  Kernels on discrete structures evaluate pairwise similarities between objects
which capture semantics and inherent topology information. Existing kernels on
discrete structures are only developed by topology information(such as
adjacency matrix of graphs), without considering original attributes of
objects. This paper proposes a two-phase paradigm to aggregate comprehensive
information on discrete structures leading to a Discount Markov Diffusion
Learnable Kernel (DMDLK). Specifically, based on the underlying projection of
DMDLK, we design a Simple Hypergraph Kernel Convolution (SHKC) for hidden
representation of vertices. SHKC can adjust diffusion steps rather than
stacking convolution layers to aggregate information from long-range
neighborhoods which prevents over-smoothing issues of existing hypergraph
convolutions. Moreover, we utilize the uniform stability bound theorem in
transductive learning to analyze critical factors for the effectiveness and
generalization ability of SHKC from a theoretical perspective. The experimental
results on several benchmark datasets for node classification tasks verified
the superior performance of SHKC over state-of-the-art methods.
