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Transcript

Artificial Neural Networks Rados Jovanovic Summary • • • • • Biological Model of Neural Networks Mathematical Model of Neural Networks Building an Artificial Neural Network Theoretical Properties Applications of Artificial Neural Networks Biological Model • The brain is responsible for all processing and memory. • The brain consists of a complex network of cells called neurons. • Neurons communicate by transimitting electrochemical signals throughout the network. • Each input signal to a neuron can inhibit or excite the neuron. When the neuron is excited enough, it will fire its own electrochemical signal. Biological Model (Cont.) A neuron: Mathematical Model • An Artificial Neural Network is a network of interconnected artificial neurons. • Like in a biological neural network, artificial neurons communicate by sending signals to one another. • Each input to an artificial neuron can either inhibit or excite the artificial neuron. Mathematical Model (Cont.) An artificial neuron: Building an Artificial Neural Network • Topology of the network • Learning type • Learning algorithm – Backpropagation • Summary of backpropagation Topology of the Network (Cont.) There are many topologies, but the main distinction can be maid between: • Feed-Forward Neural Networks • Recurrent Neural Networks Feed-Forward Neural Networks Feed-Forward Neural Networks have no connections that loop. Recurrent Neural Networks Recurrent neural networks do contain looping connections Building an Artificial Neural Network • Topology of the network • Learning type • Learning algorithm – Backpropagation • Summary of backpropagation Learning Type • Supervised Learning Requires a set of pairs of inputs and outputs to train the artificial neural network on. • Unsupervised Learning Only requires inputs. Through time an ANN learns to organize and cluster data by itself. • Reinforcement Learning An ANN from the given input produces some output, and the ANN is rewarded or punished based on the output it created. Building an Artificial Neural Network • Topology of the network • Learning type • Learning algorithm – Backpropagation • Summary of backpropagation Learning Algorithm Learning is adjustment of the weights of the connections between neurons, according to some modification rule. Backpropagation • One of the more common algorithms for supervised learning is Backpropagation. • The term is an abbreviation for “backwards propagation of errors" • Backpropagation is most useful for feedforward networks. Backpropagation (Cont.) • An input is fed into the network and the output is being calculated. • We compare the output of the network with the target output, and we get the error. • We want to minimize the error, so we greedily adjust the weights such that error for this particular input will go towards zero. • We do so using the delta rule. Delta Rule • The delta rule is a gradient descent learning rule. • For a given neuron j and a weight i the delta rule for its weight wji is: • • • • tj is the target output yj is the actual output xi is the ith input a is a small constant called the learning rate Delta Rule (Cont.) Delta Rule (Cont.) Backpropagation (Cont.) • The whole process is repeated for each of the training cases, then back to the first case again. • The cycle is repeated until the overall error value drops below some pre-determined threshold. • Backpropagation usually allows quick convergence on satisfactory local minima for error. Summary of Backpropagation -While error over all training samples > threshold -For each training sample: -Present a training sample to the neural network. -Compute the output of the network. -Calculate the error for each neuron in the last layer by comparing it to the target output. -For each layer l starting from the last output layer until the first layer -Adjust the weights for each neuron in layer l to decrease the local error. -Propagate the error to each neuron one layer back -end for -end for Theoretical Properties • • • • Computational power Capacity Generalisation Convergence Theoretical Properties • Computational power: The Cybenko theorem proved single hidden layer, feed forward neural network is capable of approximating any continuous, multivariate function to any desired degree of accuracy. Theoretical Properties (Cont.) • Capacity: It roughly corresponds to the neural network’s ability to model any given function. It is related to the amount of information that can be stored in the network. Theoretical Properties (Cont.) • Generalisation: In applications where the goal is to create a system that generalises well in unseen examples, the problem of overtraining has emerged. • To lessen the overtraining cross validation is used. Theoretical Properties (Cont.) • Convergence: Not much can be said about convergence since it depends on many factors, such as the existence of local minima, choice of optimization method, etc. Applications Application areas include: system identification and control (vehicle control, process control), quantum chemistry, gameplaying and decision making (backgammon, chess, racing), pattern recognition (radar systems, face identification, object recognition...), sequence recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial applications (automated trading systems), data mining, visualization, e-mail spam filtering... Fin Questions?