search for books and compare prices
Tables of Contents for Mathematical Foundations of Information Retrieval
Chapter/Section Title
Page #
Page Count
Preface
xv
Acknowledgments
1
2
Introduction
3
22
Information Retrieval
3
4
Information Retrieval Models
7
1
Mathematics in Information Retrieval Models
8
4
Relevance in Information Retrieval
12
3
Interaction Information Retrieval
15
4
Mathematical Foundation of Information Retrieval
19
6
Mathematics Handbook
25
70
Logics
26
9
Mathematical Logic (Classical First Order Logic)
26
1
Propositional Calculus
26
1
Proposition
26
1
Negation
26
1
Conjunction
27
1
Disjunction
27
1
Implication (subjunction, conditional)
27
1
Equivalence (bi-conditional)
28
1
Contradiction
28
1
Tautology
28
1
Rules of Inference
29
2
Normal form
31
1
Predicate Calculus
31
1
Predicate
31
1
Quantifiers
31
1
Properties
32
1
Non-Conventional Logics
32
1
Modal Logic
32
1
Temporal Logic
33
1
Three-Valued Logics
33
2
Set Theory
35
4
The Concept of a Set
35
1
Subset
35
1
Equality of Sets
36
1
Union
36
1
Intersection
36
1
Difference
37
1
Symmetrical Difference
37
1
Cartesian Product
37
1
Complement
37
1
Power Set
38
1
Cardinality
38
1
Sets of Numbers
38
1
Relations
39
1
Binary Relation
39
1
Equivalence Relation
39
1
Ordering Relation
39
1
Partially Ordered Set (Poset)
40
1
Partition
40
1
Function
40
3
The Concept of a Function
40
1
Injection
41
1
Surjection
41
1
Bijection and Inverse
42
1
Restriction of a Functions
42
1
Composition of Functions
42
1
Fixed Point
43
1
Homeomorphism
43
1
Family of Sets
43
2
The Concept of a Family of Sets
43
1
Union
44
1
Intersection
44
1
Covering
44
1
Mutually Disjoint Family of Sets
44
1
Partition
44
1
Algebra
45
9
Elementary Functions
45
1
Exponential Function
45
1
Logarithmic Function
45
1
Permutation
46
1
Combination
46
1
More Important Inequalities
47
1
Bernoulli's Inequality
47
1
Cauchy-Bunyakowsky-Schwarz's Inequality
47
1
Holder's Inequality
47
1
Matrices
47
1
Unit (Identity) Matrix
48
1
Addition
48
1
Null Matrix
49
1
Multiplication
49
1
Multiplication by a Scalar
49
1
Transpose
50
1
Symmetric Matrix
50
1
Skew-symmetric Matrix
50
1
Orthogonal Matrix
50
1
Determinant
50
1
Rank
51
1
Singular (Regular) Matrix
51
1
Inverse Matrix
51
1
Simultaneous System of Linear Equations
51
1
Singular Value Decomposition
52
1
Eingenvalues
52
1
Eigenvectors
53
1
Canonical Form
53
1
Similarity Matrix
53
1
Singular Value Decomposition
54
1
Calculus
54
5
Sequence
54
1
Limit
55
1
Cauchy Sequence
55
1
Limit of Functions
55
1
Continuous Function
56
1
Derivative
56
1
Maximum and Minimum
57
1
The Indefinite Integral
57
1
The Definite Integral
58
1
Differential Equations
59
1
Linear Equation of the First Degree (type 1 linear equation)
59
1
Cauchy Problem
59
1
Vectors
60
2
Sum of Vectors
61
1
Scalar Product
61
1
Vector (Linear) Space
61
1
Probability
62
4
Borel Algebra
62
1
Probability
62
1
Probability and Relative Frequency
62
1
Independent Events
63
1
Conditional Probability
63
1
Bayes' Theorem
64
1
Random Variable
64
1
Probability Distribution
64
1
Density Function
65
1
Fuzzy Sets
66
4
The Concept of a Fuzzy Set
66
1
α cut
67
1
Fuzzy Union
67
1
Fuzzy Intersection
68
1
Fuzzy Complement
68
1
Fuzzy Relation
69
1
Fuzzy Projections
69
1
Metric Spaces
70
2
Metric; Metric Space
70
1
Neighbourhood (Vicinity)
70
1
Open Set
71
1
Convergence
71
1
Completeness
72
1
Fixed Point
72
1
Topology
72
3
Topology; Topological Space
72
1
Vicinity
73
1
Hausdorff Space
73
1
Compactness
74
1
Graph Theory
75
4
Basic Concepts
75
1
Walk
75
1
Connected Graph
76
1
Blocks
76
1
Block Graph
77
1
Tree
77
1
Block-Cut Point Tree
78
1
Matroid Theory
79
1
Matroid
