CAREER: Updating Problems in Information Retrieval and a Mathematical Dissection Lab

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ABSTRACT0546622Amy LangvilleCollege of CharlestonUpdating Problems in Information Retrieval and a Mathematical Dissection LabThis proposal is about information retrieval, the field of organizing information in order to retrievedocuments relating to a specific information need. Information retrieval is divided into two categories: re-trieval from web collections and retrieval from smaller, nonlinked document collections, called traditionalcollections. Both types of retrieval, web and traditional, share at least one common problem: the updatingproblem. Any time a document collection changes, which inevitably happens often as documents are mod-ified, added, or deleted, several items must be updated, including performance measures, storage files, andmemory pointers. Of the many types of updating problems, this proposal deals with mathematical updatingproblems. A mathematical updating problem for web retrieval that has impact for any application, such aspopulation modeling, webpage ranking, graph theoretic measures, and email analysis, that uses the domi-nant eigenvector of a large, sparse, nonnegative matrix will be studied. For traditional information retrieval,the project will study an updating problem regarding the so-called nonnegative matrix factorization (NMF),which has impact on the many other fields to which the NMF has been applied including image processing,fingerprint query processing, music processing, signal processing, movie animations, machine learning, datamining, and summary extraction for audio and video data. This research will be enhanced by a partnershipwith SAS Institute, Inc.The Education Phase of this project proposes the design and implementation of a Mathematical DeviceDissection Lab. The proposed lab, which is similar in spirit to the mechanical dissection labs found in manyengineering schools, aims to solve a common problem with students perception of mathematics: studentsthink mathematics is merely about calculation, not concepts. To remedy this, the proposed lab allowsstudents to dissect in a hands-on, interactive manner virtual mathematical devices that demonstrate theuse of fundamental concepts. The lab requires self-study by groups of students, and as such, mimics theresearch skills needed in the real world. This lab relates to the Research Phase of this project as three ofthe labs nine modules will come from the above research in information retrieval. Each module describesa virtual mathematical device. Examples include least squares, the vector space model of informationretrieval, and Googles method of ranking webpages. All modules must be able to be described in lowdimensional space, so that students can visualize the ideas, after which point, they will understand thepower of mathematics to enable extensions to higher dimensional space. Modules also contain a scientificcomputation component as the students extend the simple models to much larger problems. Each modulewill be posted on a website, making the modules available for worldwide dissemination and adaptation. Inaddition, the lab will be used in several outreach projects. One of the labs goals is to change studentsattitudes towards mathematics by demystifying the process of mathematical invention, showing them thatmathematics is more than mere calculation, it is a creative process with broad applications.