Fixed-Rank Representation for Unsupervised Visual Learning

Abstract

Subspace clustering and feature extraction are two of the most commonly used unsupervised learning techniques in computer vision and pattern recognition. State-of-the-art techniques for subspace clustering make use of recent advances in sparsity and rank minimization. However, existing techniques are computationally expensive and may result in degenerate solutions that degrade clustering performance in the case of insufficient data sampling. To partially solve these problems, and inspired by existing work on matrix factorization, this paper proposes fixed-rank representation (FRR) as a unified framework for unsupervised visual learning. FRR is able to reveal the structure of multiple subspaces in closed-form when the data is noiseless. Furthermore, we prove that under some suitable conditions, even with insufficient observations, FRR can still reveal the true subspace memberships. To achieve robustness to outliers and noise, a sparse regularizer is introduced into the FRR framework. Beyond subspace clustering, FRR can be used for unsupervised feature extraction. As a non-trivial byproduct, a fast numerical solver is developed for FRR. Experimental results on both synthetic data and real applications validate our theoretical analysis and demonstrate the benefits of FRR for unsupervised visual learning.

accepted by CVPR 2012

References in corpus (3)

• Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation
• A geometric analysis of subspace clustering with outliers
• Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation

Cited by in corpus (8)

• Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm
• Deep Sparse Subspace Clustering
• A Counterexample for the Validity of Using Nuclear Norm as a Convex Surrogate of Rank
• Efficient Sparse Subspace Clustering by Nearest Neighbour Filtering
• Segmentation of Subspaces in Sequential Data
• Relations among Some Low Rank Subspace Recovery Models
• Collaborative Low-Rank Subspace Clustering
• Approximate Subspace-Sparse Recovery with Corrupted Data via Constrained ${\ell }_1$-Minimization