Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks

by: Gerhard X. Ritter and Gonzalo Urcid

Publisher Finelybook 出版社：Chapman and Hall/CRC; 1st edition (August 24, 2021)

Language 语言：English

pages 页数：432 pages

ISBN-10 书号：0367720299

ISBN-13 书号：9780367720292**Book Description**

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artiﬁcial intelligence and computer science in general.

Introduction to Lattice Theory: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artiﬁcial intelligence with focus on pattern recognition, multispectral image analysis, and biomimetic artiﬁcial neural networks. The book is self-contained and – depending on the student’s major – can be used at a senior undergraduate level or a ﬁrst-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines.

Features

Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Every chapter consists of exercises with solution provided online at http://www.Routledge.com/9780367720292

Contents

Preface

CHAPTER 1: Elements of Algebra

CHAPTER 2: Pertinent Properties of Euclidean Space

CHAPTER 3: Lattice Theory

CHAPTER 4: Lattice Algebra

CHAPTER 5: Matrix-Based Lattice Associative Memories

CHAPTER 6: Extreme Points of Data Sets

CHAPTER 7: Image Unmixing and Segmentation

CHAPTER 8: Lattice-Based Biomimetic Neural Networks

CHAPTER 9: Learning in Biomimetic Neural Networks

Epilogue

Bibliography

Index