Multiscale Spectral Clustering Using Random Walk Based Similarity Measure

This paper presents a new concept on characterizing the similarity between nodes of a weighted undirected graph with application to multiscale spectral clustering. The contribution may be divided into three parts. First, the generalized mean first-passage time (GMFPT) and the generalized mean recurrence time (GMRT) are proposed based on the multi-step transition probability of the random walk on graph. The GMFPT can capture similarities at different scales in data sets as the number of step of transition probability varies. Second, an efficient computational technique is proposed to present the GMFPT in term of the element of the generalized fundamental matrix. Third, a multiscale algorithm is derived based on the weight matrix-based spectral clustering. Finally, Experimental results demonstrate the effectiveness of the proposed method.