Gianna M. Del Corso

Ranking a stream of news

According to a recent survey made by Nielsen NetRatings, searching on news articles is one of the most important activity online. Indeed, Google, Yahoo, MSN and many others have proposed commercial search engines for indexing news feeds. Despite this commercial interest, no academic research has focused on ranking a stream of news articles and a set of news sources. In this paper, we introduce this problem by proposing a ranking framework which models: (1) the process of generation of a stream of news articles, (2) the news articles clustering by topics, and (3) the evolution of news story over the time. The ranking algorithm proposed ranks news information, finding the most authoritative news sources and identifying the most interesting events in the different categories to which news article belongs. All these ranking measures take in account the time and can be obtained without a predefined sliding window of observation over the stream. The complexity of our algorithm is linear in the number of pieces of news still under consideration at the time of a new posting. This allow a continuous on-line process of ranking. Our ranking framework is validated on a collection of more than 300,000 pieces of news, produced in two months by more then 2000 news sources belonging to 13 different categories (World, U.S, Europe, Sports, Business, etc). This collection is extracted from the index of comeToMyHead, an academic news search engine available online.

Fast PageRank Computation Via a Sparse Linear System

Recently, the research community has devoted increased attention to reducing the computational time needed by web ranking algorithms. In particular, many techniques have been proposed to speed up the well-known PageRank algorithm used by Google. This interest is motivated by two dominant factors: (1) the web graph has huge dimensions and is subject to dramatic updates in terms of nodes and links, therefore the PageRank assignment tends to became obsolete very soon; (2) many PageRank vectors need to be computed according to different choices of the personalization vectors or when adopting strategies of collusion detection. In this paper, we show how the PageRank computation in the original random surfer model can be transformed in the problem of computing the solution of a sparse linear system. The sparsity of the obtained linear system makes it possible to exploit the effectiveness of the Markov chain index reordering to speed up the PageRank computation. In particular, we rearrange the system matrix according to several permutations, and we apply different scalar and block iterative methods to solve smaller linear systems. We tested our approaches on web graphs crawled from the net. The largest one contains about 24 millions nodes and more than 100 million links. Upon this web graph, the cost for computing the PageRank is reduced by 65% in terms of Mflops and by 92% in terms of time respect to the power method commonly used.

Estimating an Eigenvector by the Power Method with a Random Start

This paper addresses the problem of approximating an eigenvector belonging to the largest eigenvalue of a symmetric positive definite matrix by the power method. We assume that the starting vector is randomly chosen with uniform distribution over the unit sphere. This paper provides lower and upper as well as asymptotic bounds on the randomized error in the

Qd-type methods for quasiseparable matrices

{\cal L}_p

Inversion of circulant matrices over Z m

sense,

Heuristic Spectral Techniques for the reduction of Bandwidth and Work-bound of Sparse Matrices

p\in[1,+\infty]

A multi-class approach for ranking graph nodes

. We prove that it is impossible to achieve sharp bounds that are independent of the ratio between the two largest eigenvalues. This should be contrasted to the problem of approximating the largest eigenvalue, for which Kuczynski and Wozniakowski [ SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1094--1122] proved that it is possible to bound the randomized error at the kth step with a quantity that depends only on k and on the size of the matrix. We prove that the rate of convergence depends on the ratio of the two largest eigenvalues, on their multiplicities, and on the particular norm. The rate of convergence is at most linear in the ratio of the two largest eigenvalues.

A combined approach for evaluating papers, authors and scientific journals

In the last few years many numerical techniques for computing eigenvalues of structured rank matrices have been proposed. Most of them are based on QR iterations since, in the symmetric case, the rank structure is preserved and high accuracy is guaranteed. In the unsymmetric case, however, the QR algorithm destroys the rank structure, which is instead preserved if LR iterations are used. We consider a wide class of quasiseparable matrices which can be represented in terms of the same parameters involved in their Neville factorization. This class, if assumptions are made to prevent possible breakdowns, is closed under LR steps. Moreover, we propose an implicit shifted LR method with a linear cost per step, which resembles the qd method for tridiagonal matrices. We show that for totally nonnegative quasiseparable matrices the algorithm is stable and breakdowns cannot occur if the Laguerre shift, or other shift strategy preserving nonnegativity, is used. Computational evidence shows that good accuracy is obt...

An Implicit Multishift

In this paper we consider the problem of inverting an n × n circulant matrix with entries over Zm. We show that the algorithm for inverting circulants, based on the reduction to diagonal form by means of FFT, has some drawbacks when working over Zm. We present three different algorithms which do not use this approach. Our algorithms require different degrees of knowledge of m and n, and their costs range - roughly - from n log n log log n to n log2 n log log n log m operations over Zm. We also present an algorithm for the inversion of finitely generated bi-infinite Toeplitz matrices. The problems considered in this paper have applications to the theory of linear Cellular Automata.

QR

In this paper, we present heuristic techniques for the reduction of the bandwidth of a sparse matrix as well as for the reduction of the cost of the associated Cholesky factorization. Our algorithms are inspired by the spectral method of Barnard, Pothen and Simon (1995), which derives a permutation for reducing the envelope-size of a sparse matrix by computing the second eigenvector of the associated Laplacian matrix. Two main modifications of that method are proposed and tested. The first is based on the experimental observation that it is often preferable to perform only few iterations of an iterative method converging to the second eigenvector; the second is the introduction of a weighted Laplacian. These simple ideas allow us to obtain a family of spectral methods that have been carefully tested on a set of matrices whose size ranges from few hundred to one million.