Tangles - A Structural Approach to Artificial Intelligence in Empirical

The mathematical theory of tangles, the centrepiece of the celebrated Robertson-Seymour theory of graph minors, finds precise structure in imprecise data. Assuming only basic undergraduate mathematics, this book shows how tangles can identify, relate, and structure types in data: of behaviour, political views, texts, or proteins.

List of contents

Part I. Tangles - A New Paradigm for Clusters and Types: 1. The idea behind tangles; 2. The notion of a tangle; 3. The two main tangle theorems: an informal preview; Part II. Tangles in Different Contexts - A Collection of Informal Examples: 4. Examples from the natural sciences; 5. Examples from the social sciences; 6. Examples from data science; Part III. The Mathematics of Tangles - Concepts, Theorems, Algorithms: 7. The formal setup for tangles; 8. Tangle theorems; 9. Order functions; 10. Choosing the feature system; 11. Algorithms; Part IV. Applying Tangles - Back to the Examples: 12. Applying tangles in the natural sciences; 13. Applying tangles in the social sciences; 14. Applying tangles in data science; Notes; References; Symbol index; Subject index.

About the author

Reinhard Diestel is Chair of Discrete Mathematics at Universität Hamburg, where he works on structural graph theory and combinatorics. He is the author of the leading graduate-level text 'Graph Theory' (6th edition, 2024), which has been translated into German, Russian, Japanese, and Chinese.

Summary

The mathematical theory of tangles, the centrepiece of the celebrated Robertson-Seymour theory of graph minors, finds precise structure in imprecise data. Assuming only basic undergraduate mathematics, this book shows how tangles can identify, relate, and structure types in data: of behaviour, political views, texts, or proteins.

Product details

• Authors: Reinhard Diestel, Reinhard (Universitat Hamburg) Diestel, Diestel Reinhard
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.05.2024
• EAN: 9781009473316
• ISBN: 978-1-0-0947331-6
• No. of pages: 304
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; machine learning, Economics, BUSINESS & ECONOMICS / Economics / General, POLITICAL SCIENCE / History & Theory, SCIENCE / Life Sciences / Biology, MATHEMATICS / Discrete Mathematics, COMPUTERS / Optical Data Processing, Political science & theory, Biology, life sciences, pattern recognition, Discrete Mathematics, Political science and theory, COMPUTERS / Data Science / Machine Learning, Data analysis: general, Data science and analysis: general