Maximum Entropy Subspace Clustering Network

TL;DR

This paper introduces MESC-Net, a deep subspace clustering network that maximizes affinity matrix entropy to improve subspace connectivity and decouples auto-encoder and self-expressiveness modules, leading to superior clustering performance.

Contribution

The paper proposes a novel entropy-maximizing approach and a decoupled framework for deep subspace clustering, addressing connectivity and training issues in existing methods.

Findings

MESC-Net outperforms state-of-the-art methods on benchmark datasets.

The affinity matrix satisfies the block-diagonal property under independent subspaces.

Maximizing entropy enhances intra-subspace connectivity.

Abstract

Deep subspace clustering networks have attracted much attention in subspace clustering, in which an auto-encoder non-linearly maps the input data into a latent space, and a fully connected layer named self-expressiveness module is introduced to learn the affinity matrix via a typical regularization term (e.g., sparse or low-rank). However, the adopted regularization terms ignore the connectivity within each subspace, limiting their clustering performance. In addition, the adopted framework suffers from the coupling issue between the auto-encoder module and the self-expressiveness module, making the network training non-trivial. To tackle these two issues, we propose a novel deep subspace clustering method named Maximum Entropy Subspace Clustering Network (MESC-Net). Specifically, MESC-Net maximizes the entropy of the affinity matrix to promote the connectivity within each subspace, in which its elements corresponding to the same subspace are uniformly and densely distributed. Furthermore, we design a novel framework to explicitly decouple the auto-encoder module and the self-expressiveness module. We also theoretically prove that the learned affinity matrix satisfies the block-diagonal property under the independent subspaces. Extensive quantitative and qualitative results on commonly used benchmark datasets validate MESC-Net significantly outperforms state-of-the-art methods.