Tight Frames Generated By A Graph Short-Time Fourier Transform

A graph short-time Fourier transform is defined using the eigenvectors of the graph Laplacian and a graph heat kernel as a window parametrized by a non-negative time parameter $t$. We show that the corresponding Gabor-like system forms a frame for $\mathbb{C}^d$ and give a description of the spectrum of the corresponding frame operator in terms of the graph heat kernel and the spectrum of the underlying graph Laplacian. For two classes of algebraic graphs, we prove the frame is tight and independent of the window parameter $t$.

HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks.