Spectral Methods from Tensor Networks

Numerical methods in Tensor Networks

Spectral Methods for Immunization of Large Networks

Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbor nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constra...

Spectral Clustering Methods for Multiplex Networks

Multiplex networks offer an important tool for the study of complex systems and extending techniques originally designed for single–layer networks is an important area of study. One of the most important methods for analyzing networks is clustering the nodes into communities that represent common connectivity patterns. In this paper we extend spectral clustering to multiplex structures and disc...

Spectral distortions from the dissipation of tensor perturbations

Spectral algorithms for tensor completion

Abstract. In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational resources (using, for instance, tensor nuclear norm minimization) and polynomial-time algorithms. Among the latter, the best statistical guarantees...