Kernel Truncated Regression Representation for Robust Subspace Clustering

TL;DR

This paper introduces a kernel truncated regression representation method for nonlinear subspace clustering, which is efficient, robust, and effective on large-scale datasets, outperforming current state-of-the-art approaches.

Contribution

The paper proposes a novel kernel-based method with a closed-form solution for robust nonlinear subspace clustering, addressing limitations of linear assumptions in existing approaches.

Findings

Effective on six benchmark datasets

Outperforms current state-of-the-art methods

Handles large-scale datasets efficiently

Abstract

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this assumption usually does not hold. To achieve nonlinear subspace clustering, we propose a novel method, called kernel truncated regression representation. Our method consists of the following four steps: 1) projecting the input data into a hidden space, where each data point can be linearly represented by other data points; 2) calculating the linear representation coefficients of the data representations in the hidden space; 3) truncating the trivial coefficients to achieve robustness and block-diagonality; and 4) executing the graph cutting operation on the coefficient matrix by solving a graph Laplacian problem. Our method has the advantages of a closed-form solution and the capacity of clustering data points that lie on nonlinear subspaces. The first advantage makes our method efficient in handling large-scale datasets, and the second one enables the proposed method to conquer the nonlinear subspace clustering challenge. Extensive experiments on six benchmarks demonstrate the effectiveness and the efficiency of the proposed method in comparison with current state-of-the-art approaches.