Mathematical Foundations of Information Retrieval

Background InformationRetrieval (IR) has become, mainly as aresultofthe huge impact of the World Wide Web (WWW) and CD-ROM industry, one of the most important theoretical and practical research topics in Information and Computer Science. Since the inception ofits first theoretical roots about 40 years ago, IR has made avariety ofpractical, experimental and technological advances. It is usually defined as being concerned with the organisation, storage, retrieval and evaluation of information (stored in computer databases) that is likely to be relevant to users' informationneeds (expressed in queries). A huge number ofarticles published in specialisedjournals and at conferences (such as, for example, the Journal of the American Society for Information Science, Information Processing and Management, The Computer Journal, Information Retrieval, Journal of Documentation, ACM TOIS, ACM SIGIR Conferences, etc. ) deal with many different aspects of IR. A number of books have also been written about IR, for example: van Rijsbergen, 1979; Salton and McGill, 1983; Korfhage, 1997; Kowalski, 1997;Baeza-Yates and Ribeiro-Neto, 1999; etc. . IR is typically divided and presented in a structure (models, data structures, algorithms, indexing, evaluation, human-eomputer interaction, digital libraries, WWW-related aspects, and so on) thatreflects its interdisciplinarynature. All theoretical and practical research in IR is ultimately based on a few basic models (or types) which have been elaborated over time. Every model has a formal (mathematical, algorithmic, logical) description of some sort, and these decriptions are scattered all over the literature.

Klappentext

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. br/ emAudience:/em The book will be of interest to computer or information scientists, librarians, mathematicians, undergraduate students and researchers whose work involves information retrieval.

Inhalt

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.