| Description |
1 online resource (432 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- CHAPTER 1: Elements of Algebra -- 1.1. SETS, FUNCTIONS, AND NOTATION -- 1.1.1. Special Sets and Families of Sets -- 1.1.2. Functions -- 1.1.3. Finite, Countable, and Uncountable Sets -- 1.2. ALGEBRAIC STRUCTURES -- 1.2.1. Operations on Sets -- 1.2.2. Semigroups and Groups -- 1.2.3. Rings and Fields -- 1.2.4. Vector Spaces -- 1.2.5. Homomorphisms and Linear Transforms -- CHAPTER 2: Pertinent Properties of Euclidean Space -- 2.1. ELEMENTARY PROPERTIES OF R -- 2.1.1. Foundations |
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2.1.2. Topological Properties of R -- 2.2. ELEMENTARY PROPERTIES OF EUCLIDEAN SPACES -- 2.2.1. Metrics on Rn -- 2.2.2. Topological Spaces -- 2.2.3. Topological Properties of Rn -- 2.2.4. Aspects of Rn, Artificial Intelligence, Pattern Recognition, and Artificial Neural Networks -- CHAPTER 3: Lattice Theory -- 3.1. HISTORICAL BACKGROUND -- 3.2. PARTIAL ORDERS AND LATTICES -- 3.2.1. Order Relations on Sets -- 3.2.2. Lattices -- 3.3. RELATIONS WITH OTHER BRANCHES OF MATHEMATICS -- 3.3.1. Topology and Lattice Theory -- 3.3.2. Elements of Measure Theory -- 3.3.3. Lattices and Probability |
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3.3.4. Fuzzy Lattices and Similarity Measures -- CHAPTER 4: Lattice Algebra -- 4.1. LATTICE SEMIGROUPS AND LATTICE GROUPS -- 4.2. MINIMAX ALGEBRA -- 4.2.1. Valuations, Metrics, and Measures -- 4.3. MINIMAX MATRIX THEORY -- 4.3.1. Lattice Vector Spaces -- 4.3.2. Lattice Independence -- 4.3.3. Bases and Dual Bases of l-Vector Spaces -- 4.4. THE GEOMETRY OF S (X) -- 4.4.1. Affine Structures in Rn -- 4.4.2. The Shape of S(X) -- CHAPTER 5: Matrix-Based Lattice Associative Memories -- 5.1. HISTORICAL BACKGROUND -- 5.1.1. The Classical ANN Model -- 5.2. LATTICE ASSOCIATIVE MEMORIES |
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5.2.1. Basic Properties of Matrix-Based LAMs -- 5.2.2. Lattice Auto-Associative Memories -- 5.2.3. Pattern Recall in the Presence of Noise -- 5.2.4. Kernels and Random Noise -- 5.2.5. Bidirectional Associative Memories -- 5.2.6. Computation of Kernels -- 5.2.7. Addendum -- CHAPTER 6: Extreme Points of Data Sets -- 6.1. RELEVANT CONCEPTS OF CONVEX SET THEORY -- 6.1.1. Convex Hulls and Extremal Points -- 6.1.2. Lattice Polytopes -- 6.2. AFFINE SUBSETS OF EXT(P(X)) -- 6.2.1. Simplexes and Affine Subspaces of Rn -- 6.2.2. Analysis of ext(P(X)) ˆ Rn -- 6.2.2.1. The case n = 2 |
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6.2.2.2. The case n = 3 -- 6.2.2.3. The case n >= 4 -- CHAPTER 7: Image Unmixing and Segmentation -- 7.1. SPECTRAL ENDMEMBERS AND LINEAR UNMIXING -- 7.1.1. The Mathematical Basis of the WM-Method -- 7.1.2. A Validation Test of the WM-Method -- 7.1.3. Candidate and Final Endmembers -- 7.2. AVIRIS HYPERSPECTRAL IMAGE EXAMPLES -- 7.3. ENDMEMBERS AND CLUSTERING VALIDATION INDEXES -- 7.4. COLOR IMAGE SEGMENTATION -- 7.4.1. About Segmentation and Clustering -- 7.4.2. Segmentation Results and Comparisons -- CHAPTER 8: Lattice-Based Biomimetic Neural Networks -- 8.1. BIOMIMETIC ARTIFICIAL NEURAL NETWORKS |
| Notes |
Description based upon print version of record |
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8.1.1. Biological Neurons and Their Processes |
| Form |
Electronic book
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| Author |
Urcid, Gonzalo
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| ISBN |
9781000412567 |
|
1000412563 |
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