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The Modern Algebra of Information Retrieval
of: Sándor Dominich
Springer-Verlag, 2008
ISBN: 9783540776598 , 330 Pages
Format: PDF, Read online
Copy protection: DRM
Acknowledgments
7
Contents
9
1 Introduction
15
1.1 Information Retrieval
16
1.2 Retrieval Methods
25
1.3 Modern Algebra
27
1.4 Lattice
33
1.5 Importance of Lattices
35
1.6 Lattices in Information Retrieval
36
1.7 Exercises and Problems
40
2 Mathematics Basics
41
2.1 Elements of Mathematical Logic
42
2.2 Elements of Set Theory
46
2.3 Elements of Relations Theory
52
2.4 Exercises and Problems
57
2.5 Bibliography
58
3 Elements of Lattice Theory
59
3.1 Lattice
60
3.2 Lattice and Poset
61
3.3 Duality
62
3.4 Hasse Diagram
62
3.5 Complete, Atomic Lattice
64
3.6 Modular Lattice
65
3.7 Sublattice
67
3.8 Distributive Lattice
67
3.9 Complemented, Orthomodular Lattice
70
3.10 Boolean Algebra
73
3.11 Important Lattices
73
3.12 Exercises and Problems
76
3.13 Bibliography
78
4 Basics of Information Retrieval Technology
79
4.1 Documents
80
4.2 Power Law
80
4.3 Stoplist
85
4.4 Stemming
87
4.5 Inverted File Structure
88
4.6 Term-Document Matrix
90
4.7 General Architecture of a Retrieval System
93
4.8 Elements of Web Retrieval Technology
94
4.9 Measurement of Relevance Effectiveness
101
4.10 Measurement of Search Engine Effectiveness
112
4.11 Exercises and Problems
117
5 Lattice-Based Retrieval Systems
119
5.1 Mooers’ Model
120
5.2 The FaIR System
124
5.3 Galois (Concept) Lattice-Based Models
126
5.4 Properties of the Lattices Applied
131
5.5 Exercises and Problems
137
6 Boolean Retrieval
139
6.1 Boolean Retrieval Method
140
6.2 Technology of Boolean Retrieval
142
6.3 Lattice-Based Boolean Retrieval
143
6.4 Exercises and Problems
146
7 Lattices of Subspaces and Projectors
149
7.1 Metric Space
150
7.2 Complete Metric Space
151
7.3 Linear Space
153
7.4 Subspace of Linear Space
155
7.5 Linear Operator
156
7.6 Banach Space
157
7.7 Hilbert Space
159
7.8 Euclidean Space
160
7.9 Projection Theorem
161
7.10 Projector
163
7.11 Basis of Subspace
165
7.12 Lattice of Subspaces
166
7.13 Exercises and Problems
167
7.14 Bibliography
168
8 Vector Space Retrieval
171
8.1 Introduction
172
8.2 Lattices in Vector Space Retrieval
173
8.3 Calculation of Meaning Using the Hilbert Lattice
179
8.4 Compatibility of Relevance Assessments
181
8.5 Vector Space Retrieval: Lattice-Lattice Mapping
182
8.6 Discussion
187
8.7 Exercises
191
9 Fuzzy Algebra-Based Retrieval
193
9.1 Elements of Tensor Algebra
194
9.2 Similarity Measure and Scalar Product
196
9.3 Latent Semantic Indexing Retrieval
200
9.4 Generalized Vector Space Retrieval
205
9.5 Principle of Invariance
206
9.6 Elements of Fuzzy Set Theory
207
9.7 Retrieval Using Linear Space
210
9.8 Fuzzy Algebra-Based Retrieval Methods
213
9.9 Discussion
221
9.10 Exercises and Problems
226
10 Probabilistic Retrieval
229
10.1 Elements of Probability Theory
230
10.2 Principles of Probabilistic Retrieval
232
10.3 Probabilistic Retrieval Method
234
10.4 Language Model Retrieval Method
238
10.5 Lattice Theoretical Framework for Probabilistic Retrieval
240
10.6 Bayesian Network Retrieval
245
10.7 Exercises
249
11 Web Retrieval and Ranking
251
11.1 Web Graph
252
11.2 Link Structure Analysis
260
11.3 The PageRank Method
263
11.4 The HITS Method
269
11.5 The SALSA Method
274
11.6 The Associative Interaction Method
277
11.7 Combined Methods
284
11.8 Lattice-Based View of Web Ranking
296
11.9 P2P Retrieval
306
11.10 Exercises and Problems
312
Solutions to Exercises and Problems
315
References
321
Index
335
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