Mathematical Foundations of Information Retrieval

Inhaltsverzeichnis

• 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.
• 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.