Mathematical Foundations of Information Retrieval

by S. Dominich

Overview

This book offers a comprehensive and consistent mathematical approach to information retrieval (IR) without which no implementation is possible, and sheds an entirely new light upon the structure of IR models. It contains the descriptions of all IR models in a unified formal style and language, along with examples for each, thus offering a comprehensive overview of them. The book also creates mathematical foundations and a consistent mathematical theory (including all mathematical results achieved so far) of IR as a stand-alone mathematical discipline, which thus can be read and taught independently. Also, the book contains all necessary mathematical knowledge on which IR relies, to help the reader avoid searching different sources.
Audience: The book will be of interest to computer or information scientists, librarians, mathematicians, undergraduate students and researchers whose work involves information retrieval.

Product Details

ISBN-13:	9789401038195
Publisher:	Springer Netherlands
Publication date:	10/02/2012
Series:	Mathematical Modelling: Theory and Applications , #12
Edition description:	2001
Pages:	284
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Introduction.- 1. Information Retrieval.- 2. Information Retrieval MODELS.- 3. Mathematics in Information Retrieval Models.- 4. Relevance in Information Retrieval.- 5. Interaction Information Retrieval.- 6. Mathematical Foundation of Information Retrieval.- 2. Mathematics Handbook.- 1. Logics.- 2. SET THEORY.- 3. RELATIONS.- 4. FUNCTION.- 5. Family of Sets.- 6. Algebra.- 7. Calculus.- 8. Differential Equations.- 9. Vectors.- 10. Probability.- 11. Fuzzy Sets.- 12. Metric Spaces.- 13. Topology.- 14. Graph Theory.- 15. Matroid Theory.- 16. Recursion and Complexity Theory.- 17. Artificial Neural Network.- 3. Information Retrieval Models.- 1. Classical Models of Information Retrieval.- 2. Nonclassical Models of Information Retrieval.- 3. Alternative Models of Information Retrieval.- 4. Traditional Tree Structure of Information Retrieval Models.- 4. Mathematical Theory of Information Retrieval.- 1. Information Retrieval Frame.- 2. Classical Information Retrieval.- 3. Similarity (vector space) Information Retrieval.- 4. Probabilistic Information Retrieval.- 5. Interaction Information Retrieval.- 6. Boolean Information Retrieval.- 7. Network Structure of Information Retrieval Models.- 5. Relevance Effectiveness in Information Retrieval.- 1. RELEVANCE.- 2. Effectiveness Measures.- 3. Relevance Feedback.- 4. Mathematical Structure in Relevance Feedback.- 5. OPTIMALITY.- 6. Further Topics in Information Retrieval.- 1. Information Retrieval and Decision Making.- 2. Data Fusion.- 3. Interaction and Situation Theory Models.- Appendix 1 Binary Similarity Information Retrieval.- Non-Binary Similarity Information Retrieval (NBSIR).- Appendix 2 Probabilistic Information Retrieval.- Appendix 3 Interaction Information Retrieval.- References.