  Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved
impressive performance due to the powerful representation extracted using deep
neural networks while prioritizing categorical separability. However,
self-reconstruction loss of an AE ignores rich useful relation information and
might lead to indiscriminative representation, which inevitably degrades the
clustering performance. It is also challenging to learn high-level similarity
without feeding semantic labels. Another unsolved problem facing DSC is the
huge memory cost due to $n\times n$ similarity matrix, which is incurred by the
self-expression layer between an encoder and decoder. To tackle these problems,
we use pairwise similarity to weigh the reconstruction loss to capture local
structure information, while a similarity is learned by the self-expression
layer. Pseudo-graphs and pseudo-labels, which allow benefiting from uncertain
knowledge acquired during network training, are further employed to supervise
similarity learning. Joint learning and iterative training facilitate to obtain
an overall optimal solution. Extensive experiments on benchmark datasets
demonstrate the superiority of our approach. By combining with the $k$-nearest
neighbors algorithm, we further show that our method can address the
large-scale and out-of-sample problems.
