We consider the problem of estimating a network's eigenvector centrality only from data on nodes, with no information about network topology. Leveraging versatility graph filters to model processes, supported nodes is modeled as signal obtained via output filter applied white noise. seek simplify downstream task ranking by bypassing topology inference methods and, instead, inferring structure d...

In this paper, we analyze the second eigenvector technique of spectral partitioning on the planted partition random graph model, by constructing a recursive algorithm using the second eigenvectors in order to learn the planted partitions. The correctness of our algorithm is not based on the ratio-cut interpretation of the second eigenvector, but exploits instead the stability of the eigenvector...

We develop majorization results that characterize changes in eigenvector components of a graph’s adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterize changes in dominant eigenvector components for single-row and multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of th...

Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed enable new studies of fundamental science as well more potential applications. In this work we discuss solving a system constraint equations efficiently using self-learning emulator. A emulator is an active learning protocol be used any faithfully reproduces the exact solution at selected tr...

Recursive spectral bisection (RSB) is a heuristic technique for finding a minimum cut graph bisection. To use this method the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector to induce a bisection. We prove here that this median cut method is optimal in the se...

The purpose of this report is to investigate the possibilities for accurate computation of eigenvectors of (unsymmetric) oscillatory matrices. The goal is to decide what “accurate” means, to determine whether the eigenvectors are determined “accurately” in that sense, and to engineer algorithms that will guarantee that accuracy. It is desirable for the computed eigenvector matrix to inherit the...