84 citations · 354 across the 25 of their papers we have counts for
37 papers
Nonlinear Spectral Duality
Francesco Tudisco, Dong Zhang
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including gr…
Hitting times for second-order random walks
Dario Fasino, Arianna Tonetto, Francesco Tudisco
A second-order random walk on a graph or network is a random walk where transition probabilities depend not only on the present node but also on the previous one. A notable example…
A nonlinear diffusion method for semi-supervised learning on hypergraphs
Francesco Tudisco, Konstantin Prokopchik, Austin R. Benson
Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given la…
Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs
Francesco Tudisco, Desmond J. Higham
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves definin…
Nonlinear Higher-Order Label Spreading
Francesco Tudisco, Austin R. Benson, Konstantin Prokopchik
Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph. While there are…
Computing the norm of nonnegative matrices and the log-Sobolev constant of Markov chains
Antoine Gautier, Matthias Hein, Francesco Tudisco
We analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of ent…
Nonlocal PageRank
Stefano Cipolla, Fabio Durastante, Francesco Tudisco
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neigh…
Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs
Pedro Mercado, Francesco Tudisco, Matthias Hein
We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each indi…
A framework for second order eigenvector centralities and clustering coefficients
Francesca Arrigo, Desmond J. Higham, Francesco Tudisco
We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links…
Generating large scale-free networks with the Chung-Lu random graph model
Dario Fasino, Arianna Tonetto, Francesco Tudisco
Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they s…
Shifted and extrapolated power methods for tensor -eigenpairs
Stefano Cipolla, Michela Redivo-Zaglia, Francesco Tudisco
This work is concerned with the computation of -eigenvalues and eigenvectors of square tensors with modes. In the first part we propose two possible shifted variants of…
Total variation based community detection using a nonlinear optimization approach
Andrea Cristofari, Francesco Rinaldi, Francesco Tudisco
Maximizing the modularity of a network is a successful tool to identify an important community of nodes. However, this combinatorial optimization problem is known to be NP-complete…
Ergodicity coefficients for higher-order stochastic processes
Dario Fasino, Francesco Tudisco
The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at m…
Extrapolation Methods for fixed-point Multilinear PageRank computations
Stefano Cipolla, Michela Redivo-Zaglia, Francesco Tudisco
Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and numb…
Spectral Clustering of Signed Graphs via Matrix Power Means
Pedro Mercado, Francesco Tudisco, Matthias Hein
Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed P…
Multi-Dimensional, Multilayer, Nonlinear and Dynamic HITS
Francesca Arrigo, Francesco Tudisco
We introduce a ranking model for temporal multi-dimensional weighted and directed networks based on the Perron eigenvector of a multi-homogeneous order-preserving map. The model ex…
The contractivity of cone-preserving multilinear mappings
Antoine Gautier, Francesco Tudisco
With the notion of mode- Birkhoff contraction ratio, we prove a multilinear version of the Birkhoff-Hopf and the Perron-Fronenius theorems, which provide conditions on the exist…
A Nonlinear Spectral Method for Core--Periphery Detection in Networks
Francesco Tudisco, Desmond J. Higham
We derive and analyse a new iterative algorithm for detecting network core--periphery structure. Using techniques in nonlinear Perron-Frobenius theory, we prove global convergence…
The Power Mean Laplacian for Multilayer Graph Clustering
Pedro Mercado, Antoine Gautier, Francesco Tudisco +1
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one sho…
The Perron-Frobenius theorem for multi-homogeneous mappings
Antoine Gautier, Francesco Tudisco, Matthias Hein
The Perron-Frobenius theory for nonnegative matrices has been generalized to order-preserving homogeneous mappings on a cone and more recently to nonnegative multilinear forms. We…
A unifying Perron-Frobenius theorem for nonnegative tensors via multi-homogeneous maps
Antoine Gautier, Francesco Tudisco, Matthias Hein
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases.…
Node and layer eigenvector centralities for multiplex networks
Francesco Tudisco, Francesca Arrigo, Antoine Gautier
Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extrem…
A modularity based spectral method for simultaneous community and anti-community detection
Dario Fasino, Francesco Tudisco
In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the…
On the stability of network indices defined by means of matrix functions
Stefano Pozza, Francesco Tudisco
Identifying important components in a network is one of the major goals of network analysis. Popular and effective measures of importance of a node or a set of nodes are defined in…