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

1. Elements of Algebra. 1.1. Sets, Functions, and Notations. 1.2. Algebraic Structures. 2. Pertinent Properties of R. 2.2. Elementary Properties of Euclidean Spaces. 3. Lattice Theory. 3.1. Historical Background. 3.2. Partial Orders and Lattices. 3.3. Relations with other branches of Mathematics. 4. Lattice Algebra. 4.1. Lattice Semigroups and Lattice Groups. 4.2. Minimax Algebra. 4.3. Minimax Matrix Theory. 4.4. The Geometry of S(X). 5. Matrix-Based Lattice Associative Memories. 5.1. Historical Background. 5.2. Associative Memories. 6. Extreme Points of Data Sets. 6.1. Relevant Concepts of Convex Set Theory. 6.2. Affine Subsets of EXT(ß(X)). 7. Image Unmixing and Segmentation. 7,1, Spectral Endmembers and Linear Unmixing. 7.2. Aviris Hyperspectral Image Examples. 7.3. Endmembers and Clustering Validation Indexes. 7.4. Color Image Segmentation. 8. Lattice-Based Biomimetic Neural Networks. 8.1. Biomimetics Artificial Neural Networks. 8.2. Lattice Biomimetic Neural Networks. 9. Learning in Biomimetic Neural Networks. 9.1 Learning in Single-Layer LBNNS. 9.2. Multi-Layer Lattice Biomimetic Neural Network. Epilogues. Bibliography.