Sparse Subspace Clustering via Diffusion Process

TL;DR

This paper introduces a diffusion process-based method to improve connectivity in sparse subspace clustering, achieving state-of-the-art results without additional tuning parameters.

Contribution

It proposes a simple, efficient diffusion process to enhance connectivity in L1-based subspace clustering, balancing subspace preservation and cluster connectivity.

Findings

Achieves state-of-the-art clustering performance on Hopkins 155 dataset.

Effective in improving connectivity without tuning parameters.

Outperforms existing methods in clustering accuracy.

Abstract

Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of low-dimensional subspaces. State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with L1, L2 or nuclear norms for a sparse solution. L1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be fully connected. L2 and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed L1, L2 and nuclear norm regularization could offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper focuses on using L1 norm and alleviating the corresponding connectivity problem by a simple yet efficient diffusion process on subspace affinity graphs. Without adding any tuning parameter , our method can achieve state-of-the-art clustering performance on Hopkins 155 and Extended Yale B data sets.