Subspace clustering using a low-rank constrained autoencoder.

The performance of subspace clustering is affected by data representation. Data representation for subspace clustering maps data from the original space into another space with the property of better separability. Many data representation methods have been developed in recent years. Typical among them are low-rank representation (LRR) and an autoencoder. LRR is a linear representation method that captures the global structure of data with low-rank constraint. Alternatively, an autoencoder nonlinearly maps data into a latent space using a neural network by minimizing the difference between the reconstruction and input. To combine the advantages of an LRR (globality) and autoencoder (self-supervision based locality), we propose a novel data representation method for subspace clustering. The proposed method, called low-rank constrained autoencoder (LRAE), forces the latent representation of the neural network to be of low rank, and the low-rank constraint is computed as a prior from the input space. One major advantage of the LRAE is that the learned data representation not only maintains the local features of the data, but also preserves the underlying low-rank global structure. Extensive experiments on several datasets for subspace clustering were conducted. They demonstrated that the proposed LRAE substantially outperformed state-of-the-art subspace clustering methods.