  We present a novel deep neural network architecture for unsupervised subspace
clustering. This architecture is built upon deep auto-encoders, which
non-linearly map the input data into a latent space. Our key idea is to
introduce a novel self-expressive layer between the encoder and the decoder to
mimic the "self-expressiveness" property that has proven effective in
traditional subspace clustering. Being differentiable, our new self-expressive
layer provides a simple but effective way to learn pairwise affinities between
all data points through a standard back-propagation procedure. Being nonlinear,
our neural-network based method is able to cluster data points having complex
(often nonlinear) structures. We further propose pre-training and fine-tuning
strategies that let us effectively learn the parameters of our subspace
clustering networks. Our experiments show that the proposed method
significantly outperforms the state-of-the-art unsupervised subspace clustering
methods.
