  Leveraging on the underlying low-dimensional structure of data, low-rank and
sparse modeling approaches have achieved great success in a wide range of
applications. However, in many applications the data can display structures
beyond simply being low-rank or sparse. Fully extracting and exploiting hidden
structure information in the data is always desirable and favorable. To reveal
more underlying effective manifold structure, in this paper, we explicitly
model the data relation. Specifically, we propose a structure learning
framework that retains the pairwise similarities between the data points.
Rather than just trying to reconstruct the original data based on
self-expression, we also manage to reconstruct the kernel matrix, which
functions as similarity preserving. Consequently, this technique is
particularly suitable for the class of learning problems that are sensitive to
sample similarity, e.g., clustering and semisupervised classification. To take
advantage of representation power of deep neural network, a deep auto-encoder
architecture is further designed to implement our model. Extensive experiments
on benchmark data sets demonstrate that our proposed framework can consistently
and significantly improve performance on both evaluation tasks. We conclude
that the quality of structure learning can be enhanced if similarity
information is incorporated.
