Robust Kernel Sparse Subspace Clustering
Ivica Kopriva
Kernel methods are applied to many problems in pattern recognition, including
subspace clustering (SC). That way, nonlinear problems in the input data space
become linear in mapped high-dimensional feature space. Thereby,
computationally tractable nonlinear algorithms are enabled through implicit
mapping by the virtue of kernel trick. However, kernelization of linear
algorithms is possible only if square of the Froebenious norm of the error term
is used in related optimization problem. That, however, implies normal
distribution of the error. That is not appropriate for non-Gaussian errors such
as gross sparse corruptions that are modeled by -norm. Herein, to the best of
our knowledge, we propose for the first time robust kernel sparse SC (RKSSC)
algorithm for data with gross sparse corruptions. The concept, in principle,
can be applied to other SC algorithms to achieve robustness to the presence of
such type of corruption. We validated proposed approach on two well-known
datasets with linear robust SSC algorithm as a baseline model. According to
Wilcoxon test, clustering performance obtained by the RKSSC algorithm is
statistically significantly better than corresponding performance obtained by
the robust SSC algorithm. MATLAB code of proposed RKSSC algorithm is posted on
https://github.com/ikopriva/RKSSC.