Fixed-Rank Representation for Unsupervised Visual Learning

TL;DR

This paper introduces fixed-rank representation (FRR), a unified, computationally efficient framework for unsupervised visual learning tasks like subspace clustering and feature extraction, capable of handling noise and limited data.

Contribution

The paper proposes FRR, a novel matrix factorization-based method that reveals subspace structures in closed-form and is robust to noise and data insufficiency.

Findings

FRR accurately reveals subspace structures in noiseless data.

FRR remains effective with limited observations under certain conditions.

Experimental results validate FRR's advantages over existing methods.

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.