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Local Collaborative Ranking
"... Personalized recommendation systems are used in a wide variety of applications such as electronic commerce, social networks, web search, and more. Collaborative filtering approaches to recommendation systems typically assume that the rating matrix (e.g., movie ratings by viewers) is lowrank. In th ..."
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Personalized recommendation systems are used in a wide variety of applications such as electronic commerce, social networks, web search, and more. Collaborative filtering approaches to recommendation systems typically assume that the rating matrix (e.g., movie ratings by viewers) is lowrank. In this paper, we examine an alternative approach in which the rating matrix is locally lowrank. Concretely, we assume that the rating matrix is lowrank within certain neighborhoods of the metric space defined by (user, item) pairs. We combine a recent approach for local lowrank approximation based on the Frobenius norm with a general empirical risk minimization for ranking losses. Our experiments indicate that the combination of a mixture of local lowrank matrices each of which was trained to minimize a ranking loss outperforms many of the currently used stateoftheart recommendation systems. Moreover, our method is easy to parallelize, making it a viable approach for large scale realworld rankbased recommendation systems. Categories and Subject Descriptors [Information retrieval]: Retrieval tasks and goals—Recommender systems; [Information systems applications]: Data mining—Collaborative filtering; [Machine Learning]: Supervised learning—Ranking
Colorization by PatchBased Local LowRank Matrix Completion
"... Colorization aims at recovering the original color of a monochrome image from only a few color pixels. A stateoftheart approach is based on matrix completion, which assumes that the target color image is lowrank. However, this lowrank assumption is often invalid on natural images. In this pape ..."
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Colorization aims at recovering the original color of a monochrome image from only a few color pixels. A stateoftheart approach is based on matrix completion, which assumes that the target color image is lowrank. However, this lowrank assumption is often invalid on natural images. In this paper, we propose a patchbased approach that divides the image into patches and then imposes a lowrank structure only on groups of similar patches. Each local matrix completion problem is solved by an accelerated version of alternating direction method of multipliers (ADMM), and each ADMM subproblem is solved efficiently by divideandconquer. Experiments on a number of benchmark images demonstrate that the proposed method outperforms existing approaches.
ACCAMS: Additive CoClustering to Approximate Matrices Succinctly
"... Matrix completion and approximation are popular tools to capture a user’s preferences for recommendation and to approximate missing data. Instead of using lowrank factorization we take a drastically different approach, based on the simple insight that an additive model of coclusterings allows o ..."
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Matrix completion and approximation are popular tools to capture a user’s preferences for recommendation and to approximate missing data. Instead of using lowrank factorization we take a drastically different approach, based on the simple insight that an additive model of coclusterings allows one to approximate matrices efficiently. This allows us to build a concise model that, per bit of model learned, significantly beats all factorization approaches in matrix completion. Even more surprisingly, we find that summing over small coclusterings is more effective in modeling matrices than classic coclustering, which uses just one large partitioning of the matrix. Following Occam’s razor principle, the fact that our model is more concise and yet just as accurate as more complex models suggests that it better captures the latent preferences and decision making processes present in the real world. We provide an iterative minimization algorithm, a collapsed Gibbs sampler, theoretical guarantees for matrix approximation, and excellent empirical evidence for the efficacy of our approach. We achieve stateoftheart results for matrix completion on Netflix at a fraction of the model complexity.