2017/03/13 by Jingya Chang, Chang, Jingya, Weiyang Ding +5
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1703.04275
openalex publication_date 2017/03/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
The p-spectral radius of a uniform hypergraph covers many important concepts, such as Lagrangian and spectral radius of the hypergraph, and is crucial for solving spectral extremal problems of hypergraphs. In this paper, we establish a spherically constrained maximization model and propose a first-order conjugate gradient algorithm to compute the p-spectral radius of a uniform hypergraph (CSRH). By the semialgebraic nature of the adjacency tensor of a uniform hypergraph, CSRH is globally convergent and obtains the global maximizer with a high probability. When computing the spectral radius of the adjacency tensor of a uniform hypergraph, CSRH stands out among existing approaches. Furthermore, CSRH is competent to calculate the p-spectral radius of a hypergraph with millions of vertices and to approximate the Lagrangian of a hypergraph. Finally, we show that the CSRH method is capable of ranking real-world data set based on solutions generated by the p-spectral radius model.