A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matrices are multiplied directly, with no intervening nonlinearity. Such blocks appear in LoRA adapters, low-rank compressed layers, query-key products of self-attention, and …
Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a …
We study the problem of emergency operation center placement in disaster response, where a minimal number of hubs must be selected to ensure timely coverage of all affected locations. This task can be formulated as a minimum dominating set problem on a graph encoding reachability within a target response time. We …
In many scientific contexts, obtaining complete observations of PDE coefficients and solutions proves expensive, hazardous, or unfeasible. Recent diffusion-based approaches can reconstruct fields from incomplete data, yet require fully observed examples during training. We present Ambient Physics, a framework enabling …
The COVID-19 pandemic shifted academic collaboration from in-person to remote interactions. This study explores, for the first time, the effects on scientific collaborations and impact of such a shift, comparing research output before, during, and after the pandemic. Using large-scale bibliometric data, we track the …
We study the collective dynamics of coupled Stuart–Landau oscillators, which model limit-cycle behavior near a Hopf bifurcation and serve as the amplitude-phase analogue of the Kuramoto model. Unlike the well-studied phase-reduced systems, the full Stuart–Landau model retains amplitude dynamics, enabling the emergence …
We introduce a nonlinear extension of the joint spectral radius (JSR) for switched discrete-time dynamical systems. The classical JSR characterizes the exponential growth rate of linear switched systems, but its extension to nonlinear systems has remained an open problem. Our approach builds on the framework of …
We study the approximation properties of neural ordinary differential equations (neural ODEs) in the space of continuous functions. Since a neural ODE requires input and output dimensions to be the same, while input and output dimensions of a continuous function are generally different, we need to embed an input into …
We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initial value. Since the stability depends on the logarithmic norm of the Jacobian matrix associated with the neural ODE, we control the …
Adversarial attacks on deep neural network models have seen rapid development and are extensively used to study the stability of these networks. Among various adversarial strategies, Projected Gradient Descent (PGD) is a widely adopted method in computer vision due to its effectiveness and quick implementation, making …
The self-consistent field (SCF) iteration, combined with its variants, is one of the most widely used algorithms in quantum chemistry. We propose a procedure to adapt the SCF iteration for the p-Laplacian eigenproblem, which is an important problem in the field of unsupervised learning. We formulate the p-Laplacian …
Advances in Neural Information Processing Systems (NeurIPS), 2026
U-Net-style architectures are widely adopted for modeling physical systems, as their multiscale structure enables efficient processing of high-resolution data while reflecting the hierarchical structure of many physical phenomena. The most successful U-Net-based neural physics simulators often combine convolutions, …
Springer INdAM Series, 2026
Neural networks for image classification are vulnerable to adversarial attacks; an imperceptible perturbation to an image can cause a change in classification. Standard attack algorithms use explicit or approximate partial derivative information with respect to the input data. Here, we explore the idea of using a less …
International Conference on Machine Learning (ICML), 2026
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many critical applications remain constrained by the substantial computational costs …
Advanced Quantum Technologies, 2026
Quantum architectures based on neutral atoms have gained significant attention in recent years as specialized computational machines due to their ability to directly encode the independent set constraint on graphs, exploiting the Rydberg blockade mechanism. In this work, we address the Drone Delivery Packing Problem …
Language Resources and Evaluation Conference (LREC), 2026
Approaches for compressing large-language models using low-rank decomposition have made strides, particularly with the introduction of activation and loss-aware SVD, which improves the trade-off between decomposition rank and downstream task performance. Despite these advancements, a persistent challenge …
International Conference on Learning Representations (ICLR), 2026
Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as …
SIAM Journal on Matrix Analysis and Applications, 2026
Generalized friendship paradoxes occur when, on average, our friends have more of some attribute than us. These paradoxes are relevant to many aspects of human interaction, notably in social science and epidemiology. Here, we derive new theoretical results concerning the inevitability of a paradox arising, using a …
The Web Conference (WWW), 2026
Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau Graph Neural Network (SLGNN), a novel architecture grounded in Stuart-Landau …
International Conference on Learning Representations (ICLR), 2026
