相关论文: On Joint Diagonalisation for Dynamic Network Analy…

Given a set of $p$ symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these $p$ matrices is as close as possible to a diagonal…

Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…

Joint diagonalization of a set of positive (semi)-definite matrices has a wide range of analytical applications, such as estimation of common principal components, estimation of multiple variance components, and blind signal separation.…

We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these…

This paper studies large-scale dynamical networks where the current state of the system is a linear transformation of the previous state, contaminated by a multivariate Gaussian noise. Examples include stock markets, human brains and gene…

Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure…

The approximate joint diagonalization (AJD) is an important analytic tool at the base of numerous independent component analysis (ICA) and other blind source separation (BSS) methods, thus finding more and more applications in medical…

We study the problem of maximum-likelihood (ML) estimation of an approximate common eigenstructure, i.e. an approximate common eigenvectors set (CES), for an ensemble of covariance matrices given a collection of their associated i.i.d…

Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer…

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…

We revisit the problem of spectral clustering in multimodal settings, where each data modality is encoded as a graph Laplacian. While classical approaches--including joint diagonalization, spectral co-regularization, and multiview…

These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…

Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…

Dynamic networks reflect temporal changes occurring to the graph's structure and are used to model a wide variety of problems in many application fields. We investigate the design space of dynamic graph visualization along two major…

Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…

This paper deals with a hybrid joint diagonalization (JD) problem considering both Hermitian and transpose congruences. Such problem can be encountered in certain non-circular signal analysis applications including blind source separation.…

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the…

A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…

Domain generalization (DG) is a fundamental yet very challenging research topic in machine learning. The existing arts mainly focus on learning domain-invariant features with limited source domains in a static model. Unfortunately, there is…