Matrices, Vector Spaces, and Information Retrieval

The evolution of digital libraries and the Internet has dramatically transformed the processing, storage, and retrieval of information. Efforts to digitize text, images, video, and audio now consume a substantial portion of both academic and industrial activity. Even when there is no shortage of tex...

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Bibliographic Details
Published in:SIAM review 1999-06, Vol.41 (2), p.335-362
Main Authors: Berry, Michael W., Drmač, Zlatko, Jessup, Elizabeth R.
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Approximation
Baking
Computer science
control theory
systems
Cosine function
Education
Exact sciences and technology
Factorization
Information retrieval
Information retrieval. Graph
Linear and multilinear algebra, matrix theory
Linear programming
Mathematical vectors
Mathematics
Matrices
Matrix
Memory organisation. Data processing
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Software
Theoretical computing
Vector space models
Vector spaces
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Summary:The evolution of digital libraries and the Internet has dramatically transformed the processing, storage, and retrieval of information. Efforts to digitize text, images, video, and audio now consume a substantial portion of both academic and industrial activity. Even when there is no shortage of textual materials on a particular topic, procedures for indexing or extracting the knowledge or conceptual information contained in them can be lacking. Recently developed information retrieval technologies are based on the concept of a vector space. Data are modeled as a matrix, and a user's query of the database is represented as a vector. Relevant documents in the database are then identified via simple vector operations. Orthogonal factorizations of the matrix provide mechanisms for handling uncertainty in the database itself. The purpose of this paper is to show how such fundamental mathematical concepts from linear algebra can be used to manage and index large text collections.
ISSN:0036-1445
1095-7200
DOI:10.1137/S0036144598347035