The Modern Algebra of Information Retrieval

By: Sándor Dominich

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Hardcover | 18 April 2008

At a Glance

Hardcover
344 Pages

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23.39 x 15.6 x 2.06

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$216.36

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This book takes a unique approach to information retrieval by laying down the foundations for a modern algebra of information retrieval based on lattice theory. All major retrieval methods developed so far are described in detail, along with Web retrieval algorithms, and the author shows that they all can be treated elegantly in a unified formal way, using lattice theory as the one basic concept. The book's presentation is characterized by an engineering-like approach.

Industry Reviews

From the reviews:

"... this book offers a unique approach to the important topic of information retrieval by providing mathematical foundations based on modern algebra... I can easily recommend this book as a reference for any of the technical IR courses offered at several universities." from the ACM Reviews by Donald H. Kraft, Louisiana State University, USA

"Retrieval methods and information retrieval in general are here treated in a unified manner within abstract algebraic structures ... . Each chapter is supplemented with exercises and problems (with hints to solutions in the appendix) ... . The book is beneficial both for better understanding the existing information retrieval methods and for the creation of new ones." (Antonin Riha, Zentralblatt MATH, Vol. 1149, 2008)

"This book treats retrieval methods ... and IR in general in a unified manner within the one formal framework of modern algebra, namely abstract algebraic structures (primarily lattices). ... Exercises and problems are located at the end of every chapter ... . the book should be helpful for a wide range of readers from graduate students and educators to researchers and system developers coming from a variety of fields such as computer science ... . Every chapter concludes with a References and further reading section." (John S. Griffin, SIGACT News, Vol. 41 (1), 2010)

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You Can Find This Book In

Non-Fiction Computing & I.T.Databases Information Retrieval Mathematics Topology Algebra Computer Science Mathematical Theory of Computation Maths for Computer Scientists Computer Programming & Software Development Algorithms & Data Structures

