Dominich The Modern Algebra of Information Retrieval

1. Auflage 2008
ISBN: 978-3-540-77659-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 330 Seiten

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.

Sándor Dominich is the George Pólya Professor of Computer Science, Head of the Information Retrieval Research Group, and Deputy Dean of the Faculty of Information Technology of the University of Pannonia, Veszprém, Hungary. His research interests include retrieval models, formal aspects, foundations, effectiveness measurement, and applications. He authored three books, including 'Mathematical Foundations of Information Retrieval' (Springer, 2001) and over seventy research papers. He is a founding co-organiser of the ACM SIGIR MF/IR Workshop series 2000-2005, and ICTIR International Conference 2007 (both together with C.J. van Rijsbergen). He has served as a programme committee member of major Information Retrieval conferences.

Autoren/Hrsg.

Dominich, Sándor

Inhaltsverzeichnis

1;Acknowledgments;7
2;Contents;9
3;1 Introduction;15
3.1;1.1 Information Retrieval;16
3.2;1.2 Retrieval Methods;25
3.3;1.3 Modern Algebra;27
3.4;1.4 Lattice;33
3.5;1.5 Importance of Lattices;35
3.6;1.6 Lattices in Information Retrieval;36
3.7;1.7 Exercises and Problems;40
4;2 Mathematics Basics;41
4.1;2.1 Elements of Mathematical Logic;42
4.2;2.2 Elements of Set Theory;46
4.3;2.3 Elements of Relations Theory;52
4.4;2.4 Exercises and Problems;57
4.5;2.5 Bibliography;58
5;3 Elements of Lattice Theory;59
5.1;3.1 Lattice;60
5.2;3.2 Lattice and Poset;61
5.3;3.3 Duality;62
5.4;3.4 Hasse Diagram;62
5.5;3.5 Complete, Atomic Lattice;64
5.6;3.6 Modular Lattice;65
5.7;3.7 Sublattice;67
5.8;3.8 Distributive Lattice;67
5.9;3.9 Complemented, Orthomodular Lattice;70
5.10;3.10 Boolean Algebra;73
5.11;3.11 Important Lattices;73
5.12;3.12 Exercises and Problems;76
5.13;3.13 Bibliography;78
6;4 Basics of Information Retrieval Technology;79
6.1;4.1 Documents;80
6.2;4.2 Power Law;80
6.3;4.3 Stoplist;85
6.4;4.4 Stemming;87
6.5;4.5 Inverted File Structure;88
6.6;4.6 Term-Document Matrix;90
6.7;4.7 General Architecture of a Retrieval System;93
6.8;4.8 Elements of Web Retrieval Technology;94
6.9;4.9 Measurement of Relevance Effectiveness;101
6.10;4.10 Measurement of Search Engine Effectiveness;112
6.11;4.11 Exercises and Problems;117
7;5 Lattice-Based Retrieval Systems;119
7.1;5.1 Mooers’ Model;120
7.2;5.2 The FaIR System;124
7.3;5.3 Galois (Concept) Lattice-Based Models;126
7.4;5.4 Properties of the Lattices Applied;131
7.5;5.5 Exercises and Problems;137
8;6 Boolean Retrieval;139
8.1;6.1 Boolean Retrieval Method;140
8.2;6.2 Technology of Boolean Retrieval;142
8.3;6.3 Lattice-Based Boolean Retrieval;143
8.4;6.4 Exercises and Problems;146
9;7 Lattices of Subspaces and Projectors;149
9.1;7.1 Metric Space;150
9.2;7.2 Complete Metric Space;151
9.3;7.3 Linear Space;153
9.4;7.4 Subspace of Linear Space;155
9.5;7.5 Linear Operator;156
9.6;7.6 Banach Space;157
9.7;7.7 Hilbert Space;159
9.8;7.8 Euclidean Space;160
9.9;7.9 Projection Theorem;161
9.10;7.10 Projector;163
9.11;7.11 Basis of Subspace;165
9.12;7.12 Lattice of Subspaces;166
9.13;7.13 Exercises and Problems;167
9.14;7.14 Bibliography;168
10;8 Vector Space Retrieval;171
10.1;8.1 Introduction;172
10.2;8.2 Lattices in Vector Space Retrieval;173
10.3;8.3 Calculation of Meaning Using the Hilbert Lattice;179
10.4;8.4 Compatibility of Relevance Assessments;181
10.5;8.5 Vector Space Retrieval: Lattice-Lattice Mapping;182
10.6;8.6 Discussion;187
10.7;8.7 Exercises;191
11;9 Fuzzy Algebra-Based Retrieval;193
11.1;9.1 Elements of Tensor Algebra;194
11.2;9.2 Similarity Measure and Scalar Product;196
11.3;9.3 Latent Semantic Indexing Retrieval;200
11.4;9.4 Generalized Vector Space Retrieval;205
11.5;9.5 Principle of Invariance;206
11.6;9.6 Elements of Fuzzy Set Theory;207
11.7;9.7 Retrieval Using Linear Space;210
11.8;9.8 Fuzzy Algebra-Based Retrieval Methods;213
11.9;9.9 Discussion;221
11.10;9.10 Exercises and Problems;226
12;10 Probabilistic Retrieval;229
12.1;10.1 Elements of Probability Theory;230
12.2;10.2 Principles of Probabilistic Retrieval;232
12.3;10.3 Probabilistic Retrieval Method;234
12.4;10.4 Language Model Retrieval Method;238
12.5;10.5 Lattice Theoretical Framework for Probabilistic Retrieval;240
12.6;10.6 Bayesian Network Retrieval;245
12.7;10.7 Exercises;249
13;11 Web Retrieval and Ranking;251
13.1;11.1 Web Graph;252
13.2;11.2 Link Structure Analysis;260
13.3;11.3 The PageRank Method;263
13.4;11.4 The HITS Method;269
13.5;11.5 The SALSA Method;274
13.6;11.6 The Associative Interaction Method;277
13.7;11.7 Combined Methods;284
13.8;11.8 Lattice-Based View of Web Ranking;296
13.9;11.9 P2P Retrieval;306
13.10;11.10 Exercises and Problems;312
14;Solutions to Exercises and Problems;315
15;References;321
16;Index;335