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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

Windows PC,Mac OSX Apple iPad, Android Tablet PC's Read Online for: Windows PC,Mac OSX,Linux

Price: 118,99 EUR



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The Modern Algebra of Information Retrieval


 

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