Another look at automatic text-retrieval systems
Communications of the ACM
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Term-weighting approaches in automatic text retrieval
Information Processing and Management: an International Journal
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Generalized vector spaces model in information retrieval
SIGIR '85 Proceedings of the 8th annual international ACM SIGIR conference on Research and development in information retrieval
A language modeling approach to information retrieval
Proceedings of the 21st annual international ACM SIGIR conference on Research and development in information retrieval
Understanding search engines: mathematical modeling and text retrieval
Understanding search engines: mathematical modeling and text retrieval
A vector space model for automatic indexing
Communications of the ACM
Information Retrieval
Modern Information Retrieval
Text Information Retrieval Systems
Text Information Retrieval Systems
Fuzzy Measure Theory
Vector space model of information retrieval: a reevaluation
SIGIR '84 Proceedings of the 7th annual international ACM SIGIR conference on Research and development in information retrieval
The Geometry of Information Retrieval
The Geometry of Information Retrieval
Discriminative models for information retrieval
Proceedings of the 27th annual international ACM SIGIR conference on Research and development in information retrieval
Hi-index | 0.00 |
The vector space model of information retrieval is one of the classical and widely applied retrieval models. Paradoxically, it has been characterized by a discrepancy between its formal framework and implementable form. The underlying concepts of the vector space model are mathematical terms: linear space, vector, and inner product. However, in the vector space model, the mathematical meaning of these concepts is not preserved. They are used as mere computational constructs or metaphors. Thus, the vector space model actually does not follow formally from the mathematical concepts on which it has been claimed to rest. This problem has been recognized for more than two decades, but no proper solution has emerged so far. The present article proposes a solution to this problem. First, the concept of retrieval is defined based on the mathematical measure theory. Then, retrieval is particularized using fuzzy set theory. As a result, the retrieval function is conceived as the cardinality of the intersection of two fuzzy sets. This view makes it possible to build a connection to linear spaces. It is shown that the classical and the generalized vector space models, as well as the latent semantic indexing model, gain a correct formal background with which they are consistent. At the same time it becomes clear that the inner product is not a necessary ingredient of the vector space model, and hence of Information Retrieval (IR). The Principle of Object Invariance is introduced to handle this situation. Moreover, this view makes it possible to consistently formulate new retrieval methods: in linear space with general basis, entropy-based, and probability-based. It is also shown that Information Retrieval may be viewed as integral calculus, and thus it gains a very compact and elegant mathematical way of writing. Also, Information Retrieval may thus be conceived as an application of mathematical measure theory. © 2007 Wiley Periodicals, Inc.