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Dohy Hong

Publications and source records attributed to Dohy Hong.

At least 19 recordsLinked to original sources
arXiv2015

D-Iteration: diffusion approach for solving PageRank

In this paper we present a new method that can accelerate the computation of the PageRank importance vector. Our method, called D-Iteration (DI), is based on the decomposition of the matrix-vector product that can be seen as a fluid diffusion model and is potentially adapted to asynchronous implementation. We give theoretical results about the convergence of our algorithm and we show through experimentations on a real Web graph that DI can improve the computation efficiency compared to other classical algorithm like Power Iteration, Gauss-Seidel or OPIC.

cs.DS↗
arXiv2013

Fast ranking algorithm for very large data

In this paper, we propose a new ranking method inspired from previous results on the diffusion approach to solve linear equation. We describe new mathematical equations corresponding to this method and show through experimental results the potential computational gain. This ranking method is also compared to the well known PageRank model.

cs.DS↗
arXiv2013

Introducing One Step Back Iterative Approach to Solve Linear and Non Linear Fixed Point Problem

In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the coordinates on which the iterative update computations are done. The method requires the increase of the size of the state vectors and one iteration step loss from the initial vector. We illustrate the approach in linear and non linear iterative equations.

math.NA↗
arXiv2013

Convergence of the D-iteration algorithm: convergence rate and asynchronous distributed scheme

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme, including for distributed computation framework. The approach can be understood as a decomposition of the matrix-vector product operation in elementary operations at the vector entry level.

math.NA↗
arXiv2012

Note on the equations of diffusion operators associated to a positive matrix

In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme. The approach can be understood as a decomposition of the matrix-vector product operation in elementary operation at the vector entry level.

math.NA↗
arXiv2012

Publication Induced Research Analysis (PIRA) - Experiments on Real Data

This paper describes the first results obtained by implementing a novel approach to rank vertices in a heterogeneous graph, based on the PageRank family of algorithms and applied here to the bipartite graph of papers and authors as a first evaluation of its relevance on real data samples. With this approach to evaluate research activities, the ranking of a paper/author depends on that of the papers/authors citing it/him or her. We compare the results against existing ranking methods (including methods which simply apply PageRank to the graph of papers or the graph of authors) through the analysis of simple scenarios based on a real dataset built from DBLP and CiteseerX. The results show that in all examined cases the obtained result is most pertinent with our method which allows to orient our future work to optimizing the execution of this algorithm.

cs.DL↗
arXiv2012

Understanding differential equations through diffusion point of view: non-symmetric discrete equations

In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the boundary or initial conditions are replaced by fluid catalysts. It has been shown that pre-computing the diffusion process for an elementary catalyst case as a fundamental block of a class of differential equations, the computation efficiency can be greatly improved. Here, we explain how the diffusion point of view can be applied to decompose the fluid diffusion process per direction and how to handle non-symmetric discrete equations. The method can be applied on the class of problems that can be addressed by the Gauss-Seidel iteration, based on the linear approximation of the differential equations.

math.NA↗
arXiv2012

Revisiting the D-iteration method: runtime comparison

In this paper, we revisit the D-iteration algorithm in order to better explain different performance results that were observed for the numerical computation of the eigenvector associated to the PageRank score. We revisit here the practical computation cost based on the execution runtime compared to the theoretical number of iterations.

math.NA↗
arXiv2012

Understanding differential equations through diffusion point of view

In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the boundary or initial conditions are replaced by fluid catalysts. Pre-computing the diffusion process for an elementary catalyst case as a fundamental block of a class of differential equations, we show that the computation efficiency can be greatly improved. The method can be applied on the class of problems that can be addressed by the Gauss-Seidel iteration, based on the linear approximation of the differential equations.

math.NA↗
arXiv2012

D-iteration: application to differential equations

In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the Gauss-Seidel iteration, based on the linear approximation of the differential equations.

math.NA↗
arXiv2012

Revisiting the D-iteration method: from theoretical to practical computation cost

In this paper, we revisit the D-iteration algorithm in order to better explain its connection to the Gauss-Seidel method and different performance results that were observed. In particular, we study here the practical computation cost based on the execution runtime compared to the theoretical number of iterations. We also propose an exact formula of the error for PageRank class of equations.

math.NA↗
arXiv2012

D-iteration: Evaluation of a Dynamic Partition Strategy

The aim of this paper is to present a first evaluation of a dynamic partition strategy associated to the recently proposed asynchronous distributed computation scheme based on the D-iteration approach. The D-iteration is a fluid diffusion point of view based iteration method to solve numerically linear equations. Using a simple static partition strategy, it has been shown that, when the computation is distributed over K virtual machines (PIDs), the memory size to be handled by each virtual machine decreases linearly with K and the computation speed increases almost linearly with K with a slope becoming closer to one when the number N of linear equations to be solved increases. Here, we want to evaluate how further those results can be improved when a simple dynamic partition strategy is deployed and to show that the dynamic partition strategy allows one to control and equalize the computation load between PIDs without any deep analysis of the matrix or of the underlying graph structure.

cs.DC↗
arXiv2012

D-iteration: evaluation of the update algorithm

The aim of this paper is to analyse the gain of the update algorithm associated to the recently proposed D-iteration: the D-iteration is a fluid diffusion based new iterative method. It exploits a simple intuitive decomposition of the product matrix-vector as elementary operations of fluid diffusion (forward scheme) associated to a new algebraic representation. We show through experimentations on real datasets how much this approach can improve the computation efficiency in presence of the graph evolution.

cs.DM↗
arXiv2012

Optimized on-line computation of PageRank algorithm

In this paper we present new ideas to accelerate the computation of the eigenvector of the transition matrix associated to the PageRank algorithm. New ideas are based on the decomposition of the matrix-vector product that can be seen as a fluid diffusion model, associated to new algebraic equations. We show through experiments on synthetic data and on real data-sets how much this approach can improve the computation efficiency.

cs.DM↗
arXiv2012

D-iteration: Evaluation of the Asynchronous Distributed Computation

The aim of this paper is to present a first evaluation of the potential of an asynchronous distributed computation associated to the recently proposed approach, D-iteration: the D-iteration is a fluid diffusion based iterative method, which has the advantage of being natively distributive. It exploits a simple intuitive decomposition of the matrix-vector product as elementary operations of fluid diffusion associated to a new algebraic representation. We show through experiments on real datasets how much this approach can improve the computation efficiency when the parallelism is applied: with the proposed solution, when the computation is distributed over $K$ virtual machines (PIDs), the memory size to be handled by each virtual machine decreases linearly with $K$ and the computation speed increases almost linearly with $K$ with a slope becoming closer to one when the number $N$ of linear equations to be solved increases.

math.NA↗