Accuracy-cost trade-offs are a fundamental aspect of scientific computing. Classical numerical methods inherently offer such a trade-off: increasing resolution, order, or precision typically yields more accurate solutions at higher computational cost. We introduce \textbf{Recurrent-Depth Simulator} (\textbf{RecurrSim}) …
Medical & Biological Engineering & Computing, vol. 64, pp. 827–845, 2026
Synthetic data generation plays a crucial role in medical research by mitigating privacy concerns and enabling large-scale patient data analysis. This study presents a beta-Variational Autoencoder Graph Convolutional Neural Network framework for generating synthetic Abdominal Aorta Aneurysms (AAA). Using a small …
SIAM Review, 2026
Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defined on a graph and topological properties of the graph itself. Many of these relationships get tighter when going from the linear to the …
SIAM Journal on Mathematics of Data Science, 2026
Simplicial complexes (SCs), a generalization of graph models for relational data that account for higher-order relations between data items, have become a popular abstraction for analyzing complex data using tools from topological data analysis or topological signal processing. However, the analysis of many real-world …
SIAM Journal on Mathematical Analysis, 2026
We analyze various formulations of the $\infty$-Laplacian eigenvalue problem on graphs, comparing their properties and highlighting their respective advantages and limitations. First, we investigate the graph $\infty$-eigenpairs arising as limits of $p$-Laplacian eigenpairs, extending key results from the continuous …
Quantum Machine Intelligence, 2026
Using drones to perform human-related tasks can play a key role in various fields, such as defense, disaster response, agriculture, healthcare, and many others. The drone delivery packing problem (DDPP) arises in the context of logistics in response to an increasing demand in the delivery process along with the …
Mathematics of Computation, vol. 95, pp. 293–319, 2026
We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of a one layer weight-tied neural ODE $\dot{u}(t)=σ(Au(t)+b)$ (with $u,b \in {\mathbb R}^n$, $A$ is a given $n \times n$ matrix, $σ: {\mathbb …
Transactions on Machine Learning Research (TMLR), 2026
Recent work in deep learning has shown strong empirical and theoretical evidence of an implicit low-rank bias: weight matrices in deep networks tend to be approximately low-rank. Moreover, removing relatively small singular values during training, or from available trained models, may significantly reduce model size …
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2026
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By considering different notions of duality transforms from both classical and recent …
Lobachevskii Journal of Mathematics, vol. 46, pp. 3804–3814, 2025
In this article, we introduce eigenvector centralities for higher-order multilayer networks and suggest to use nonnegative tensor train decomposition for fast computations of dominant eigenvectors of multi-homogeneous maps via power iterates. The analysis of the approximation error for using nonnegative tensor train …
NeurIPS Workshop on Machine Learning and the Physical Sciences, 2025
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are ill-conditioned. Existing numerical methods for ill-conditioned systems often …
Physical Review Letters, 2025
Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of a network into core nodes, which are highly connected across the network, and …
Journal of Complex Networks, vol. 13, 2025
Influence Maximization (IM) is a pivotal concept in social network analysis, involving the identification of influential nodes within a network to maximize the number of influenced nodes, and has a wide variety of applications that range from viral marketing and information dissemination to public health campaigns. IM …
AAAI Conference on Artificial Intelligence (AAAI), Workshop on Connecting Low-Rank Representations in AI, 2025
Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as …
International Conference on Learning Representations (ICLR), 2025
Low-rank adaptation methods are a popular approach for parameter-efficient fine-tuning of large-scale neural networks. However, selecting the optimal rank for each layer remains a challenging problem that significantly affects both performance and efficiency. In this paper, we introduce a novel bilevel optimization …
International Conference on Learning Representations (ICLR), 2025
Low-Rank Adaptation (LoRA) has become a widely used method for parameter-efficient fine-tuning of large-scale, pre-trained neural networks. However, LoRA and its extensions face several challenges, including the need for rank adaptivity, robustness, and computational efficiency during the fine-tuning process. We …
Nonlinearity, 2025
The modeling of opinion dynamics has seen much study in varying academic disciplines. Understanding the complex ways information can be disseminated is a complicated problem for mathematicians as well as social scientists. We present a nonlinear model of opinion dynamics that utilizes an environmental averaging …
Nature Human Behaviour, vol. 8, pp. 1631–1634, 2024
Authors of COVID-19 papers produced during the pandemic were overwhelmingly not subject matter experts. Such a massive inflow of scholars from different expertise areas is both an asset and a potential problem. Domain-informed scientific collaboration is the key to preparing for future crises.
