Education

Abstract

When you think of searching for information on the Web, you probably think of search engines such as Google. But do you think of eigenvectors? You should! Faithful readers of the Education section may recall the connection between information retrieval and numerical linear algebra from the second issue of the Education section, in 1999. In the article "Matrices, Vector Spaces, and Information Retrieval" (volume 41, pp. 335--362), Berry, Drmac, and Jessup described the use of latent semantic analysis, which is based upon the singular value decomposition, for searching document collections. The paper in this issue's Education section, "A Survey of Eigenvector Methods for Web Information Retrieval," extends this topic to the modern world of the Web. As the authors, Amy Langville and Carl Meyer, point out, information retrieval on the Web is significantly more challenging and difficult than information retrieval in a collection of documents, due to the enormous scale of the information space, the critical role of the hyperlink structure of the Web, and the greater fluidity of the space. Their paper summarizes the main approaches that have been taken to ranking Web pages in response to queries in search engines. It shows readily that the two basic approaches both lead to an eigenvector problem that is naturally solved by the power method. In the case of the PageRank method used by Google, this problem can have several billion variables! Fortunately, it does not have to be solved very often. The paper provides examples of the use of many concepts in matrix algebra, including stochastic and irreducible matrices. It also points to various promising areas for additional research. As such, it will be useful both in introductory numerical analysis and numerical linear algebra courses, where its very pleasant style and real-world context should make it popular with students, and in more advanced courses where it will provide a foundation for deeper study. It is fitting that as this paper on information retrieval brings the Education section full circle after six years, leadership of the section is changing hands. By the time this issue is published, the Section Editor role will be in the very capable hands of Professor Andrew Bernoff of Harvey Mudd College. It has been a true pleasure serving as editor of this section, due to the wonderful support of the SIAM staff (thanks particularly to Brian Fauth, Lou Primus, Mitch Chernoff, and Mary Rose Muccie), to a superb editorial board, and, most of all, to the many authors who have contributed their excellent work to SIAM Review. Thanks so much to all of you!