Mathematical foundations of information retrieval:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
2001
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| Schriftenreihe: | Mathematical modelling
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 284 S. graph. Darst. |
| ISBN: | 0792368614 |
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Datensatz im Suchindex
| _version_ | 1809403458351005696 |
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MATHEMATICAL FOUNDATIONS OF INFORMATION RETRIEVAL BY SANDOR DOMINICH
UNIVERSITY OF VESZPREM, DEPARTMENT OF COMPUTER SCIENCE, VESZPREM,
HUNGARY AND BUCKINGHAMSHIRE CHILTEMS UNIVERSITY COLLEGE, HIGH WYCOMBE,
UNITED KINGDOM KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
CONTENTS PREFACE XV ACKNOWLEDGMENTS 1 CHAPTER 1. INTRODUCTION 3 1.
INFORMATION RETRIEVAL 3 2. INFORMATION RETRIEVAL MODELS 7 3. MATHEMATICS
IN INFORMATION RETRIEVAL MODELS 8 4. RELEVANCE IN INFORMATION RETRIEVAL
12 5. INTERACTION INFORMATION RETRIEVAL 15 6. MATHEMATICAL FOUNDATION OF
INFORMATION RETRIEVAL 19 CHAPTER 2. MATHEMATICS HANDBOOK 25 1. LOGICS 26
1.1 MATHEMATICAL LOGIC (CLASSICAL FIRST ORDER LOGIC) 26 1.1.1
PROPOSITIONAL CALCULUS 26 1.1.1.1 PROPOSITION 26 1.1.1.2 NEGATION 26
1.1.1.3 CONJUNCTION 27 1.1.1.4 DISJUNCTION 27 1.1.1.5 IMPLICATION
(SUBJUNCTION, CONDITIONAL) 27 1.1.1.6 EQUIVALENCE (BI-CONDITIONAL) 28
1.1.1.7 CONTRADICTION 28 1.1.1.8 TAUTOLOGY 28 1.1.1.9 RULES OF INFERENCE
29 1.1 1.1.2 1.1 .1.10 .2.1 1.1.2.2 1.1 .2.3 NORMAL FORM PREDICATE
CALCULUS PREDICATE QUANTIFIERS PROPERTIES VIII MATHEMATICAL FOUNDATIONS
OFIR 31 31 31 31 32 1.2 NON-CONVENTIONAL LOGICS 32 1.2.1 MODAL LOGIC 32
1.2.2 TEMPORAL LOGIC 33 1.2.3 THREE-VALUED LOGICS 33 35 35 35 36 36 36
37 37 37 37 38 38 38 39 39 39 39 40 40 40 40 41 41 42 42 42 43 43 43 43
44 44 44 44 44 2. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 3.
3.1 3.2 3.3 3.4 3.5 4. 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 5. 5.1 5.2 5.3
5.4 5.5 5.6 SET THEORY THE CONCEPT OF A SET SUBSET EQUALITY OF SETS
UNION INTERSECTION DIFFERENCE SYMMETRICAL DIFFERENCE CARTESIAN PRODUCT
COMPLEMENT POWER SET CARDINALITY SETS OF NUMBERS RELATIONS BINARY
RELATION EQUIVALENCE RELATION ORDERING RELATION PARTIALLY ORDERED SET
(POSET) PARTITION . FUNCTION THE CONCEPT OF A FUNCTION INJECTION
SURJECTION BIJECTION AND INVERSE RESTRICTION OF A FUNCTION COMPOSITION
