The Geometry of Information Retrieval
Review of Keith van Rijsbergen's book on a quantum mechanic theory for the foundations of information retrieval measurements
Dr. E. Garcia
Mi Islita.com
Email | Last Update: 09/09/05
Topics
The Geometry of Information Retrieval
Audience
Structure
Highlights
Comments
Recommendations
References
The Geometry of Information Retrieval
By Keith van Rijsbergen. Cambridge, 1st Edition, 2004, 150p., illus., biblio., index. ISBN 0-521-83805-3 (HB) $50.00.
Audience
The Geometry of Information Retrieval is a reading material for IR scientists and for scientists from other disciplines with a background in quantum computation.
Structure
The 150 pages of this book consists of a Preface, a Prologue, six chapters, three appendices, a Bibliography, Author index and Index.
Subjects: Information Retrieval, Quantum Mechanics, Geometry, Hilbert Spaces
Table of Contents
Preface ix
Prologue 1
1. Introduction 15
2. On sets and kinds for IR 28
3. Vector and Hilbert sapces 41
4. Linear transformations, operators and matrices 50
5. conditional logic in IR 62
6. The geometry of 73 IR
Appendix I 101
Appendix II 109
Appendix III 116
Bibliography 120
Author index 145
Index 148
Highlights
In Chapter 1 the author explains why IR should be examined in terms of quantum mechanics as opposed to the conventional approach.
Chapter 2 shows how non-Boolean structures arise when classes are properly defined.
Chapter 3 introduces Hilbert spaces and vectors to the IR practitioner.
Chapter 4 discusses linear operations and hermitian operators.
Chapter 5 establishes the basis of the new IR theory, showing how conditionals in logic can be represented as objects in Hilbert space.
Chapter 6 discusses the geometry nature of information retrieval in terms of Dirac notations.
Comments
This book is not yet another conventional book about information retrieval. Instead, Van Rijsbergen uses the mathematical language of quantum mechanics to formulate a new theory for the foundations of IR measurements (1). I view this book as a guide for the next generation of information scientists.
The author shows how three keystone models used in information retrieval -a vector space model, a probabilistic model and a logical model- can be described in Hilbert space, where a document can be represented by a vector and relevance by a Hermitian Operator.
In the Preface, the author suggests six different ways of reading the book. In one embodiment, he suggests to read the Prologue, the Introduction and the appendices, skipping momentarily the chapters. For readers with a mathematical background, the author suggests to read the Prologue last or begin with Chapter 2 or Chapter 6.
The Prologue is a hypothetical, yet enjoyable, discussion between three unidentified players: K, N and B. K is described as "an academic of some seniority judging by his white beard", B is "a younger academic" and friend of K. N is described as "not so young" and seem to be obsessed with usability issues. Both B and N seem to play devil's advocate with K and question whether reformulating IR in terms of quantum mechanics can be justified. I can think of more than one friend that I could take for K, B or N.
Each chapter ends with a Further reading section. Combined with chapter footnotes, this provides readers with guidances and further clarifications.
Appendix I covers Hilbert spaces, operators, linear functions, Dirac notation, dyads and Cauchy-Schwartz inequality. Appendix II covers quantum mechanics, physical states and Heisenberg Uncertainty Priciple. Appendix III covers classical and quantum probability.
The Bibliography is annotated, with plenty of comments. In this way those researching the literature can read the comments and make a decision before reading the original source.
The Author index and Index sections consist of 3 and 2 pages, respectively. Combined with the Bibliography, these sections improve the book usability, considering that the text is limited to 150 pages.
The best features of the book is the fact that it was written in a succinct style; i.e. key concepts are presented in a "to-the-point" manner and -when required- followed by examples.
Recommendations
This book is recommended for information retrieval researchers and for those working on artificial intelligence and quantum computation.
References
- Report on the 27th European Conference on Information Retrieval Research ACM SIGIR: ECIR Conference Report; Vol.39 No. 1 June (2005).
