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Neural Networks An Introduction A Neuron Dendrites Axon Cell Body Synapse An Introduction to Neural Networks Computer Representation p w n f a b 1 Output= a(n) = a(pw+b) An Introduction to Neural Networks A Single Neuron with Multiple Inputs p1 p2 w1,1 w . 1,2 . . pr n f a b w1,r 1 An Introduction to Neural Networks Single Layer Neural Network with Multiple Neurons p1 w1,1 f a1 b1 p2 1 p3 . . . pr n1 n2 f a2 b2 . . . 1 ws,r ns f . . . as bs 1 An Introduction to Neural Networks Multiple Layer Neural Network First Layer Inputs p1 w1,1 n1 f a1 w1,1 b1 p2 1 p3 . . . pr Second Layer f a1 w1,1 n2 a2 f ns f . . . n2 ws,r bs a1 a2 f n2 f a2 b2 . . . 1 as f 1 b2 . . . n1 b1 1 1 1 n1 b1 b2 ws,r Third Layer ns f .. . .. . . . 1 as ws,r bs 1 An Introduction to Neural Networks bs 1 ns f . . . as Activation Functions Hard Limit a = 0 n<0 a = 1 n >= 0 Symmetrical Hard Limit a = -1 n<0 a = +1 n >= 0 Saturating Linear a = 0 n<0 a = n 0 <= n <= 1 a = 1 n>1 An Introduction to Neural Networks Activation Functions Linear a = n Symmetric Saturating Linear a = -1 a=n a=1 n < -1 -1 <= n <= 1 n>1 Log-Sigmoid a = 1 1+ e-n An Introduction to Neural Networks Activation Functions Hyperbolic Tangent Sigmoid a = en - e-n en + e-n Positive Linear a = 0 n<0 a = n n >= 0 Competitive a=1 a=0 neuron with max n all other neurons An Introduction to Neural Networks The History of Development of Neural Networks The Beginning of Neural Networks (1940's) McCulloch Pitts Neuron Hebb Learning The First Golden Age of Neural Networks (1950's and 1960's) Perceptrons Adaline The Quiet Years: 1970's Kohonen Anderson Grossberg Carpenter Renewed Enthusiasm: 1980's Backpropagation Hopfield nets Neocognitron Boltzman machine Hardware Implementation An Introduction to Neural Networks Developing a Neural Network System Choose a neural network architecture Train the neural network using a training set Apply the neural network to identify patterns. This involves implementing the application algorithm An Introduction to Neural Networks Choosing a Neural Network Architecture Identify the number of inputs Identify the number of outputs Number of network inputs = number of problem inputs. Number of neurons in output layer = number of problem outputs. The output layer transfer function is partly determined by problem specification of the outputs. An Introduction to Neural Networks