OF FUNCTIONS FIXED POINT HOMEOMORPHISM FAMILY OF SETS THE CONCEPT OF A
FAMILY OF SETS UNION INTERSECTION COVERING MUTUALLY DISJOINT FAMILY OF
SETS PARTITION IX 6. ALGEBRA 45 6.1 ELEMENTARY FUNCTIONS 45 6.1.1
EXPONENTIAL FUNCTION 45 6.1.2 LOGARITHMIC FUNCTION 45 6.2 PERMUTATION 46
6.3 COMBINATION 46 6.4 MORE IMPORTANT INEQUALITIES 47 6.4.1 BERNOULLI'S
INEQUALITY 47 6.4.2 CAUCHY-BUNYAKOWSKY-SCHWARZ'S INEQUALITY 47 6.4.3
HOLDER'S INEQUALITY 47 6.5 MATRICES 47 6.5.1 UNIT (IDENTITY) MATRIX 48
6.5.2 ADDITION 48 6.5.3 NULL MATRIX 49 6.5.4 MULTIPLICATION 49 6.5.5
MULTIPLICATION BY A SCALAR 49 6.5.6 TRANSPOSE 50 6.5.7 SYMMETRIC MATRIX
50 6.5.8 SKEW-SYMMETRIC MATRIX 50 6.5.9 ORTHOGONAL MATRIX 50 6.6
DETERMINANT 50 6.6.1 RANK ' 51 6.6.2 SINGULAR (REGULAR) MATRIX 51 6.6.3
INVERSE MATRIX 51 6.7 SIMULTANEOUS SYSTEM OF LINEAR EQUATIONS 51 6.8
SINGULAR VALUE DECOMPOSITION 52 6.8.1 EINGENVALUES 52 6.8.2 EIGENVECTORS
53 6.8.3 CANONICAL FORM 53 6.8.4 SIMILARITY MATRIX 53 6.8.5 SINGULAR
VALUE DECOMPOSITION 54 7. CALCULUS 54 7.1 SEQUENCE 54 7.2 LIMIT 55 7.3
CAUCHY SEQUENCE 55 7.4 LIMIT OF FUNCTIONS 55 7.5 CONTINUOUS FUNCTION 56
7.6 DERIVATIVE 56 7.7 MAXIMUM AND MINIMUM 57 7.8 THE INDEFINITE INTEGRAL
57 7.9 THE DEFINITE INTEGRAL 58 8. DIFFERENTIAL EQUATIONS 59 8.1 LINEAR
EQUATION OF THE FIRST DEGREE (TYPE 1 LINEAR EQUATION) 59 8.2 CAUCHY
PROBLEM 59 9. 9.1 9.2 9.3 10. 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8
10.9 11. 11.1 11.2 11.3 11.4 11.5 11.6 11.7 12. 12.1 12.2 12.3 12.4 12.5
12.6 13. 13.1 13.2 13.3 13.4 14. 14.1 14.2 14.3 14.3.1 14.4 14.5 14.5.1
VECTORS SUM OF VECTORS SCALAR PRODUCT VECTOR (LINEAR) SPACE PROBABILITY
BOREL ALGEBRA PROBABILITY PROBABILITY AND RELATIVE FREQUENCY INDEPENDENT
EVENTS CONDITIONAL PROBABILITY BAYES' THEOREM RANDOM VARIABLE
PROBABILITY DISTRIBUTION DENSITY FUNCTION FUZZY SETS THE CONCEPT OF A
FUZZY SET A CUT FUZZY UNION FUZZY INTERSECTION FUZZY COMPLEMENT FUZZY
RELATION FUZZY PROJECTIONS METRIC SPACES METRIC; METRIC SPACE
NEIGHBOURHOOD (VICINITY) OPEN SET CONVERGENCE COMPLETENESS FIXED POINT
TOPOLOGY TOPOLOGY; TOPOLOGICAL SPACE VICINITY HAUSDORFF SPACE
COMPACTNESS GRAPH THEORY BASIC CONCEPTS WALK CONNECTED GRAPH BLOCKS
BLOCK GRAPH TREE BLOCK-CUT POINT TREE MATHEMATICAL FOUNDATIONS OF IR 60
61 61 61 62 62 62 62 63 63 64 64 64 65 66 66 67 67 68 68 69 69 70 70 70
71 71 72 72 72 72 73 73 74 75 75 75 76 76 77 77 78 XI 15. 15.1 15.2 16.
