Thursday, May 21, 2015

Low-rank Modeling and its Applications in Image Analysis

Xiaowei Zhou sent me the following the other day:

Dear Dr Carron,

We had the following survey paper published several months ago:

X. Zhou, C. Yang, H. Zhao, W. Yu. Low-Rank Modeling and its Applications in Image Analysis. ACM Computing Surveys, 47(2): 36, 2014. (

Could you kindly post it on your matrix factorization jungle website? I hope it will be helpful to some new comers.



Thanks Xiaowei ! Here is the review that I will shortly add to the Advanced Matrix Factorization Jungle page. 

Low-rank Modeling and its Applications in Image Analysis by Xiaowei Zhou, Can Yang, Hongyu Zhao, Weichuan Yu . ACM Computing Surveys, 47(2): 36, 2014.
Low-rank modeling generally refers to a class of methods that solves problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing, and bioinformatics. Recently, much progress has been made in theories, algorithms, and applications of low-rank modeling, such as exact low-rank matrix recovery via convex programming and matrix completion applied to collaborative filtering. These advances have brought more and more attention to this topic. In this article, we review the recent advances of low-rank modeling, the state-of-the-art algorithms, and the related applications in image analysis. We first give an overview of the concept of low-rank modeling and the challenging problems in this area. Then, we summarize the models and algorithms for low-rank matrix recovery and illustrate their advantages and limitations with numerical experiments. Next, we introduce a few applications of low-rank modeling in the context of image analysis. Finally, we conclude this article with some discussions.

From the paper:

In this paper, we have introduced the concept of low-rank modeling and reviewed some representative low-rank models, algorithms and applications in image analysis. For additional reading on theories, algorithms and applications, the readers are referred to online documents such as the Matrix Factorization Jungle3 and the Sparse and Low-rank Approximation Wiki4, which are updated on a regular basis. 
Yes !
I also note that in the Robust PCA comparison, GoDec does consistently better than the other solvers. GoDec also happens being the reason Cable and I used it in "It's CAI, Cable And Igor's Adventures in Matrix Factorization ". Here is an example: CAI: A Glimpse of Lana and Robust PCA

More can be found here.
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