Abstract
Recently, spectral kernels have attracted wide attention in complex dynamic environments. These
advanced kernels mainly focus on breaking through
the crucial limitation on locality, that is, the stationarity and the monotonicity. But actually, owing to the inefficiency of shallow models in computational elements, they are more likely unable to
accurately reveal dynamic and potential variations.
In this paper, we propose a novel deep spectral
kernel network (DSKN) to naturally integrate nonstationary and non-monotonic spectral kernels into
elegant deep architectures in an interpretable way,
which can be further generalized to cover most
kernels. Concretely, we firstly deal with the general form of spectral kernels by the inverse Fourier
transform. Secondly, DSKN is constructed by embedding the preeminent spectral kernels into each
layer to boost the efficiency in computational elements, which can effectively reveal the dynamic
input-dependent characteristics and potential longrange correlations by compactly representing complex advanced concepts. Thirdly, detailed analyses
of DSKN are presented. Owing to its universality,
we propose a unified spectral transform technique
to flexibly extend and reasonably initialize domainrelated DSKN. Furthermore, the representer theorem of DSKN is given. Systematical experiments
demonstrate the superiority of DSKN compared to
state-of-the-art relevant algorithms on varieties of
standard real-world tasks