Robust and Efficient Subspace Segmentation via Least Squares Regression

TL;DR

This paper introduces a novel Least Squares Regression (LSR) method for subspace segmentation that leverages data correlation to improve accuracy and efficiency, outperforming existing methods on standard datasets.

Contribution

The paper proposes a new LSR-based approach for subspace segmentation that theoretically guarantees block diagonal affinity matrices under certain conditions and demonstrates superior performance.

Findings

LSR achieves higher segmentation accuracy than state-of-the-art methods.

LSR is significantly more computationally efficient.

Theoretical analysis confirms conditions for block diagonal affinity matrices.

Abstract

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much attention. If the subspaces from which the data drawn are independent or orthogonal, they are able to obtain a block diagonal affinity matrix, which usually leads to a correct segmentation. The main differences among them are their objective functions. We theoretically show that if the objective function satisfies some conditions, and the data are sufficiently drawn from independent subspaces, the obtained affinity matrix is always block diagonal. Furthermore, the data sampling can be insufficient if the subspaces are orthogonal. Some existing methods are all special cases. Then we present the Least Squares Regression (LSR) method for subspace segmentation. It takes advantage of data correlation, which is common in real data. LSR encourages a grouping effect which tends to group highly correlated data together. Experimental results on the Hopkins 155 database and Extended Yale Database B show that our method significantly outperforms state-of-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.