arbitary pairs of vertices is essential in solving several language processing problems on these datasets. Random walk based measures perform better than other path based measures like shortest-path. We evaluate several random walk measures and propose a new measure based on commute time. We use the psuedo inverse of the Laplacian to derive estimates for commute times in graphs. Further, we show that this pseudo inverse based measure could be improved by discarding the least significant eigenvectors, corresponding to the noise in the graph construction process, using singular value decomposition.