20 March 2013 CONTENTS Introduction. Artificial Neural Networks. Model of Artificial Neurons. Neural Network Architecture. Single Layer Feed Forward Networks. Learning of ANN. Applications of ANN. References.
20 March 2013 3 INTRODUCTION Neural networks are the simplified models of the biological neuron systems. Neural networks are typically organized in layers. Layers are made up of a number of interconnected nodes .which contain an activation function. Patterns are presented to the network via the input layer, which communicates to one or more hidden layers where the actual processing is done via a system of weighted connections. The hidden layers then link to an output layer where the answer is output
20 March 2013 ARTIFICIAL NEURAL NETWORKS OutputInputs An artificial neural network is composed of many artificial neurons that are linked together according to a specific network architecture. The objective of the neural network is to transform the inputs into meaningful outputs.
20 March 2013 5 MODEL OF ARTIFICIAL NEURON An appropriate model/simulation of the nervous system should be able to produce similar responses and behaviours in artificial systems. The nervous system is build by relatively simple units, the neurons, so copying their behaviour and functionality should be the solution.
20 March 2013 MODEL OF ARTIFICIAL NEURONNeuron consists of three basic components weights, thresholds and a single activation functionA set of synapses, or connection link: each of which is characterized by a weight or strength of its own wkj. Specifically, a signal xj at the input synapse „j‟ connected to neuron „k‟ is multiplied by the synaptic wkjAn adder: For summing the input signals, weighted by respective synaptic strengths of the neuron in a linear operation. I w1 x1 w2 x2 ....... wn xn n wi xi i 1
20 March 2013 MODEL OF ARTIFICIAL NEURONThreshold for a Neuron:- The total input for each neuron is the sum of the weighted inputs to the neuron minus its threshold value. This is then passed through the sigmoid function. The equation for the transition in a neuron is : a = 1/(1 + exp(- x)) where x = ai wi - Q a is the activation for the neuron ai is the activation for neuron i wi is the weight Q is the threshold subtracted
20 March 2013 MODEL OF ARTIFICIAL NEURONActivation function: An activation function f performs a mathematical operation on the signal output. The most common activation functions are: - Linear Function, - Threshold Function, - Sigmoidal (S shaped) function,The activation functions are chosen depending upon the type of problem to be solved by the network.
20 March 2013 MODEL OF ARTIFICIAL NEURONActivation Functions f – Types:-Threshold Function A threshold (hard-limiter) activation function is either a binary type or a bipolar type.Output of a binary threshold function produces : 1 if I 0 1 if the weighted sum of the inputs is Y f (I ) +ve, 0 if 0 0 if the weighted sum of the inputs is –ve. 1if I 0 Output(I) a bipolar threshold function produces : Y f of 1if I 0 1 if the weighted sum of the inputs is +ve, -1 if the weighted sum of the inputs is –ve.
20 March 2013 MODEL OF ARTIFICIAL NEURONActivation Functions f – Types:-Sigmoidal Function (S-shape function):-The nonlinear curved S-shape function is called the sigmoid function. This is most common type of activation used to construct the neural networks. It is mathematically well behaved, differentiable and strictly increasing function. 1 Y f (I) I ,0 f ( I ) 1 1 e 1 /(1 exp( I )), 0 f ( I ) 1This is explained as ≈ 0 for large -ve input values, 1 for large +ve values, with a smooth transition between the two. α is slope parameter also called shape parameter symbol the λ is also used to represented this parameter.
20 March 2013 11 NEURAL NETWORK ARCHITECTURE An artificial Neural Network is defined as a data processing system consisting of a large number of interconnected processing elements or artificial neurons. There are three fundamentally different classes of neural networks. Those are. 1. Single layer feedforward Networks. 2. Multilayer feedforward Networks. 3. Recurrent Networks. Here we have to discuss the single layer feed forward network.
20 March 2013SINGLE-LAYER FEED FORWARD NETWORK - Input layer of source nodes that projects directly onto an output layer of neurons. - “Single-layer” referring to the output layer of computation nodes (neuron).
20 March 2013 SINGLE-LAYER FEED FORWARD NETWORK Ii1 Oi1 1 W11 Io1 Yo1 Ii2 W21 1 Oi2 2 Io2 Yo2 Ii3 W31 Oi3 2 3 Iom Yo Iin Wn1 3 m Oin 4 The above figure is a single layer feed forward neural network. It consists an input layer to receive the inputs and an output layer to output the vectors. The input layer consists of „n‟ neurons, and the output layer contains „m‟ neurons . The weight of synapse connecting ith input neuron the jth output neuron is Wij.
20 March 2013 14SINGLE-LAYER FEED FORWARD NETWORKHere the inputs of the input layer and the outputs of the output layer is given as I i1 Oo1 I i2 Oo2 I1 Oo .. .. I in Oom m 1 n 1So I oj W1 j I I 1 W2 j I I 2 ...... Wnj I INHence, the input to the output layer can be given as T T Io m1 W OI m n W II n 1Because OI n 1 II m 1 I F(I,W) OThe block diagram of a single layer feed forward network.
20 March 2013 15 LEARNING IN ANNLearning methods in neural networks can be broadly classified in three basic types. - Supervised Learning - Unsupervised Learning - Reinforcement LearningSupervised Learning:- In supervised learning, both the inputs and the outputs are provided. The network then processes the inputs and compares its resulting outputs against the desired outputs Errors are then calculated, causing the system to adjust the weights which control the network. Here a teacher is assume to be present during the learning process.
20 March 2013 16 LEARNING IN ANNUnsupervised Learning:- Here the target output is not presented to the network, Because there is no teacher to present the described patterns. So the system learns of its own by discovering and adapting to structural features of the input patterns.Reinforcement Learning:- In this method, a teacher though available, does not present the expected answer but only indicates if the computed output is correct or incorrect. The information provided helps the network in its learning process. Here a reward is given for correct answer computed and a penalty for a wrong answer.
20 March 2013 17 APPLICATIONS OF NEURAL NETWORKS Character Recognition:- Neural networks can be used to recognize handwritten characters. Image Compression:- Neural networks can receive and process vast amounts of information at once, making them useful in image compression. Stock Market Prediction:- Neural networks can examine a lot of information quickly and sort it all out, they can be used to predict stock prices. Travelling Salesman Problem:- Neural networks can solve the traveling salesman problem, but only to a certain degree of approximation. Security and Loan Applications:- With the acceptation of a neural network that will decide whether or not to grant a loan.
20 March 2013 18 REFERENCES Neural Networks, Fuzzy logic and Genetic Algorithms, Synthesis and Applications‘ by S.Rajasekaran and G.A Vijayalakshmi Pai. Bertsekas, D.P., Tsitsiklis, J.N. (1996). Neuro-dynamic programming. Athena Scientific. De Rigo, D., Castelletti, A., Rizzoli, A.E., Soncini-Sessa, R., Weber, E. (January 2005). "A selective improvement technique for fastening Neuro-Dynamic Programming in Water Resources Network Management". Ferreira, C. (2006). "Designing Neural Networks Using Gene Expression Programming". In A. Abraham, B. de Baets, M. Köppen, and B. Nickolay, eds., Applied Soft Computing Technologies: The Challenge of Complexity, pages 517–536, Springer-Verlag.