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1,351
Joint Schatten p-norm and p-norm robust matrix completion for . . .
- KNOWL INF SYST
, 2013
"... The low-rank matrix completion problem is a fundamental machine learning and data mining problem with many important applications. The standard low-rank matrix com-pletion methods relax the rank minimization problem by the trace norm minimization. How-ever, this relaxation may make the solution ser ..."
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seriously deviate from the original solution. Meanwhile, most completion methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix comple-tion method to address these two problems. The joint Schatten p-norm and p-norm
Optimal Mean Robust Principal Component Analysis
"... Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduc-tion approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the `2-norm ..."
Abstract
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Cited by 2 (0 self)
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Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduc-tion approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the `2-norm
Robust Matrix Completion via Joint Schatten
"... Abstract—The low-rank matrix completion problem is a fundamental machine learning problem with many important applications. The standard low-rank matrix completion meth-ods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously de ..."
Abstract
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Cited by 3 (1 self)
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deviate from the original solution. Meanwhile, most completion methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix completion method to address these two problems. The joint Schatten
On conformal field theories
- in fourdimensions,” Nucl. Phys. B533
, 1998
"... We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last ..."
Abstract
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Cited by 366 (1 self)
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We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. Submitted to Reviews of Modern Physics.
Minimal Shrinkage for Noisy Data Recovery Using Schatten-p Norm Objective
"... Abstract. Noisy data recovery is an important problem in machine learning field, which has widely applications for collaborative prediction, recommendation systems, etc. One popular model is to use trace norm model for noisy data recovery. However, it is ignored that the reconstructed data could be ..."
Abstract
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Cited by 1 (1 self)
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be shrank (i.e., singular values could be greatly suppressed). In this paper, we present novel noisy data recovery models, which replaces the standard rank constraint (i.e., trace norm) using Schatten-p Norm. The proposed model is attractive due to its suppression on the shrinkage of singular values
Schatten-p Quasi-Norm Regularized Matrix Optimization via Iterative Reweighted Singular Value Minimization∗
, 2015
"... In this paper we study general Schatten-p quasi-norm (SPQN) regularized matrix minimiza-tion problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized vec-tor minimization ..."
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In this paper we study general Schatten-p quasi-norm (SPQN) regularized matrix minimiza-tion problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized vec-tor minimization
Hessian Schatten-Norm Regularization for Linear Inverse Problems
"... Abstract — We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which are computed at every pixel of the ..."
Abstract
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Cited by 11 (8 self)
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well for a wide range of applications. To solve the corresponding optimization problems, we propose an algorithm that is based on a primaldual formulation. A fundamental ingredient of this algorithm is the projection of matrices onto Schatten norm balls of arbitrary radius. This operation is performed
PAPAMAKARIOS, PANAGAKIS, ZAFEIRIOU: GENERALISED SCALABLE ROBUST PCA 1 Generalised Scalable Robust Principal Component Analysis
"... The robust estimation of the low-dimensional subspace that spans the data from a set of high-dimensional, possibly corrupted by gross errors and outliers observations is fun-damental in many computer vision problems. The state-of-the-art robust principal com-ponent analysis (PCA) methods adopt conve ..."
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-lating the robust PCA problem using the Schatten p-norm and the `q-norm subject to orthonormality constraints, resulting in a better non-convex approximation of the origi-nal sparsity regularised rank minimisation problem. It is worth noting that the common robust PCA variants are special cases of the GSRPCA when p
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