Maximum Entropy Subspace Clustering Network
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Deep subspace clustering network (DSC-Net) and its numerous variants have achieved impressive performance for subspace clustering, in which an auto-encoder non-linearly maps input data into a latent space, and a fully connected layer named self-expressiveness module is introduced between the encoder and the decoder to learn an affinity matrix. However, the adopted regularization on the affinity matrix (e.g., sparse, Tikhonov, or low-rank) is still insufficient to drive the learning of an ideal affinity matrix, thus limiting their performance. In addition, in DSC-Net, the self-expressiveness module and the auto-encoder module are tightly coupled, making the training of the DSC-Net non-trivial. To this end, in this paper, we propose a novel deep learning-based clustering method named Maximum Entropy Subspace Clustering Network (MESC-Net). Specifically, MESC-Net maximizes the learned affinity matrix's entropy to encourage it to exhibit an ideal affinity matrix structure. We theoretically prove that the affinity matrix driven by MESC-Net obeys the block-diagonal property, and experimentally show that its elements corresponding to the same subspace are uniformly and densely distributed, which gives better clustering performance. Moreover, we explicitly decouple the auto-encoder module and the self-expressiveness module. Extensive quantitative and qualitative results on commonly used benchmark datasets validate MESC-Net significantly outperforms state-of-the-art methods.
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