  The one-class kernel spectral regression (OC-KSR), the regression-based
formulation of the kernel null-space approach has been found to be an effective
Fisher criterion-based methodology for one-class classification (OCC),
achieving state-of-the-art performance in one-class classification while
providing relatively high robustness against data corruption. This work extends
the OC-KSR methodology to a multi-task setting where multiple one-class
problems share information for improved performance. By viewing the multi-task
structure learning problem as one of compositional function learning, first,
the OC-KSR method is extended to learn multiple tasks' structure
\textit{linearly} by posing it as an instantiation of the separable kernel
learning problem in a vector-valued reproducing kernel Hilbert space where an
output kernel encodes tasks' structure while another kernel captures input
similarities. Next, a non-linear structure learning mechanism is proposed which
captures multiple tasks' relationships \textit{non-linearly} via an output
kernel. The non-linear structure learning method is then extended to a sparse
setting where different tasks compete in an output composition mechanism,
leading to a sparse non-linear structure among multiple problems. Through
extensive experiments on different data sets, the merits of the proposed
multi-task kernel null-space techniques are verified against the baseline as
well as other existing multi-task one-class learning techniques.
