Analysis and Improvement of Low Rank Representation for Subspace segmentation

07/08/2011
by   Wei Siming, et al.
0

We analyze and improve low rank representation (LRR), the state-of-the-art algorithm for subspace segmentation of data. We prove that for the noiseless case, the optimization model of LRR has a unique solution, which is the shape interaction matrix (SIM) of the data matrix. So in essence LRR is equivalent to factorization methods. We also prove that the minimum value of the optimization model of LRR is equal to the rank of the data matrix. For the noisy case, we show that LRR can be approximated as a factorization method that combines noise removal by column sparse robust PCA. We further propose an improved version of LRR, called Robust Shape Interaction (RSI), which uses the corrected data as the dictionary instead of the noisy data. RSI is more robust than LRR when the corruption in data is heavy. Experiments on both synthetic and real data testify to the improved robustness of RSI.

READ FULL TEXT
research
09/05/2017

Subspace Segmentation by Successive Approximations: A Method for Low-Rank and High-Rank Data with Missing Entries

We propose a method to reconstruct and cluster incomplete high-dimension...
research
09/22/2011

Sparse Online Low-Rank Projection and Outlier Rejection (SOLO) for 3-D Rigid-Body Motion Registration

Motivated by an emerging theory of robust low-rank matrix representation...
research
10/28/2014

Non-convex Robust PCA

We propose a new method for robust PCA -- the task of recovering a low-r...
research
01/27/2018

Robust Multi-subspace Analysis Using Novel Column L0-norm Constrained Matrix Factorization

We study the underlying structure of data (approximately) generated from...
research
01/05/2016

Low-Rank Representation over the Manifold of Curves

In machine learning it is common to interpret each data point as a vecto...
research
12/17/2018

Robust Graph Learning from Noisy Data

Learning graphs from data automatically has shown encouraging performanc...
research
02/21/2019

A Dictionary Based Generalization of Robust PCA

We analyze the decomposition of a data matrix, assumed to be a superposi...

Please sign up or login with your details

Forgot password? Click here to reset