BHDG is a new multi-label feature selection approach that employs binary hashing for pseudo-labels and dynamic graphs, showing superior performance on benchmarks.
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.html
verdicts
UNVERDICTED 4representative citing papers
LRMC is a deep-unfolded non-convex algorithm for large-scale robust matrix completion that learns its parameters for linear convergence and better empirical results than prior methods.
Presents iterative algorithms, efficient implementation strategies for structured H, and a preconditioning technique with theoretical guarantees for solving the convex optimization formulation of the generalized matrix separation problem.
An iteratively re-weighted method (IRW) is introduced for optimization problems with sparsity-inducing norms, supported by a convergence guarantee and shown to outperform alternatives on robust feature selection.
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