Abstract
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Multiple kernel clustering (MKC) algorithms optimally combine
a group of pre-specified base kernels to improve clustering
performance. However, existing MKC algorithms cannot
efficiently address the situation where some rows and
columns of base kernels are absent. This paper proposes a
simple while effective algorithm to address this issue. Different
from existing approaches where incomplete kernels are
firstly imputed and a standard MKC algorithm is applied to
the imputed kernels, our algorithm integrates imputation and
clustering into a unified learning procedure. Specifically, we
perform multiple kernel clustering directly with the presence
of incomplete kernels, which are treated as auxiliary variables
to be jointly optimized. Our algorithm does not require that
there be at least one complete base kernel over all the samples.
Also, it adaptively imputes incomplete kernels and combines
them to best serve clustering. A three-step iterative algorithm
with proved convergence is designed to solve the resultant
optimization problem. Extensive experiments are conducted
on four benchmark data sets to compare the proposed
algorithm with existing imputation-based methods. Our algorithm
consistently achieves superior performance and the improvement
becomes more significant with increasing missing
ratio, verifying the effectiveness and advantages of the proposed
joint imputation and clustering.