Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering

TL;DR

This paper introduces L2-Graph, a novel similarity graph construction method that enhances robustness and accuracy in subspace clustering and learning by eliminating errors in the projection space, not input space.

Contribution

The paper proposes a new approach to construct a robust similarity graph using projection space properties, avoiding prior error structure assumptions and complex convex optimization.

Findings

L2-Graph outperforms state-of-the-art methods in accuracy.

L2-Graph demonstrates superior robustness in experiments.

L2-Graph is more time-efficient than existing approaches.

Abstract

Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intra-subspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that $\ell_1$-, $\ell_2$-, $\ell_{\infty}$-, and nuclear-norm based linear projection spaces share the property of Intra-subspace Projection Dominance (IPD), i.e., the coefficients over intra-subspace data points are larger than those over inter-subspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-Graph. The subspace clustering and subspace learning algorithms are developed upon L2-Graph. Experiments show that L2-Graph algorithms outperform the state-of-the-art methods for feature extraction, image clustering, and motion segmentation in terms of accuracy, robustness, and time efficiency.