Advances in Neural Information Processing Systems (NeurIPS), 2024
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format …
International Conference on Machine Learning (ICML), 2024
Implicit-depth neural networks have grown as powerful alternatives to traditional networks in various applications in recent years. However, these models often lack guarantees of existence and uniqueness, raising stability, performance, and reproducibility issues. In this paper, we present a new analysis of the …
NeurIPS Workshop on Foundation Models for Science, 2024
Foundation models have demonstrated remarkable success across various scientific domains, motivating our exploration of their potential in solar physics. In this paper, we present Solaris, the first foundation model for forecasting the Sun’s atmosphere. We leverage 13 years of full-disk, multi-wavelength solar imagery …
ICLR Workshop on AI4DifferentialEquations in Science, 2024
Traditional numerical solvers for time-dependent partial differential equations (PDEs) notoriously require high computational resources and necessitate recomputation when faced with new problem parameters. In recent years, neural surrogates have shown great potential to overcome these limitations. However, it has been …
SIAM Journal on Matrix Analysis and Applications, 2024
Techniques based on $k$-th order Hodge Laplacian operators $L_k$ are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplicial complexes. In all of them, it is required to solve a number of least square problems with $L_k$ as coefficient matrix, for example in …
Scientific Reports, vol. 14, pp. 1258, 2024
Collaboration is a key driver of science and innovation. Mainly motivated by the need to leverage different capacities and expertise to solve a scientific problem, collaboration is also an excellent source of information about the future behavior of scholars. In particular, it allows us to infer the likelihood that …
Proceedings of the Royal Society A, 2024
Core-periphery detection aims to separate the nodes of a complex network into two subsets: a core that is densely connected to the entire network and a periphery that is densely connected to the core but sparsely connected internally. The definition of core-periphery structure in multiplex networks that record …
Science Advances, 2024
Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the …
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 58, pp. 131–155, 2024
We consider the problem of attaining either the maximal increase or reduction of the robustness of a complex network by means of a bounded modification of a subset of the edge weights. We propose two novel strategies combining Krylov subspace approximations with a greedy scheme and with the limited-memory BFGS. The …
Advances in Neural Information Processing Systems (NeurIPS), 2023
With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training costs, a prominent line of work uses low-rank matrix factorizations to …
SIAM Review (SIGEST paper), vol. 65, pp. 495–536, 2023
We present a unifying Perron–Frobenius theory for nonlinear spectral problems defined in terms of nonnegative tensors. By using the concept of tensor shape partition, our results include, as a special case, a wide variety of particular tensor spectral problems considered in the literature and can be applied to a broad …
EURO Journal on Computational Optimization, 2023
Graph Semi-Supervised learning is an important data analysis tool, where given a graph and a set of labeled nodes, the aim is to infer the labels to the remaining unlabeled nodes. In this paper, we start by considering an optimization-based formulation of the problem for an undirected graph, and then we extend this …
Journal of Scientific Computing, vol. 97, 2023
The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current work, we study the stability in terms of the smallest perturbation sufficient to …
International Conference on Machine Learning (ICML), 2023
Clustering (or community detection) on multilayer graphs poses several additional complications with respect to standard graphs as different layers may be characterized by different structures and types of information. One of the major challenges is to establish the extent to which each layer contributes to the cluster …
SIAM Journal on Mathematics of Data Science, vol. 5, 2023
Core-periphery detection is a key task in exploratory network analysis where one aims to find a core, a set of nodes well-connected internally and with the periphery, and a periphery, a set of nodes connected only (or mostly) with the core. In this work we propose a model of core-periphery for higher-order networks …
Applied and Computational Harmonic Analysis, vol. 64, pp. 1–32, 2023
Inspired by the linear Schrödinger operator, we consider a generalized $p$-Laplacian operator on discrete graphs and present new results that characterize several spectral properties of this operator with particular attention to the nodal domain count of its eigenfunctions. Just like the one-dimensional continuous …
Advances in Neural Information Processing Systems (NeurIPS), 2022
Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. …
Journal of Complex Networks, 2022
In this paper, we focus on the community detection problem in multiplex networks, i.e., networks with multiple layers having same node sets and no inter-layer connections. In particular, we look for groups of nodes that can be recognized as communities consistently across the layers. To this end, we propose a new …
ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), 2022
We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be …
European Journal of Applied Mathematics, vol. 34, pp. 642–666, 2022
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 is the non-backtracking random walk, where the walker is not allowed to revisit a node in one step. Second-order random walks can model …
International Conference on Machine Learning (ICML), 2022
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 labels on just a few nodes. Diffusions and label spreading are classical techniques for semi-supervised learning in the graph setting, and …
Communications Physics, vol. 4:201, 2021
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 defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting …
The Web Conference (WWW), pp. 2402–2413, 2021
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 many variants of label spreading, nearly all of them are linear models, where the incoming information to a node is a weighted sum of …
Journal of Scientific Computing, vol. 88, pp. 21, 2021
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 entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate $\ell^p$ matrix norms. In particular, …
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, pp. 77–97, 2021
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 neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not …
SIAM Journal on Mathematics of Data Science, vol. 2, pp. 740–769, 2020
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 modeling high dimensional data and nonlinear dynamics in numerous application settings. In many cases of practical interest, these processes …
Proceedings of the Royal Society A, vol. 476, pp. 20190724, 2020
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 with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods …
Networks, 2020
Being able to produce synthetic networks by means of generative random graph models and scalable algorithms is a recurring tool-of-the-trade in network analysis, as it provides a well founded basis for the statistical analysis of various properties in real-world networks. In this paper, we illustrate how to generate …
Electronic Transactions on Numerical Analysis (ETNA), vol. 53, pp. 1–27, 2020
This work is concerned with the computation of $\ell^p$-eigenvalues and eigenvectors of square tensors with $d$ modes. In the first part we propose two possible shifted variants of the popular (higher-order) power method for the computation of $\ell^p$-eigenpairs proving the convergence of both the schemes to the …
SIAM Journal on Applied Mathematics, vol. 80, pp. 1392–1419, 2020
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-hard. Inspired by recent nonlinear modularity eigenvector approaches, we introduce the modularity total variation $TV_Q$ and show that its …
Numerical Linear Algebra with Applications, vol. 27, pp. e2280, 2020
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 number of operations per step, the (shifted) higher-order power method is one of the most commonly used technique for the computation of …
Advances in Neural Information Processing Systems (NeurIPS), 2019
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 individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that …
Applied Network Science, vol. 4:75, 2019
Many graph mining tasks can be viewed as classification problems on high dimensional data. Within this class we consider the issue of discovering core-periphery structure, which has wide applications in the economic and social sciences. In contrast to many current approaches, we allow for weighted and directed edges …
International Conference on Machine Learning (ICML), pp. 4526–4536, 2019
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 Power Mean Laplacians, defined as the matrix power mean of normalized standard and signless Laplacians of positive and negative edges. We …
SIAM International Conference on Data Mining (SDM), pp. 369–377, 2019
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 extends to the temporal multilayer setting the HITS algorithm and defines five centrality vectors: two for the nodes, two for the layers, and …
SIAM Journal on Mathematics of Data Science, vol. 1, pp. 269–292, 2019
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 to the unique solution of a relaxed version of a natural discrete optimization problem. On sparse networks, the cost of each iteration scales …
Nonlinearity, vol. 32, pp. 4713, 2019
With the notion of mode-$j$ Birkhoff contraction ratio, we prove a multilinear version of the Birkhoff-Hopf and the Perron-Fronenius theorems, which provide conditions on the existence and uniqueness of a solution to a large family of systems of nonlinear equations of the type $$f_i(x_1,…,x_ν)= λ_i x_i, ,$$ being $x_i$ …
SIAM Journal on Matrix Analysis and Applications, vol. 40, pp. 1206–1231, 2019
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. We formulate irreducibility and symmetry properties of a nonnegative tensor $T$ in terms of the associated shape partition. We recast the …
SIAM Journal on Matrix Analysis and Applications, vol. 40, pp. 1179–1205, 2019
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 unify both approaches by introducing the concept of order-preserving multi-homogeneous mappings, their associated nonlinear spectral …
International Conference on Artificial Intelligence and Statistics (AISTATS), vol. 84, pp. 1828–1838, 2018
