Related papers: Spectral Ranking
This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses…
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link function is possibly infinite rank and also possibly…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
In this paper we consider so-called Google matrices and show that all eigenvalues ($\lambda$) of them have a fundamental property $|\lambda|\leq 1$. The stochastic eigenvector corresponding to $\lambda=1$ called the PageRank vector plays a…
Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…
The purpose of the research is to find a centrality measure that can be used in place of PageRank and to find out the conditions where we can use it in place of PageRank. After analysis and comparison of graphs with a large number of nodes…
Square matrices often arise in microeconomics, particularly in network models addressing applications from opinion dynamics to platform regulation. Spectral theory provides powerful tools for analyzing their properties. We present an…
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the…
Spectral network identification aims at inferring the eigenvalues of the Laplacian matrix of a network from measurement data. This allows to capture global information on the network structure from local measurements at a few number of…
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture…
We provide a detailed description of the maps associated with spectral interlacing, for rank one perturbations and bordering of symmetric and Hermitian matrices. The arguments rely on standard techniques of nonlinear analysis.
Semantic networks qualify the meaning of an edge relating any two vertices. Determining which vertices are most "central" in a semantic network is difficult because one relationship type may be deemed subjectively more important than…
Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however,…
Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal…
There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…
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…
Spectral graph theory gives an algebraical approach to analyze the dynamics of a network by using the matrix that represents the network structure. However, it is not easy for social networks to apply the spectral graph theory because the…