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http://hdl.handle.net/10397/79624
Title: | Computing the p-spectral radii of uniform hypergraphs with applications | Authors: | Chang, JY Ding, WY Qi, LQ Yan, H |
Keywords: | Eigenvalue Hypergraph Large scale tensor Network analysis Pagerank P-spectral radius |
Issue Date: | 2018 | Publisher: | Springer | Source: | Journal of scientific computing, Apr. 2018, v. 75, no. 1, p. 1-25 How to cite? | Journal: | Journal of scientific computing | Abstract: | 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 outperforms 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. | URI: | http://hdl.handle.net/10397/79624 | ISSN: | 0885-7474 | DOI: | 10.1007/s10915-017-0520-x |
Appears in Collections: | Journal/Magazine Article |
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