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 should merge the information form different layers. We introduce in this paper a one-parameter family of matrix power means for merging the …
Special Matrices, vol. 6, pp. 110–121, 2018
We provide explicit expressions for the eigenvalues and eigenvectors of matrices that can be written as the Hadamard product of a block partitioned matrix with constant blocks and a rank one matrix. Such matrices arise as the expected adjacency or modularity matrices in certain random graph models that are widely used …
SIAM Journal on Applied Mathematics, vol. 78, pp. 853–876, 2018
Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their …
Linear Algebra and its Applications, vol. 542, pp. 605–623, 2018
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 simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrix-based definitions of the …
SIAM Journal on Matrix Analysis and Applications, vol. 39, pp. 1521–1546, 2018
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 terms of suitable entries of functions of matrices $f(A)$. These kinds of measures are particularly relevant as they are able to capture …
SIAM Journal on Applied Mathematics, vol. 78, pp. 2393–2419, 2018
Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function $Q$ is an established measure quantifying the quality of a community, being identified as a set of nodes having high modularity. In our terminology, a set of nodes with positive …
EMS Journal of Spectral Theory, vol. 8, pp. 883–908, 2018
We consider the nonlinear graph $p$-Laplacian and its set of eigenvalues and associated eigenfunctions of this operator defined by a variational principle. We prove a nodal domain theorem for the graph $p$-Laplacian for any $p\geq 1$. While for $p>1$ the bounds on the number of weak and strong nodal domains are the …
Journal of Mathematical Inequalities, vol. 11, pp. 701–714, 2017
Nodal theorems for generalized modularity matrices ensure that the cluster located by the positive entries of the leading eigenvector of various modularity matrices induces a connected subgraph. In this paper we obtain lower bounds for the modularity of that set of nodes showing that, under certain conditions, the …
Electronic Journal of Linear Algebra, vol. 32, pp. 254–272, 2017
Let $S$ be a column stochastic matrix with at least one full row. Then $S$ describes a Pagerank-like random walk since the computation of the Perron vector $x$ of $S$ can be tackled by solving a suitable M-matrix linear system $Mx = y$, where $M = I − \tau A$, $A$ is a column stochastic matrix and $\tau$ is a positive …
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, pp. 1054–1075, 2017
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order optimization problem subject to the assignment constraints which turns out to be NP-hard. …
Czechoslovak Mathematical Journal, vol. 66, pp. 881–893, 2016
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix $A$. The result exploits the Frobenius inner product between $A$ and a given rank-one landmark matrix $X$. Different choices for $X$ may be used, depending on the problem under investigation. In particular, we show …
Linear Algebra and its Applications, vol. 502, pp. 327–345, 2016
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various …
Advances in Neural Information Processing Systems (NeurIPS), vol. 29, 2016
Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no …
Linear Algebra and its Applications, vol. 496, pp. 510–526, 2016
We prove that the Bernoulli numbers satisfy some special lower triangular Toeplitz systems of linear equations. One of these systems has a strong link with eleven Ramanujan’s linear equations satisfied by the first eleven Bernoulli numbers.
Special Matrices, vol. 3, pp. 175–185, 2015
We investigate two ergodicity coefficients $\phi_{|| \cdot ||}$ and $\tau_{n-1}$, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far. We provide …
Linear Algebra and its Applications, vol. 471, pp. 544–568, 2015
In this paper we study adaptive $L(k)QN$ methods, involving special matrix algebras of low complexity, to solve general (non-structured) unconstrained minimization problems. These methods, which generalize the classical BFGS method, are based on an iterative formula which exploits, at each step, an ad hoc chosen matrix …
Linear Algebra and its Applications, vol. 471, pp. 449–468, 2015
Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of …
SIAM Journal on Matrix Analysis and Applications, vol. 35, pp. 997–1018, 2014
One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the maximization of a quality function called modularity, which in turn is based upon particular quadratic forms associated to a real symmetric …
Linear Algebra and its Applications, vol. 438, pp. 405–427, 2013
When a linear system $Ax = y$ is solved by means of iterative methods (mainly CG and GMRES) and the convergence rate is slow, one may consider a preconditioner $P$. The use of such preconditioner changes the spectrum of the matrix defining the system and could result into a great acceleration of the convergence rate. …
Linear Algebra and its Applications, vol. 435, pp. 2222–2246, 2011
Some spectral properties of the transition matrix of an oriented graph indicate the preconditioning of Euler-Richardson (ER) iterative scheme as a good way to compute efficiently the vertexrank vector associated with such graph. We choose the preconditioner from an algebra $\mathcal U$ of matrices, thereby obtaining an …
