The linear algebra behind Google

• Autor(a) principal: Bah, Tijan
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Texto Completo: http://hdl.handle.net/10773/41897
• topic: PageRank; Linear algebra; Eigenvector; Eigenvalues; Google matrix; Link matrix

Google PageRank model helps evaluate the relative importance of nodes in a large graph, such as the graph of links on the World Wide Web. An important piece of the PageRank model is the damping factor d. Google relies on foundational concepts from linear algebra to evaluate and rank web pages based on their importance and relevance. In this thesis, the underlying mathematical basics for understanding how the algorithms function are provided. The concept of graphs and matrix theories are in the background, while the most important steps are in a linear algebra context especially the eigenvalue and eigenvectors of a matrix. It discusses the power iteration algorithm as an iterative method for finding the principal eigenvector, which represents PageRank scores. Google PageRank model helps evaluate the relative importance of nodes in a large graph, such as the graph of links on the World Wide Web. An important piece of the PageRank model is the damping factor d. Google relies on foundational concepts from linear algebra to evaluate and rank web pages based on their importance and relevance. In this thesis, the underlying mathematical basics for understanding how the algorithms function are provided. The concept of graphs and matrix theories are in the background, while the most important steps are in a linear algebra context especially the eigenvalue and eigenvectors of a matrix. It discusses the power iteration algorithm as an iterative method for finding the principal eigenvector, which represents PageRank scores.