
Structured LowRank Matrix Factorization: Global Optimality, Algorithms, and Applications
Recently, convex formulations of lowrank matrix factorization problems ...
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kMeans Clustering Is Matrix Factorization
We show that the objective function of conventional kmeans clustering c...
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Expectile Matrix Factorization for Skewed Data Analysis
Matrix factorization is a popular approach to solving matrix estimation ...
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Matrix Factorization with Side and Higher Order Information
The problem of predicting unobserved entries of a partially observed mat...
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Unsupervised Selective Manifold Regularized Matrix Factorization
Manifold regularization methods for matrix factorization rely on the clu...
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Supervised Quantile Normalization for Lowrank Matrix Approximation
Low rank matrix factorization is a fundamental building block in machine...
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Tight convex relaxations for sparse matrix factorization
Based on a new atomic norm, we propose a new convex formulation for spar...
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Matrix factorization with Binary Components
Motivated by an application in computational biology, we consider lowrank matrix factorization with {0,1}constraints on one of the factors and optionally convex constraints on the second one. In addition to the nonconvexity shared with other matrix factorization schemes, our problem is further complicated by a combinatorial constraint set of size 2^m · r, where m is the dimension of the data points and r the rank of the factorization. Despite apparent intractability, we provide  in the line of recent work on nonnegative matrix factorization by Arora et al. (2012)  an algorithm that provably recovers the underlying factorization in the exact case with O(m r 2^r + mnr + r^2 n) operations for n datapoints. To obtain this result, we use theory around the LittlewoodOfford lemma from combinatorics.
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