79
1
Cycle Matroid
79
1
Recursion and Complexity Theory
80
7
Primitive Recursive Function
80
1
Function-forming Operations
80
1
Composition
80
1
Primitive Recursion
80
1
Primitive (partial) Recursive Function
81
1
Recursive Function
81
1
Turing Machine
81
1
Turing computability
82
1
Recursion and Computability
82
1
Recursive and Recursively Enumerable Set
82
1
Fixed Point
83
1
Index
83
1
Fixed Point
84
1
The P Class
85
1
The NP Class
85
2
Artificial Neural Network
87
8
Artificial Neuron
87
1
Artifical Neural Network
87
1
The Fundamental State Equation
88
1
Operation
88
1
Energy Function
89
1
Equilibrium and Stability
89
1
The Winner Takes All Strategy
89
1
Learning
90
5
Information Retrieval Models
95
66
Classical Models of Information Retrieval
97
19
Boolean Model
97
4
Vector Space Model
101
6
Bibliographical Remarks
107
1
Probabilistic Model
108
7
Bibliographical Remarks
115
1
Nonclassical Models of Information Retrieval
116
22
Information Logic Model
116
1
Basic Concepts
117
1
Document
117
1
Query
117
1
Retrieval
117
1
Information Retrieval
118
2
Situation Theory Model
120
1
Basic Concepts
121
1
Infon
121
1
Support
121
1
Type
122
1
Constraint
122
1
Channel
122
1
Information Retrieval
123
1
Bibliographical Remarks
124
1
Interaction Model
125
2
Qualitative Model
127
4
Quantitative Model
131
6
Bibliographical Remarks
137
1
Alternative Models of Information Retrieval
138
21
Cluster Model
138
3
Fuzzy Model
141
3
Latent Semantic Indexing Model
144
4
Artificial Intelligence in Information Retrieval
148
1
Artificial Neural Networks Model
148
2
Genetic Algorithms Model
150
1
Basic Concepts
150
1
Information Retrieval
151
3
Knowledge Bases, Natural Language Processing
154
1
Natural Language Processing
155
1
Semantic Network
155
1
Knowledge Base
156
1
Information Retrieval
156
1
Query Expansion
156
1
Image Retrieval
157
1
Thesauri Federation
158
1
Bibliographical Remarks
158
1
Traditional Tree Structure of Information Retrieval Models
159
2
Mathematical Theory of Information Retrieval
161
54
Information Retrieval Frame
161
3
Classical Information Retrieval
164
4
Classical Information Retrieval
164
2
Similarity Information Retrieval
166
1
Probabilistic Information Retrieval
167
1
Similarity (Vector Space) Information Retrieval
168
20
Binary Similarity Information Retrieval
175
9
Conclusions
184
1
Non-Binary Similarity Information Retrieval
185
2
Conclusions
187
1
Bibliographical Remarks
188
1
Probabilistic Information Retrieval
188
10
Conclusions
197
1
Bibliographical Remarks
198
1
Interaction Information Retrieval
198
9
D-Net
199
1
Interaction Information Retrieval
200
1
Associative Interaction Model
201
5
Classical Information Retrieval: Pseudo-interaction
206
1
Boolean Information Retrieval
207
6
Classical Boolean Model
207
3
Weighted Boolean Model
210
2
Bibliographical Remarks
212
1
Network Structure of Information Retrieval Models
213
2
Relevance Effectiveness in Information Retrieval
215
18
Relevance
215
3
Effectiveness Measures
218
3
Relevance Feedback
221
1
Mathematical Structure in Relevance Feedback
222
8
Recursion
224
1
Fixed Point
225
1
Diophantine Set
225
1
Level surface
225
1
Mathematical Structure of Relevance Effectiveness
226
4
Optimality
230
3
Further Topics in Information Retrieval
233
8
Information Retrieval and Decision Making
233
3
Data Fusion
236
3
Interaction and Situation Theory Models
239
2
Appendix 1 Binary Similarity Information Retrieval
241
8
Non-Binary Similarity Information Retrieval (NBSIR)
246
3
Appendix 2 Probabilistic Information Retrieval
249
8
Appendix 3 Interaction Information Retrieval
257
6
References
263
18
Index
281