  Deep auto-encoders (DAEs) have achieved great success in learning data
representations via the powerful representability of neural networks. But most
DAEs only focus on the most dominant structures which are able to reconstruct
the data from a latent space and neglect rich latent structural information. In
this work, we propose a new representation learning method that explicitly
models and leverages sample relations, which in turn is used as supervision to
guide the representation learning. Different from previous work, our framework
well preserves the relations between samples. Since the prediction of pairwise
relations themselves is a fundamental problem, our model adaptively learns them
from data. This provides much flexibility to encode real data manifold. The
important role of relation and representation learning is evaluated on the
clustering task. Extensive experiments on benchmark data sets demonstrate the
superiority of our approach. By seeking to embed samples into subspace, we
further show that our method can address the large-scale and out-of-sample
problem.
