DEPSCOR: Learning Multilayer and Hypergraph Networks From Data

This proposal presents a collaborative research effort aimed at developing a new hyper- and multi-layer graph signal processing (HGSP and MGSP) framework based on tensor representations, capable of exploiting multi-way interactions of data from complex systems. HGSP generalizes and subsumes the concepts and tools developed under the umbrella of graph signal processing (GSP) which only consider pairwise couplings between data and, thus, cannot capture high-dimensional interactions among multiple nodes in complex biological, social, and engineering networks. The proposed research radically departs from prior work that relies on symmetric canonical polyadic (CP) tensor decompositions. Instead, the theoretical underpinnings are based on the more recently introduced t-product multiplication operation in tensor algebra which allows tensor factorizations that are analogous to matrix factorizations such as the SVD and eigendecompositions. The advantages of adopting t-eigendecompositions are compelling — they preserve the intrinsic structure of tensors and the high-dimensional nature of signal representations; most importantly, the orthogonal eigenbasis derived from this formulation allows for a loss-free Fourier decomposition and computationally efficient calculations.