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Abstract
The deep subspace clustering method, which adopts deep neural networks to learn a representation matrix for subspace clustering, has shown good performance. However, this representation matrix ignores the structural constraint when it is applied to subspace clustering. It is known that samples from different classes can be taken as embedding in independent subspaces. Thus, the representation matrix should have a block diagonal structure. This paper presents the Deep Subspace Clustering with Block Diagonal Constraint (DSC-BDC), a model which constrains the representation matrix with block diagonal structure and gives a block diagonal regularizer for learning a suitable representation. Furthermore, to enhance the representation capacity, DSC-BDC reforms the block-diagonal structure constraint by performing a separation strategy on the representation matrix. Specifically, the separation strategy ensures that the most compact samples are selected to the represent data. An alternative optimization algorithm is designed for our model. Extensive experiments on four public and real-world databases demonstrate the effectiveness and superiority of our proposed model.
Highlights
Subspace clustering is a significant unsupervised learning method in many applications, such as image representation [1,2,3], face clustering [4,5,6], motion segmentation [7,8], bioinformatics [9], medical image analysis [10], etc
Abundant subspace clustering methods have been proposed, and most methods [2,13,14,15] are based on Spectral Clustering, which constructs a representation matrix measuring similarity between data points and segments input data based on this representation matrix
A deep subspace clustering method based on an auto-encode is proposed, and block-diagonal constraints on representation matrix are used for better cluster performance
Summary
Subspace clustering is a significant unsupervised learning method in many applications, such as image representation [1,2,3], face clustering [4,5,6], motion segmentation [7,8], bioinformatics [9], medical image analysis [10], etc. Introduced block-diagonal constraints on multi-view representation matrices to obtain accurate heterogeneous information Those methods demonstrate that the subspace clustering performance is improved by adding the block diagonal prior on the representation matrix. Peng et al [29] presented the first deep learning-based subspace clustering method that progressively transforms input data into nonlinear latent space. Peng et al [36] presented the first work revealing the sample-assignment invariance prior based on the idea of treating labels as ideal representations These deep learning-based methods outperform other state-of-the-art subspace clustering methods significantly. Because of the good performance demonstrated by the deep neural network and block-diagonal constraint, this paper employs the deep neural network to set up the subspace clustering model with. A deep subspace clustering method based on an auto-encode is proposed, and block-diagonal constraints on representation matrix are used for better cluster performance.
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