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We present a new view of image segmentation by pairwise similarities. We interpret the similarities as edge ows in a Markov random walk and study the eigenvalues and eigenvectors of the walk's transition matrix. This interpretation shows that spectral methods for clustering and segmentation have a probabilistic foundation. In particular, we prove that the(More)
One of the challenges of density estimation as it is used in machine learning is that usually the data are multivariate and often the dimensionality is large. Operating with joint distributions over multidimensional domains raises specific problems that are not encountered in the univariate case. Graphical models are representations of joint densities that(More)
This paper views clusterings as elements of a lattice. Distances between clusterings are analyzed in their relationship to the lattice. From this vantage point, we first give an axiomatic characterization of some criteria for comparing clusterings, including the variation of information and the unadjusted Rand index. Then we study other distances between(More)
We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty arises from the global constraint that the graph structure has(More)