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Yair Weiss School of CS & Engr. The Hebrew Univ. Despite many empirical successes of spectral clustering methods-algorithms that cluster points using eigenvectors of matrices derived from the data-there are several unresolved issues. First, there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these… (More)

Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only… (More)

Interactive digital matting, the process of extracting a foreground object from an image based on limited user input, is an important task in image and video editing. From a computer vision perspective, this task is extremely challenging because it is massively ill-posed - at each pixel we must estimate the foreground and the background colors, as well as… (More)

Semantic hashing[1] seeks compact binary codes of data-points so that the Hamming distance between codewords correlates with semantic similarity. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we… (More)

Colorization is a computer-assisted process of adding color to a monochrome image or movie. The process typically involves segmenting images into regions and tracking these regions across image sequences. Neither of these tasks can be performed reliably in practice; consequently, colorization requires considerable user intervention and remains a tedious,… (More)

" Inference " problems arise in statistical physics, computer vision, error-correcting coding theory , and AI. We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing local messages. We develop a unified approach with examples, notation, and graphical models borrowed from… (More)

Belief propagation (BP) was only supposed to work for tree-like networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs. We show that BP can only converge to a stationary point of an… (More)

Learning good image priors is of utmost importance for the study of vision, computer vision and image processing applications. Learning priors and optimizing over whole images can lead to tremendous computational challenges. In contrast, when we work with small image patches, it is possible to learn priors and perform patch restoration very efficiently.… (More)

Algorithms such as Latent Dirichlet Allocation (LDA) have achieved significant progress in modeling word document relationships. These algorithms assume each word in the document was generated by a hidden topic and explicitly model the word distribution of each topic as well as the prior distribution over topics in the document. Given these parameters , the… (More)

Recently, researchers have demonstrated that "loopy belief propagation"-the use of Pearl's polytree algorithm in a Bayesian network with loops-can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performance of "Turbo Codes"-codes whose decoding algorithm is equivalent to loopy belief… (More)