independently without explicitly considering their intrinsic relatedness. In this paper, we propose Max Margin Multi-Attribute Learning with Low-rank Constraint, which learns a set of attributes simultaneously, using only relative ranking of the attributes for the data. By learning all the attributes

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately

measurement. Given a number of labeled data followed by a sequential input of unseen testing samples, the similarity metric is learned to maximize the margin of the distance among different classes of samples. By considering the low rank constraint, our online metric learning model not only can provide

Abstract Low-rank matrix factorizations arise in a wide variety of applications -including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing

© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:

separated representation from the discriminative learning stage, we achieve both by the same method. Our framework, ”Low-Rank separators”, studies the use of a separating hyperplane which are constrained to have the structure of low-rank matrices. We first prove that the low-rank constraint provides

of the observed entries are corrupted by non-Gaussian noise, typically outliers. The method relies on the idea of smoothing the `1 norm and using Riemannian optimization to deal with the low-rank constraint. We first state the algorithms as the successive minimization of smooth approximations of the `1 norm

is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. Key words. low-rank constraints, cone of symmetric positive definite matrices, Riemannian quotient manifold, sparse principal component analysis, maximum-cut algorithms, large-scale algorithms

remarkable features making this attractive for low-rank matrix completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal

basically build a solution by solving a sequence of small scale subproblems. Our current effort is concentrated on the rank of the kernel matrix as a source for further enhancement of the training procedure. We first show that for a low rank kernel matrix it is possible to design a better interior point