Collaborative Research: CIF Core: Small: Hypergraph Signal Processing and Networks via t-Product Decompositions

Grants and Contracts Details


Collaborative Research: CIF Core: Small: Hypergraph and Multi-Layer Graph Signal Processing via t-Product Decompositions Project Summary Overview This proposal presents a collaborative research e?ort aimed at developing a new hypergraph signal processing (HGSP) 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 cou- plings 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 factoriza- tions 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 e?cient calculations. Keywords: Graph signal processing; point cloud imaging; hyperspectral imaging; multilayer graphs. Intellectual Merit The new HGSP framework based on t-product tensor factorization is used to formulate a loss- free hypergraph Fourier space from which a broad set of application tools can be developed for digital signal processing such as ?ltering, sampling, denoising, and upsampling. By taking ad- vantage of the relationship between hypergraphs and multi-layer graphs, the proposed framework can be generalized to model complex structures with multi-layer relationships, thus broadening the applications of the proposed work to signals modeled on multilayer systems having layers of connectivity and encompassing multiple types of relationships. In order to experimentally validate the new theories and algorithms, these will be applied on real hyperspectral point clouds supported by NASA’s Goddard’s LiDAR, Hyperspectral, and Thermal (G-LiTH) airborne imaging system, which provides massive sets of data for learning and experimentation. Broader Impacts Of The Proposed Work HGSP has numerous application areas — from robotics and self-driving navigation to remote sens- ing and cyber-physical systems. Point cloud 3D perception, for instance, is an emerging critical technology in these application areas and as such the application of the proposed work will focus on this signal modality for remote sensing. In concert with the scienti?c goals of the project, the PI’s will develop a short course on graph and hypergraph signal processing so as to introduce this emerging ?eld to a broad set of students in our home institutions. The PI’s will present techni- cal seminars on graph signal processing at the annual Society of Hispanic Professional Engineers (SHPE) Conference, the largest technical and career conference for Hispanics in the country. All the algorithms developed under this project will be open sourced to the scienti?c community. B–1
Effective start/end date7/1/236/30/26


  • National Science Foundation: $254,145.00


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