Signal processing on heterogeneous network based on tensor decomposition

Recent researches on graph signal processing (GSP) have been successfully applied on homogeneous networks. However, in real-world network, nodes and relationships of multiple types are usually heterogeneous. In this paper, we discuss signal processing on heterogeneous networks. Heterogeneous networks are modeled as hypergraphs by adjacency tensor. An algorithm called signal processing on tensor (TSP) is proposed to analyze signal propagation in vertex and frequency domain. In vertex domain, TSP propagates signals not only on homogeneous subgraphs but also on hypergraphs including hyperlinks of multi-subgraphs. In frequency domain, tensor Fourier transform is defined based on factor matrices of higher-order singular value decomposition (HOSVD), which is used to describe high and low frequencies of signals on hypergraphs. Finally, we verify algorithm by data classification on network generated randomly. Comparing to classification on homogeneous subgraphs merely, our algorithm achieves higher accuracy.