  Spectral Embedding (SE) has often been used to map data points from
non-linear manifolds to linear subspaces for the purpose of classification and
clustering. Despite significant advantages, the subspace structure of data in
the original space is not preserved in the embedding space. To address this
issue subspace clustering has been proposed by replacing the SE graph affinity
with a self-expression matrix. It works well if the data lies in a union of
linear subspaces however, the performance may degrade in real-world
applications where data often spans non-linear manifolds. To address this
problem we propose a novel structure-aware deep spectral embedding by combining
a spectral embedding loss and a structure preservation loss. To this end, a
deep neural network architecture is proposed that simultaneously encodes both
types of information and aims to generate structure-aware spectral embedding.
The subspace structure of the input data is encoded by using attention-based
self-expression learning. The proposed algorithm is evaluated on six publicly
available real-world datasets. The results demonstrate the excellent clustering
performance of the proposed algorithm compared to the existing state-of-the-art
methods. The proposed algorithm has also exhibited better generalization to
unseen data points and it is scalable to larger datasets without requiring
significant computational resources.
