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E-raamat: Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks [Taylor & Francis e-raamat]

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Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural NetworksSuurem pilt
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"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 aspecial 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"--

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 arti?cial 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 arti?cial intelligence with focus on pattern recognition, multispectral image analysis, and biomimetic arti?cial neural networks. The book is self-contained and – depending on the student’s major – can be used at a senior undergraduate level or a ?rst-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 www.Routledge.com/9780367720292



      • This book 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 arti?cial intelligence with focus on pattern recognition, multispectral image analysis, and biomimetic arti?cial neural networks.

      Preface xi
      Chapter 1 Elements of Algebra 1(35)
      1.1 Sets, Functions, And Notation
      		1(15)
      1.1.1 Special Sets and Families of Sets
      		5(3)
      1.1.2 Functions
      		8(4)
      1.1.3 Finite, Countable, and Uncountable Sets
      		12(4)
      1.2 Algebraic Structures
      		16(20)
      1.2.1 Operations on Sets
      		16(2)
      1.2.2 Semigroups and Groups
      		18(3)
      1.2.3 Rings and Fields
      		21(5)
      1.2.4 Vector Spaces
      		26(4)
      1.2.5 Homomorphisms and Linear Transforms
      		30(6)
      Chapter 2 Pertinent Properties of Euclidean Space 36(45)
      2.1 Elementary Properties Of R
      		36(16)
      2.1.1 Foundations
      		36(4)
      2.1.2 Topological Properties of R
      		40(12)
      2.2 Elementary Properties Of Euclidean Spaces
      		52(29)
      2.2.1 Metrics on Rn
      		53(3)
      2.2.2 Topological Spaces
      		56(7)
      2.2.3 Topological Properties of Rn
      		63(9)
      2.2.4 Aspects of IV, Artificial Intelligence, Pattern Recognition, and Artificial Neural Networks
      		72(9)
      Chapter 3 Lattice Theory 81(29)
      3.1 Historical Background
      		81(1)
      3.2 Partial Orders And Lattices
      		82(16)
      3.2.1 Order Relations on Sets
      		82(7)
      3.2.2 Lattices
      		89(9)
      3.3 Relations With Other Branches Of Mathematics
      		98(12)
      3.3.1 Topology and Lattice Theory
      		98(2)
      3.3.2 Elements of Measure Theory
      		100(5)
      3.3.3 Lattices and Probability
      		105(2)
      3.3.4 Fuzzy Lattices and Similarity Measures
      		107(3)
      Chapter 4 Lattice Algebra 110(59)
      4.1 Lattice Semigroups And Lattice Groups
      		110(4)
      4.2 Minimax Algebra
      		114(12)
      4.2.1 Valuations, Metrics, and Measures
      		121(5)
      4.3 Minimax Matrix Theory
      		126(30)
      4.3.1 Lattice Vector Spaces
      		135(4)
      4.3.2 Lattice Independence
      		139(9)
      4.3.3 Bases and Dual Bases of P-Vector Spaces
      		148(8)
      4.4 The Geometry Of S(X)
      		156(13)
      4.4.1 Affine Structures in Rn
      		156(7)
      4.4.2 The Shape of S (X)
      		163(6)
      Chapter 5 Matrix-Based Lattice Associative Memories 169(60)
      5.1 Historical Background
      		169(3)
      5.1.1 The Classical ANN Model
      		171(1)
      5.2 Lattice Associative Memories
      		172(57)
      5.2.1 Basic Properties of Matrix-Based LAMS
      		173(8)
      5.2.2 Lattice Auto-Associative Memories
      		181(5)
      5.2.3 Pattern Recall in the Presence of Noise
      		186(4)
      5.2.4 Kernels and Random Noise
      		190(20)
      5.2.5 Bidirectional Associative Memories
      		210(14)
      5.2.6 Computation of Kernels
      		224(4)
      5.2.7 Addendum
      		228(1)
      Chapter 6 Extreme Points of Data Sets 229(36)
      6.1 Relevant Concepts Of Convex Set Theory
      		229(9)
      6.1.1 Convex Hulls and Extremal Points
      		229(4)
      6.1.2 Lattice Polytopes
      		233(5)
      6.2 Affine Subsets Of EXT(B(X))
      		238(27)
      6.2.1 Simplexes and Affine Subspaces of Rn
      		238(2)
      6.2.2 Analysis of ext(B(X)) subset Rn
      		240(25)
      6.2.2.1 The case n = 2
      		240(3)
      6.2.2.2 The case n = 3
      		243(10)
      6.2.2.3 The case n > or = to 4
      		253(12)
      Chapter 7 Image Unmixing and Segmentation 265(49)
      7.1 Spectral Endmembers And Linear Unmixing
      		265(13)
      7.1.1 The Mathematical Basis of the WM-Method
      		269(2)
      7.1.2 A Validation Test of the WM-Method
      		271(5)
      7.1.3 Candidate and Final Endmembers
      		276(2)
      7.2 Aviris Hyperspectral Image Examples
      		278(15)
      7.3 Endmembers And Clustering Validation Indexes
      		293(6)
      7.4 Color Image Segmentation
      		299(15)
      7.4.1 About Segmentation and Clustering
      		300(4)
      7.4.2 Segmentation Results and Comparisons
      		304(10)
      Chapter 8 Lattice-Based Biomimetic Neural Networks 314(22)
      8.1 Biomimetic Artificial Neural Networks
      		314(4)
      8.1.1 Biological Neurons and Their Processes
      		315(2)
      8.1.2 Biomimetic Neurons and Dendrites
      		317(1)
      8.2 Lattice Biomimetic Neural Networks
      		318(18)
      8.2.1 Simple Examples of Lattice Biomimetic Neural Networks
      		321(15)
      Chapter 9 Learning in Biomimetic Neural Networks 336(45)
      9.1 Learning In Single-Layer LBNNS
      		336(19)
      9.1.1 Training Based on Elimination
      		339(3)
      9.1.2 Training Based on Merging
      		342(3)
      9.1.3 Training for Multi-Class Recognition
      		345(1)
      9.1.4 Training Based on Dual Lattice Metrics
      		346(9)
      9.2 Multi-Layer Lattice Biomimetic Neural Networks
      		355(26)
      9.2.1 Constructing a Multi-Layer DLAM
      		356(10)
      9.2.2 Learning for Pattern Recognition
      		366(7)
      9.2.3 Learning Based on Similarity Measures
      		373(8)
      Epilogue 381(2)
      Bibliography 383(28)
      Index 411
      Gerhard X. Ritter received both his B.A. degree with honors in 1966 and his Ph.D. degree in Mathematics in 1971 from the University of Wisconsin-Madison. He is a Florida Blue Key Distinguished Professor Emeritus in both the Department of Mathematics and the Department of Computer and Information Science and Engineering (CISE) of the University of Florida. He was the Chair of the CISE department from 1994 to 2001, and Acting Chair from 2011 to 2012.

