相关论文: A Note on the Eigenvalues of the Google Matrix
In this paper, we discuss the sensitivity of quantum PageRank. By using the finite dimensional perturbation theory, we estimate the change of the quantum PageRank under a small analytical perturbation on the Google matrix. In addition, we…
A new methodology has been introduced to clean the correlation matrix of single stocks returns based on a constrained principal component analysis using financial data. Portfolios were introduced, namely "Fundamental Maximum Variance…
We present new algorithms for Personalized PageRank estimation and Personalized PageRank search. First, for the problem of estimating Personalized PageRank (PPR) from a source distribution to a target node, we present a new bidirectional…
Let $G = (V, E)$ be a graph. We define matrices $M(G; \alpha, \beta)$as $\alpha D + \beta A$, where $\alpha$, $\beta$ are real numbers such that $(\alpha, \beta) \neq (0, 0)$ and $D$ and $A$ are the diagonal matrix and adjacency matrix of…
Web search data are a valuable source of business and economic information. Previous studies have utilized Google Trends web search data for economic forecasting. We expand this work by providing algorithms to combine and aggregate search…
This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matrix sum is dominated by the maximum eigenvalue of a Gaussian…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
We study algorithms called rank-revealers that reveal a matrix's rank structure. Such algorithms form a fundamental component in matrix compression, singular value estimation, and column subset selection problems. While column-pivoted QR…
In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First,…
Matrix game, which is also known as two person zero sum game, is a famous model in game theory. There are some well established theories about it, such as von Neumann minimax theorem. However, almost no literature have reported the…
Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world…
We study the map which takes an elementwise positive matrix to the k-th root of the principal eigenvector of its k-th Hadamard power. We show that as $k$ tends to 0 one recovers the row geometric mean vector and discuss the geometric…
We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The…
In this paper, we develop a new technique which we call representation theory of the real hyperrectangle, which describes how to compute the eigenvectors and eigenvalues of certain matrices arising from hyperrectangles. We show that these…
In this paper we have modified the existing page ranking mechanism as an advanced Page Rank Algorithm based on Semantics Inlinks Outlinks and Google Analytics. We have used Semantics page ranking to rank pages according to the word searched…
A particle-swarm is a set of indivisible processing elements that traverse a network in order to perform a distributed function. This paper will describe a particular implementation of a particle-swarm that can simulate the behavior of the…
We apply the Google PageRank algorithm to assess the relative importance of all publications in the Physical Review family of journals from 1893--2003. While the Google number and the number of citations for each publication are positively…
We review our recent work on applying the Google PageRank algorithm to find scientific "gems" among all Physical Review publications, and its extension to CiteRank, to find currently popular research directions. These metrics provide a…
It is known that for a totally positive (TP) matrix, the eigenvalues are positive and distinct and the eigenvector associated with the smallest eigenvalue is totally nonzero and has an alternating sign pattern. Here, a certain weakening of…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…