Link prediction is a fundamental challenge in network science. Among various methods, similarity-based algorithms are popular for their simplicity, interpretability, high efficiency and good performance. In this paper, we show that the most elementary local similarity index Common Neighbor (CN) can be linearly decomposed by eigenvectors of adjacency matrix target network, with each eigenvector’...

The pattern-recognition algorithms based on eigenvector analysis (group 2) are theoretically and experimentally compared. Group 2 consists of Foley-Sammon (F-S) transform, Hotelling trace criterion (HTC), FukunagaKoontz (F-K) transform, linear discriminant function (LDF), and generalized matched filter (GMF) algorithms. It is shown that all eigenvector-based algorithms can be represented in a g...

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of n observations (samples), each with p variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation between the eigenvalues and eigenvectors of PCA computed on a finite sample of size n, and those of the limiting population PCA as n→∞. As in machine learning, we pres...

This study aims to analyze the characteristics of global virtual water trade (GVWT), such as the connectivity of each trader, vulnerable importers, and influential countries, using degree and eigenvector centrality during the period 2006–2010. The degree centrality was used to measure the connectivity, and eigenvector centrality was used to measure the influence on the entire GVWT network. Mexi...

We solve the inverse problem corresponding to fundamental of classical dynamics a material particle through matrix treatment: assuming knowing mass and position (the trajectory, in relation an inertial reference) at all times, we impose that this corresponds eigenvector “position matrix". Subsequent development leads “force matrix", which has resultant force on as its eigenvector. identified so...

Eigenvector centrality is a linear algebra based graph invariant used in various rating systems such as webpage ratings for search engines. A generalization of the eigenvector centrality invariant is defined which is motivated by the need to design rating systems for bipartite graph models of time-sensitive and other processes. The linear algebra connection and some applications are described.

This note gives converses to the well-known result: for any vector e u such that sin (u; e u) = O( ), we have e u Ae u e u e u = + O( ) where is an eigenvalue and u is the corresponding eigenvector of a Hermitian matrix A, and \ " denotes complex conjugate transpose. It shows that if e u Ae u=e u e u is close to A's largest eigenvalue, then e u is close to the corresponding eigenvector with an ...