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From Pythagoras’s harmonic sequence to Einstein’s theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space—the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the Geometry of Meaning provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded.

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319 pages | 6 x 9 | © 2004

Lecture Notes

Computer Science

Mathematics and Statistics

Table of Contents

Foreword, by Pentti Kanerva
Introduction and Timeline
1. Geometry, Numbers and Sets
2. The Graph Model: Networks of Concepts
3. The Vertical Direction: Concept Hierarchies
4. Measuring Similarity and Distance
5. Word-Vectors and Search Engines
6. Exploring Vector Spaces in One and More Languages
7. Logic with Vectors: Ambiguous Words and Quantum States
8. Concept Lattices: Binding Everything Loosely Together
Epilogue: Conclusions and Curtain Call

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