      Professor Ritter has written more than 140 research papers in subjects ranging from pure and applied mathematics to pattern recognition, computer vision, and artificial neural networks. He is the founding editor of the Journal of Mathematical Imaging and Vision, and founding member and first chair of the Society for Industrial and Applied Mathematics (SIAM) Activity Group on Imaging Science (SIAG-IS). He was a member of the Deputy Undersecretary of Defense for Research and Advanced Technologys advanced technology research on emerging technologies panel (1988) and a member of the advanced sensors committee on key technologies for the 1990s, formed by the same undersecretary (1989). Among other U.S. government-requested briefings attended by Professor Ritter were the annual Automatic Target Recognition Working Group (ATRWG) meetings held across the U.S. (19841996 and 2003). For his contribution, he was awarded the General Ronald W. Yates Award for Excellence in Technology Transfer by the U.S. Air Force Research Laboratory (1998). Among honors outside the realm of the Department of Defense are the Silver Core Award of the International Federation for Information Processing (1989); the Best Session Award at the American Society for Engineering Education (ASEE) Conference for Industry and Education Collaboration in San Jose, CA (1996); and the Best Paper Presentation Award at the International Joint Conference on Neural Networks (IJCNN) sponsored by the Institute of Electrical and Electronics Engineers Neural Networks Council (IEEE/NNC) and the International Neural Network Society (INNS) in Washington, DC (1999).

      Gonzalo Urcid received his Bachelor degree in Communications and Electronic Engineering (1982) and his Master degree in Computational and Information Systems (1985) both from the University of the Americas in Puebla (UDLAP), Mexico. He has a Ph.D. degree (1999) in Optical Sciences from the National Institute of Astrophysics, Optics, and Electronics (INAOE) in Tonantzintla, Mexico and made a postdoctoral residence, between 2001 and 2002, as invited faculty at the CISE Department, University of Florida. Also, from 2001 to 2020 was awarded the distinction of National Researcher from the Mexican National Council of Science and Technology (SNI-CONACYT). Currently is an Associate Professor in the Optics Department at INAOE. His research interests include digital image processing and analysis, artificial neural networks based on lattice algebra, and lattice computing applied to artificial intelligence and pattern recognition.
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