Low Rank

ROUTE: Robust Outlier Estimation for Low Rank Matrix Recovery

This paper designs a method for recovering the low rank matrix with robust outlier estimation, termed as ROUTE, in a unified manner.

Provable Accelerated Gradient Method for Nonconvex Low Rank Optimization

Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the nonconvex …

A New Retraction for Accelerating the Riemannian Three-Factor Low-Rank Matrix Completion Algorithm

We proposed a new retraction for the quotient manifold used in R3MC, which is a geometric optimization algorithm for the matrix completion problem.

Generalized Singular Value Thresholding

This paper studied the Generalized Singular Value Thresholding (GSVT) operator associated with the nonconvex function g on the singular values.

Low Rank Global Geometric Consistency for Partial-Duplicate Image Search

We have proposed a new global geometric verification method called LRGGC for partial-duplicate image search.

Proximal Iteratively Reweighted Algorithm with Multiple Splitting for Nonconvex Sparsity Optimization

This paper proposes the PIRE algorithm for solving the general optimization problem.

Generalized Nonconvex Nonsmooth Low-Rank Minimization

In this work, the nonconvex surrogate functions of L_0-norm are extended on the singular values to approximate the rank function. It is observed that all the existing nonconvex surrogate functions are concave and monotonically increasing on [0, \infty). Then a general solver IRNN is proposed.

Tensor LRR Based Subspace Clustering

We proposed a tensor based low-rank representation for subspace clustering.

A Counterexample for The Validaity of Using Nuclear Norm as A Comvex Surrogate of Rank

We conclude that even for rank minimization problems as simple as noiseless LatLRR, replacing rank with nuclear norm is not valid and LatLRR is actually problematic because the solution to its nuclear norm minimization formation is not unique in this paper

Rectification of Optical Characters as Transform Invariant Low-rank Textures

We have presented an effective method for rectifying Chinese and English characters or words as robust low-rank textures.