Library & Info Sciences Data Capture & Analysis

Introduction	p. 1
Information Retrieval	p. 2
Brief History of Information Retrieval	p. 2
"Definition" of Information Retrieval	p. 7
Retrieval Methods	p. 11
Modern Algebra	p. 13
Equations	p. 13
Solving by Radicals	p. 14
Birth of Modern Algebra	p. 16
Modern Algebra	p. 18
Lattice	p. 19
Importance of Lattices	p. 21
Lattices in Information Retrieval	p. 22
Retrieval Systems	p. 22
Boolean Retrieval	p. 23
Vector Space Retrieval	p. 23
Fuzzy-Algebra-Based Retrieval Methods	p. 24
Probabilistic Retrieval	p. 25
Web Retrieval and Ranking	p. 25
Exercises and Problems	p. 26
Mathematics Basics	p. 27
Elements of Mathematical Logic	p. 28
Proposition	p. 28
Negation	p. 29
Conjunction	p. 29
Disjunction	p. 30
Implication	p. 30
Equivalence	p. 31
Elements of Set Theory	p. 32
Set	p. 32
Subset	p. 33
Equality of Sets	p. 34
Set Union	p. 34
Set Intersection	p. 35
Set Difference	p. 35
Cartesian Product	p. 36
Set Complement	p. 37
Powerset	p. 37
Cardinality of Set	p. 37
Properties of Set Operations	p. 38
Elements of Relations Theory	p. 38
Binary Relations	p. 39
Function	p. 40
Predicate	p. 41
Equivalence Relation	p. 41
Ordering Relation	p. 42
Partially Ordered Set	p. 42
Partition	p. 42
Exercises and Problems	p. 43
Bibliography	p. 44
Elements of Lattice Theory	p. 45
Lattice	p. 46
Lattice and Poset	p. 47
Duality	p. 48
Hasse Diagram	p. 48
Complete, Atomic Lattice	p. 50
Modular Lattice	p. 51
Sublattice	p. 53
Distributive Lattice	p. 53
Complemented, Orthomodular Lattice	p. 56
Boolean Algebra	p. 59
Important Lattices	p. 59
Powerset Lattice	p. 60
Lattice of Logical Propositions	p. 60
Lattice of Logical Predicates	p. 60
Lattice of Logical Implications	p. 61
Lattice Types	p. 61
Exercises and Problems	p. 62
Bibliography	p. 64
Basics of Information Retrieval Technology	p. 65
Documents	p. 66
Power Law	p. 66
Stoplist	p. 71
Stemming	p. 73
Inverted File Structure	p. 74
Term-Document Matrix	p. 76
General Architecture of a Retrieval System	p. 79
Elements of Web Retrieval Technology	p. 80
World Wide Web	p. 80
Major Characteristics of the Web	p. 80
General Architecture of a Web Search Engine	p. 84
General Architecture of a Web Metasearch Engine	p. 86
Measurement of Relevance Effectiveness	p. 87
Relevance	p. 87
Measures	p. 87
Precision-Recall Graph Method	p. 91
Uncertainty of Measurement	p. 93
Measurement of Search Engine Effectiveness	p. 98
M-L-S Method	p. 99
RP Method	p. 102
Exercises and Problems	p. 103
Lattice-Based Retrieval Systems	p. 105
Mooers' Model	p. 106
Lattice of Documents	p. 106
Lattice of Unstructured Queries	p. 106
Lattice of Term Hierarchies	p. 107
Lattice of Boolean Queries and Documents	p. 108
The FaIR System	p. 110
Galois (Concept) Lattice-Based Models	p. 112
Galois (Concept) Lattice	p. 112
Term-Document Matrix and Concept Lattice	p. 113
BR-Explorer System	p. 115
Rajapakse-Denham System	p. 115
The FooCA System	p. 116
Query Refinement, Thesaurus Representation	p. 116
Properties of the Lattices Applied	p. 117
Exercises and Problems	p. 123
Boolean Retrieval	p. 125
Boolean Retrieval Method	p. 126
Technology of Boolean Retrieval	p. 128
Lattice-Based Boolean Retrieval	p. 129
Exercises and Problems	p. 132
Lattices of Subspaces and Projectors	p. 135
Metric Space	p. 136
Complete Metric Space	p. 137
Linear Space	p. 139
Subspace of Linear Space	p. 141
Linear Operator	p. 142
Banach Space	p. 143
Hilbert Space	p. 145
Euclidean Space	p. 146
Projection Theorem	p. 147
Projector	p. 149
Basis of Subspace	p. 151
Lattice of Subspaces	p. 152
Exercises and Problems	p. 153
Bibliography	p. 154
Vector Space Retrieval	p. 157
Introduction	p. 158
Lattices in Vector Space Retrieval	p. 159
Vector Space Retrieval	p. 159
Technology of Vector Space Retrieval	p. 163
Calculation of Meaning Using the Hilbert Lattice	p. 165
Queries with Negation	p. 165
Queries with Disjunction	p. 166
Compatibility of Relevance Assessments	p. 167
Vector Space Retrieval: Lattice-Lattice Mapping	p. 168
Discussion	p. 173
Query Lattice and Free Will	p. 173
Vector Space Retrieval?	p. 173
Vector Space Retrieval and Quantum Mechanics	p. 174
Exercises	p. 177
Fuzzy Algebra-Based Retrieval	p. 179
Elements of Tensor Algebra	p. 180
Similarity Measure and Scalar Product	p. 182
Latent Semantic Indexing Retrieval	p. 186
Eigenvalue, Eigenvector	p. 186
Singular Value Decomposition	p. 188
Latent Semantic Indexing	p. 188
Generalized Vector Space Retrieval	p. 191
Principle of Invariance	p. 192
Elements of Fuzzy Set Theory	p. 193
Fuzzy Set	p. 193
Fuzzy Intersection	p. 195
Fuzzy Union	p. 195
Fuzzy Complement	p. 195
Fuzzy Subset	p. 195
Retrieval Using Linear Space	p. 196
Fuzzy Algebra-Based Retrieval Methods	p. 199
Fuzzy Jordan Measure	p. 200
Fuzzy Entropy Retrieval Method	p. 203
Fuzzy Probability Retrieval Method	p. 204
Experimental Results	p. 206
Discussion	p. 207
More on Measures	p. 207
More on Algebra, Entropy, and Probability	p. 208
Information Retrieval and Integration Theory	p. 209
Principle of Invariance and String Theory	p. 210
Exercises and Problems	p. 212
Probabilistic Retrieval	p. 215
Elements of Probability Theory	p. 216
Principles of Probabilistic Retrieval	p. 218
Probabilistic Retrieval Method	p. 220
Language Model Retrieval Method	p. 224
Lattice Theoretical Framework for Probabilistic Retrieval	p. 226
Bayesian Network Retrieval	p. 231
Exercises	p. 235
Web Retrieval and Ranking	p. 237
Web Graph	p. 238
Link Structure Analysis	p. 246
The PageRank Method	p. 249
The HITS Method	p. 255
Application of the HITS Method in Web Retrieval	p. 257
Latent Semantic Indexing and HITS	p. 259
The SALSA Method	p. 260
The Associative Interaction Method	p. 263
Artificial Neural Networks	p. 263
Associative Interaction Method	p. 266
Application of the Associative Interaction Method in Web Retrieval	p. 270
Combined Methods	p. 270
Similarity Merge	p. 271
Belief Network	p. 272
Inference Network	p. 274
Aggregated Method	p. 274
Lattice-Based View of Web Ranking	p. 282
Web Lattice	p. 282
Chain	p. 283
Ranking	p. 284
Global Ranking	p. 284
Structure-Based Ranking	p. 288
P2P Retrieval	p. 292
P2P Network	p. 292
Information Retrieval	p. 293
Lattice-Based Indexing	p. 296
Exercises and Problems	p. 298
Solutions to Exercises and Problems	p. 301
Reference	p. 307
Index	p. 321
Table of Contents provided by Publisher. All Rights Reserved.

The Modern Algebra of Information Retrieval

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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