| Titre : | Matrice Stochastique Et Applications Au Problème De Page Rank | | Type de document : | projet fin études | | Auteurs : | Benkou Soumia, Auteur | | Langues : | Français (fre) | | Catégories : | BIG DATA
| | Index. décimale : | mast 275/19 | | Résumé : | The stochastic matrix is a matrix that has a great importance in the computer field through its uses. Among these are the Page Rank algorithm founded by Larry Page and Sergey Brin, which Google uses to classify web pages according to their relevance and the links between them.
The Page Rank algorithm calculates a vector of positive real numbers by considering navigation as a graph whose nodes are the web pages and arcs are the links that connect to each other. The same algorithm models the navigation on the Internet by the Markovian chain which makes it possible to calculate the stationary distribution of the studied chain which presents the probability of following the links proposed by a page.
In this modest work, we will talk about matrix algebra reminders while introducing the stochastic matrix and its properties, the Page Rank and its definition, its algorithm and how to use it in different situations.
The Markovian chain models Internet browsing in the case of irreducibility and aperiodicity, which makes it possible to determine the page ranking vector as being the stationary distribution of this chain.
The probability of following or not the proposed links represents the parameter of the Page Rank algorithm which makes it numerically stable.
The first chapter is devoted to the mathematical reminder of the basic notions necessary for the study of Page Rank.
The second chapter talks about the Page Rank model and its properties.
The third chapter introduces the Page Rank model and the fourth chapter is devoted to the algorithm.
In the last chapter, we talked about two examples of Page Rank and how they work.
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Matrice Stochastique Et Applications Au Problème De Page Rank [projet fin études] / Benkou Soumia, Auteur . - [s.d.]. Langues : Français ( fre) | Catégories : | BIG DATA
| | Index. décimale : | mast 275/19 | | Résumé : | The stochastic matrix is a matrix that has a great importance in the computer field through its uses. Among these are the Page Rank algorithm founded by Larry Page and Sergey Brin, which Google uses to classify web pages according to their relevance and the links between them.
The Page Rank algorithm calculates a vector of positive real numbers by considering navigation as a graph whose nodes are the web pages and arcs are the links that connect to each other. The same algorithm models the navigation on the Internet by the Markovian chain which makes it possible to calculate the stationary distribution of the studied chain which presents the probability of following the links proposed by a page.
In this modest work, we will talk about matrix algebra reminders while introducing the stochastic matrix and its properties, the Page Rank and its definition, its algorithm and how to use it in different situations.
The Markovian chain models Internet browsing in the case of irreducibility and aperiodicity, which makes it possible to determine the page ranking vector as being the stationary distribution of this chain.
The probability of following or not the proposed links represents the parameter of the Page Rank algorithm which makes it numerically stable.
The first chapter is devoted to the mathematical reminder of the basic notions necessary for the study of Page Rank.
The second chapter talks about the Page Rank model and its properties.
The third chapter introduces the Page Rank model and the fourth chapter is devoted to the algorithm.
In the last chapter, we talked about two examples of Page Rank and how they work.
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Matrice Stochastique Et Applications Au Problème De Page Rank / Benkou Soumia
