ACM Computing Surveys (CSUR)
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
On clusterings-good, bad and spectral
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Maximum margin clustering made practical
IEEE Transactions on Neural Networks
Hierarchical verb clustering using graph factorization
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
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We consider the problem of clustering in its most basic form where only a local metric on the data space is given. No parametric statistical model is assumed, and the number of clusters is learned from the data. We introduce, analyze and demonstrate a novel approach to clustering where data points are viewed as nodes of a graph, and pairwise similarities are used to derive a transition probability matrix P for a Markov random walk between them. The algorithm automatically reveals structure at increasing scales by varying the number of steps taken by this random walk. Points are represented as rows of Pt, which are the t-step distributions of the walk starting at that point; these distributions are then clustered using a KL-minimizing iterative algorithm. Both the number of clusters, and the number of steps that 'best reveal' it, are found by optimizing spectral properties of P.