This thesis proposes four novel geometric neurodynamical classifier models, namely GBAM, Lie-derivative, Lie-Poisson, and FAM, applied to breast cancer detection. All these models have been published in a paper and/or in a book form. All theoretical material of this thesis (Chapter 2) has been published in my monographs (see my publication list), as follows: 2.1 Tensorial Neurodynamics has been published in Natural Biodynamics (Chapters 3, 5 and 7), Geometrical Dynamics of Complex Systems; (Chapter 1 and Appendix), 2006) as well as Applied Differential Geometry:A Modern Introduction(Chapter 3) 2.2 GBAM Neurodynamical Classifier has been published in Natural Biodynamics (Chapter 7) and Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling (Chapter 3), as well as in the KES–Conference paper with the same title; 2.3 Lie-Derivative Neurodynamical Classifier has been published in Geometrical Dynamics of Complex Systems; (Chapter 1) and Applied Differential Geometry: A Modern Introduction (Chapter 3); 2.4 Lie-Poisson Neurodynamical Classifier has been published in Geometrical Dynamics of Complex Systems; (Chapter 1) and Applied Differential Geometry: A Modern Introduction (Chapter 3); 2.5 Fuzzy Associative Dynamical Classifier has been published in Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling (Chapter 4), as well as in the KES-Conference paper with the same title. Besides, Section 1.2 Artificial Neural Networks has been published in Natural Biodynamics (Chapter 7) and Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling (Chapter 3). Also, Sections 4.1. and 4.5. have partially been published in Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling (Chapters 3 and 4, respectively) and in the corresponding KES–Conference papers. A. The GBAM (generalized bidirectional associative memory) classifier is a neurodynamical, tensor-invariant classifier based on Riemannian geometry. The GBAM is a tensor-field system resembling a two-phase biological neural oscillator in which an excitatory neural field excites an inhibitory neural field, which reciprocally inhibits the excitatory one. This is a new generalization of Kosko’s BAM neural network, with a new biological (oscillatory, i.e., excitatory/inhibitory)interpretation. The model includes two nonlinearly-coupled (yet non-chaotic and Lyapunov stable) subsystems, activation dynamics and self-organized learning dynamics, including a symmetric synaptic 2-dimensional tensor-field, updated by differential Hebbian associative learning innovations. Biologically, the GBAM describes interacting excitatory and inhibitory populations of neurons found in the cerebellum, olfactory cortex, and neocortex, all representing the basic mechanisms for the generation of oscillating (EEG-monitored) activity in the brain. B. Lie-derivative neurodynamical classifier is an associative-memory, tensor-invariant neuro-classifier, based on the Lie-derivative operator from geometry of smooth manifolds. C. Lie-Poisson neurodynamical classifier is an associative-memory, tensor-invariant neuro-classifier based on the Lie-Poisson bracket from the generalized symplectic geometry. D. The FAM-matrix (fuzzy associative memory) dynamical classifier is a fuzzy-logic classifier based on a FAM-matrix (fuzzy phase-plane). All models are formulated and simulated in Mathematica computer algebra system. All models are applied to breast cancer detection, using the database from the University of Wisconsin and Mammography database. Classification results outperformed those obtained with standard MLP trained with backpropagation algorithm. / Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2008
| Identifer | oai:union.ndltd.org:ADTP/285345 |
| Date | January 2008 |
| Creators | Ivancevic, Tijana T. |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
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