16.1 16.2 16.2.1 16.2.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.9.1 16.9.2
16.10 16.11 17. 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 MATROID THEORY
MATROID CYCLE MATROID RECURSION AND COMPLEXITY THEORY PRIMITIVE
RECURSIVE FUNCTION FUNCTION-FORMING OPERATIONS COMPOSITION PRIMITIVE
RECURSION PRIMITIVE (PARTIAL) RECURSIVE FUNCTION RECURSIVE FUNCTION
TURING MACHINE TURING COMPUTABILITY RECURSION AND COMPUTABILITY
RECURSIVE AND RECURSIVELY ENUMERABLE SET FIXED POINT INDEX FIXED POINT
THE P CLASS THE NP CLASS ARTIFICIAL NEURAL NETWORK ARTIFICIAL NEURON
ARTIFICIAL NEURAL NETWORK THE FUNDAMENTAL STATE EQUATION OPERATION
ENERGY FUNCTION EQUILIBRIUM AND STABILITY THE WINNER TAKES ALL STRATEGY
LEARNING CHAPTER 3. INFORMATION RETRIEVAL MODELS 1. 1.1 1.2 1.2.1 1.3
1.3.1 2. 2.1 2.1.1 2.1.1 2.1.1 2.1.1 2.1.2 CLASSICAL MODELS OF
INFORMATION RETRIEVAL BOOLEAN MODEL VECTOR SPACE MODEL BIBLIOGRAPHICAL
REMARKS PROBABILISTIC MODEL BIBLIOGRAPHICAL REMARKS NONCLASSICAL MODELS
OF INFORMATION RETRIEVAL INFORMATION LOGIC MODEL BASIC CONCEPTS .1
DOCUMENT .2 QUERY .3 RETRIEVAL INFORMATION RETRIEVAL 79 79 79 80 80 80
80 80 81 81 81 82 82 82 83 83 84 85 85 87 87 87 88 88 89 89 89 90 95 97
97 101 107 108 115 116 116 117 117 117 117 118 XII MATHEMATICAL
FOUNDATIONS OF IR 2.2 SITUATION THEORY MODEL 120 2.2.1 BASIC CONCEPTS
121 2.2.1.1 INFON 121 2.2.1.2 SUPPORT 121 2.2.1.3 TYPE 122 2.2.1.4
CONSTRAINT 122 2.2.1.5 CHANNEL 122 2.2.2 INFORMATION RETRIEVAL 123 2.2.3
BIBLIOGRAPHICAL REMARKS 124 2.3 INTERACTION MODEL 125 2.3.1 QUALITATIVE
MODEL 127 2.3.2 QUANTITATIVE MODEL 131 2.3.3 BIBLIOGRAPHICAL REMARKS 137
3. ALTERNATIVE MODELS OF INFORMATION RETRIEVAL 138 3.1 CLUSTER MODEL 138
3.2 FUZZY MODEL 141 3.3 LATENT SEMANTIC INDEXING MODEL 144 3.4
ARTIFICIAL INTELLIGENCE IN INFORMATION RETRIEVAL 148 3.4.1 ARTIFICIAL
NEURAL NETWORKS MODEL 148 3.4.2 GENETIC ALGORITHMS MODEL 150 3.4.2.1
BASIC CONCEPTS 150 3.4.2.2 INFORMATION RETRIEVAL 151 3.4.3 KNOWLEDGE
BASES, NATURAL LANGUAGE PROCESSING 154 3.4.3.1 NATURAL LANGUAGE
PROCESSING 155 3.4.3.2 SEMANTIC NETWORK 155 3.4.3.3 KNOWLEDGE BASE 156
3.4.3.4 INFORMATION RETRIEVAL 156 3.4.3.4.1 QUERY EXPANSION 156
3.4.3.4.2 IMAGE RETRIEVAL 157 3.4.3.5 THESAURI FEDERATION 158 3.5
BIBLIOGRAPHICAL REMARKS 158 4. TRADITIONAL TREE STRUCTURE OF INFORMATION
RETRIEVAL MODELS 159 CHAPTER 4. MATHEMATICAL THEORY OF INFORMATION
RETRIEVAL 161 1. INFORMATION RETRIEVAL FRAME 161 2. CLASSICAL
INFORMATION RETRIEVAL 164 2.1 CLASSICAL INFORMATION RETRIEVAL 164 2.1.1
SIMILARITY INFORMATION RETRIEVAL 166 2.1.2 PROBABILISTIC INFORMATION
RETRIEVAL 167 3. SIMILARITY (VECTOR SPACE) INFORMATION RETRIEVAL 168 3.1
BINARY SIMILARITY INFORMATION RETRIEVAL 175 3.1.1 CONCLUSIONS 184 XLLL
3.2 NON-BINARY SIMILARITY INFORMATION RETRIEVAL 185 3.3 CONCLUSIONS 187
3.4 BIBLIOGRAPHICAL REMARKS 188 4. PROBABILISTIC INFORMATION RETRIEVAL
188 4.1 CONCLUSIONS 197 4.2 BIBLIOGRAPHICAL REMARKS 198 5. INTERACTION
INFORMATION RETRIEVAL 198 5.1 D-NET 199 5.2 INTERACTION INFORMATION
RETRIEVAL 200 5.2.1 ASSOCIATIVE INTERACTION MODEL 201 5.2.2 CLASSICAL
INFORMATION RETRIEVAL: PSEUDO-INTERACTION 206 6. BOOLEAN INFORMATION
RETRIEVAL 207 6.1 CLASSICAL BOOLEAN MODEL 207 6.2 WEIGHTED BOOLEAN MODEL
210 6.3 BIBLIOGRAPHICAL REMARKS 212 7. NETWORK STRUCTURE OF INFORMATION
RETRIEVAL MODELS 213 CHAPTER 5. RELEVANCE EFFECTIVENESS IN INFORMATION
RETRIEVAL 215 1. RELEVANCE 215 2. EFFECTIVENESS MEASURES 218 3.
