Subspace sparse coding (SSC) algorithms have proven to be beneficial to
clustering problems. They provide an alternative data representation in which
the underlying structure of the clusters can be better captured. However, most
of the research in this area is mainly focused on enhancing the sparse coding
part of the problem. In contrast, we introduce a novel objective term in our
proposed SSC framework which focuses on the separability of data points in the
coding space. We also provide mathematical insights into how this
local-separability term improves the clustering result of the SSC framework.
Our proposed non-linear local SSC algorithm (NLSSC) also benefits from the
efficient choice of its sparsity terms and constraints. The NLSSC algorithm is
also formulated in the kernel-based framework (NLKSSC) which can represent the
nonlinear structure of data. In addition, we address the possibility of having
redundancies in sparse coding results and its negative effect on graph-based
clustering problems. We introduce the link-restore post-processing step to
improve the representation graph of non-negative SSC algorithms such as ours.
Empirical evaluations on well-known clustering benchmarks show that our
proposed NLSSC framework results in better clusterings compared to the
state-of-the-art baselines and demonstrate the effectiveness of the
link-restore post-processing in improving the clustering accuracy via
correcting the broken links of the representation graph.Comment: 15 pages, IDA 2018 conferenc