Multidamping simulation framework for link-based ranking

We review methods for the approximate computation of PageRank. Standard methods are based on the eigenvector and linear system characterizations. Our starting point are recent methods based on series representation whose coefficients are damping functions, for example Linear Rank, HyperRank and TotalRank, etc. We propose a multidamping framework for interpreting PageRank and these methods. Multidamping is based on some new useful properties of Google type matrices. The approach can be generalized and could help in the exploration of new approximations for list-based ranking. This is joint work with Georgios Kollias and is supported by a Pythagoras-EPEAEK-II grant

Asynchronous iterative computations with Web information retrieval structures: The PageRank case

There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied to the set of pages returned by the Google search engine in response to posting a search query. PageRank is based in part on two simple common sense concepts: (i)A page is important if many important pages include links to it. (ii)A page containing many links has reduced impact on the importance of the pages it links to. In this paper we focus on asynchronous iterative schemes to compute PageRank over large sets of Web pages. The elimination of the synchronizing phases is expected to be advantageous on heterogeneous platforms. The motivation for a possible move to such large scale distributed platforms lies in the size of matrices representing Web structure. In orders of magnitude: $10^{10}$ pages with $10^{11}$ nonzero elements and $10^{12}$ bytes just to store a small percentage of the Web (the already crawled); distributed memory machines are necessary for such computations. The present research is part of our general objective, to explore the potential of asynchronous computational models as an underlying framework for very large scale computations over the Grid. The area of ``internet algorithmics'' appears to offer many occasions for computations of unprecedent dimensionality that would be good candidates for this framework.Comment: 8 pages to appear at ParCo2005 Conference Proceeding

Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse

A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the evaluation of the function is expensive, the task is computationally challenging because the standard approach is based on a Monte Carlo method which converges slowly. We present a different approach that exploits the pattern correlation, if present, between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively. We leverage various sampling and fitting techniques to fit the diagonal of the approximation to the diagonal of the inverse. Depending on the quality of the approximate inverse, our method may serve as a standalone kernel for providing a fast trace estimate with a small number of samples. Furthermore, the method can be used as a variance reduction method for Monte Carlo in some cases. This is decided dynamically by our algorithm. An extensive set of experiments with various technique combinations on several matrices from some real applications demonstrate the potential of our method. (C) 2016 Published by Elsevier Inc

Processor Arrays for Problems in Computational Physics (Parallel)

174 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985.As the cost of hardware components drops, the design and development of processor array systems, consisting of thousands of relatively simple processing elements, becomes possible. An example of such an architecture is the Goodyear Aerospace Massively Parallel Processor, which was originally conceived as a machine to support high-speed image processing. Starting from this existing system configuration, we show how such a design is used very effectively to solve large-scale scientific problems with heavy floating-point computation requirements. Results from the implementation of algorithms for the fast solution of equations occurring in numerical weather prediction and computational fluid dynamics on such systems are presented.The underlying architecture imposes various constraints on the types of problems that may be solved effectively. Consequently, the process of finding efficient methods for circumventing some of these constraints is discussed as an integral part of algorithm design for processor arrays. As a conclusion, possible advancements to the design are indicated that will enhance the architecture to provide an even more effective computational tool.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Asynchronous Computation of PageRank computation in an interactive multithreading environment

Numerical Linear Algebra has become almost indispensable in Web Information Retrieval. In this presentation we suggest that the asynchronous computation model is an attractive paradigm for organizing concurrent computations spanning data on Web scale. This suggestion is supported by experiments which highlight some interesting characteristics of this model as applied to \u27page ranking\u27 methods. After an introduction on asynchronous computing in general and \u27page ranking\u27 in particular, we present results from the asynchronous compution of PageRank using typical combinations of execution units (processes, threads) and communication mechanisms (message passing, shared memory). Sound convergence properties predicted by theory are numerically verified and interesting patterns of behavior are unveiled. Our experiments were performed on Jylab, an evolving environment enabling interactive multithreading and multiprocessing computations. This work is supported by a Pythagoras-EPEAEK-II grant and is conducted in collaboration with Daniel Szyld

CLSI: A flexible approximation scheme from clustered term-document matrices

We investigate a methodology for matrix approximation and IR. A central feature of these techniques is an initial clustering phase on the columns of the term-document matrix, followed by partial SVD on the columns constituting each cluster. The extracted information is used to build effective low rank approximations to the original matrix as well as for IR. The algorithms can be expressed by means of rank reduction formulas. Experiments indicate that these methods can achieve good overall performance for matrix approximation and IR and compete well with existing schemes. Keywords: Low rank approximations, Clustering, LSI. 1 Introduction an