Related papers: Computing the smallest eigenpairs of the graph Lap…
The spectral properties of the Laplacian operator on ``small-world'' lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a…
The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…
Quantifying the relations (e.g., similarity) between complex networks paves the way for studying the latent information shared across networks. However, fundamental relation metrics are not well-defined between networks. As a compromise,…
The Lanczos method with implicit restarting is one of the most popular methods for finding a few exterior eigenpairs of a large symmetric matrix $A$. Usually based on polynomial filtering, restarting is crucial to limit memory and the cost…
An efficient and relatively fast algorithm for the detection of communities in complex networks is introduced. The method exploits spectral properties of the graph Laplacian-matrix combined with hierarchical-clustering techniques, and…
We develop a formalism to compute the statistics of the second largest eigenpair of weighted sparse graphs with $N\gg 1$ nodes, finite mean connectivity and bounded maximal degree, in cases where the top eigenpair statistics is known. The…
This paper presents a parallel algorithm for finding the smallest eigenvalue of a particular form of ill-conditioned Hankel matrix, which requires the use of extremely high precision arithmetic. Surprisingly, we find that commonly-used…
In this paper, we investigate synchronization in a small-world network of coupled nonlinear oscillators. This network is constructed by introducing random shortcuts in a nearest-neighbors ring. The local stability of the synchronous state…
We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. After considering classical graphs for which the spectrum is known, we focus on…
We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…
We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication…
For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…
We consider a Canonical Polyadic (CP) decomposition approach to low-rank tensor completion (LRTC) by incorporating external pairwise similarity relations through graph Laplacian regularization on the CP factor matrices. The usage of graph…
The problem of connectivity assessment in an asymmetric network represented by a weighted directed graph is investigated in this article. A power iteration algorithm in a centralized implementation is developed first to compute the…
We present sharp inequalities relating the number of vertices, edges, and triangles of a graph to the smallest eigenvalue of its adjacency matrix and the largest eigenvalue of its Laplacian.
We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution $\rho$ supported on a manifold $M$. The operators discussed in the paper are relevant in unsupervised learning and in particular…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
The grounded Laplacian matrix $\LL_{-S}$ of a graph $\calG=(V,E)$ with $n=|V|$ nodes and $m=|E|$ edges is a $(n-s)\times (n-s)$ submatrix of its Laplacian matrix $\LL$, obtained from $\LL$ by deleting rows and columns corresponding to…
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method to compute a few eigenvalues of a Hermitian matrix $A$. It falls in the category of inner-outer…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…