RELEVANCE FEEDBACK 221 4. MATHEMATICAL STRUCTURE IN RELEVANCE FEEDBACK
222 4.1 RECURSION 224 4.2 FIXED POINT 225 4.3 "' DIOPHANTINE SET 225 4.4
LEVEL SURFACE 225 4.5 MATHEMATICAL STRUCTURE OF RELEVANCE EFFECTIVENESS
226 5. OPTIMALITY 230 CHAPTER 6. FURTHER TOPICS IN INFORMATION RETRIEVAL
233 1. INFORMATION RETRIEVAL AND DECISION MAKING 233 2. DATA FUSION 236
3. INTERACTION AND SITUATION THEORY MODELS 239 APPENDIX 1 BINARY
SIMILARITY INFORMATION RETRIEVAL 241 XIV MATHEMATICAL FOUNDATIONS OF IR
NON-BINARY SIMILARITY INFORMATION RETRIEVAL (NBSIR) 246 APPENDIX 2
PROBABILISTIC INFORMATION RETRIEVAL 249 APPENDIX 3 INTERACTION
INFORMATION RETRIEVAL 257 REFERENCES 263 INDEX 281 |
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| spelling | Dominich, Sándor Verfasser aut Mathematical foundations of information retrieval by Sándor Dominich Dordrecht [u.a.] Kluwer 2001 XX, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical modelling 12 Informatique - Mathématiques Informatique - Mathématiques ram Informatique documentaire ram Systèmes d'information Systèmes d'information ram informatique documentaire inriac informatique inriac mathematique inriac systeme d'information inriac Informatik Mathematik Computer science -- Mathematics Information storage and retrieval Information Retrieval (DE-588)4072803-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Information Retrieval (DE-588)4072803-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 Mathematical modelling 12 (DE-604)BV011613239 12 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009441970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dominich, Sándor Mathematical foundations of information retrieval Mathematical modelling Informatique - Mathématiques Informatique - Mathématiques ram Informatique documentaire ram Systèmes d'information Systèmes d'information ram informatique documentaire inriac informatique inriac mathematique inriac systeme d'information inriac Informatik Mathematik Computer science -- Mathematics Information storage and retrieval Information Retrieval (DE-588)4072803-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4072803-1 (DE-588)4155620-3 |
| title | Mathematical foundations of information retrieval |
| title_auth | Mathematical foundations of information retrieval |
| title_exact_search | Mathematical foundations of information retrieval |
| title_full | Mathematical foundations of information retrieval by Sándor Dominich |
| title_fullStr | Mathematical foundations of information retrieval by Sándor Dominich |
| title_full_unstemmed | Mathematical foundations of information retrieval by Sándor Dominich |
| title_short | Mathematical foundations of information retrieval |
| title_sort | mathematical foundations of information retrieval |
| topic | Informatique - Mathématiques Informatique - Mathématiques ram Informatique documentaire ram Systèmes d'information Systèmes d'information ram informatique documentaire inriac informatique inriac mathematique inriac systeme d'information inriac Informatik Mathematik Computer science -- Mathematics Information storage and retrieval Information Retrieval (DE-588)4072803-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Informatique - Mathématiques Informatique documentaire Systèmes d'information informatique documentaire informatique mathematique systeme d'information Informatik Mathematik Computer science -- Mathematics Information storage and retrieval Information Retrieval Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009441970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011613239 |
| work_keys_str_mv | AT dominichsandor mathematicalfoundationsofinformationretrieval |