NEURO & FUZZY SYSTEMS

VI SEMESTER

ICE-322

Department of Instrumentation and Control Engineering, BVCOE, New Delhi

Subject: NEURO & FUZZY SYSTEMS

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UNIT-I�Neural Networks

• Fundamental of neural network
• Overview of biological Neuro-system
• Mathematical Models of Neurons
• ANN architecture, Learning Methods, Learning Paradigms-

Supervised, Unsupervised and reinforcement Learning

• ANN training Algorithms-perceptions, Training rules, Delta, Back

Propagation Algorithm, Multilayer Perception Model, Radial Basis

functions, Hopfield Networks, Associative Memories

• Applications of Artificial Neural Networks.

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Department of Instrumentation and ControlsEngineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Department of instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

FUNDAMENTAL OF NEURAL NETWORK

A. What is neural net?

1. A neural net is an artificial representation of the human brain that tries to simulate its learning process. An ANN is often called a Neural network or simply neural net.

2. Neural network is referred to a network of biological neurons in the nervous system that process and transmit information.

3. ANN is an interconnected group of artificial neurons that uses mathematical model or computational model for information processing.

4. ANN ,like people learn by example.

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Department of of Instrumentation and ControlsEngineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Problem Domains

• Storing and recalling patterns
• Classifying patterns
• Mapping inputs onto outputs
• Grouping similar patterns
• Finding solutions to constrained optimization problems

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Department of of Instrumentation and ControlsEngineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Biological Neuron Model

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Biological Neuron Model

• The human brain consists of a large number, more than billions of neural cells that process information.
• Each cell works like a simple processor.
• Dendrites are branching fibers that extend from the cell body or soma.
• Soma or cell body of a neuron contains the nucleus and other structures , support chemical processing and production of neuro transmitters.
• Axon is a singular fiber carries information away from the soma to the synaptic sites of the other neurons, muscles or glands.
• Axon Hillock is the site of summation for incoming information.
• Synapse is the point of connection between two neurons or a neuron .Electrochemical communication between neurons takes place at these junctions.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Components of a neuron

• The dendrites of a neuron receive the information by special connections, the synapses (Incoming signals from other neurons or cells are transferred to a neuron by synapses).

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• The signals are electric impulses that are transmitted across a synaptic gap by means of a chemical process. The action of the chemical transmitter modifies the incoming signal (typically, by scaling the frequency of the signals that are received) in a manner similar to the action of the weights in an artificial neural network.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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• Some synapses transfer a strongly stimulating signal, some only weakly stimulating ones.
• Dendrites branch like trees and receive electrical signals from many different sources, which are then transferred into the nucleus of the cell.
• In the soma the weighted information is accumulated.
• After the cell nucleus (soma) has received a plenty of activating (=stimulating) and inhibiting (=diminishing) signals by synapses, the soma accumulates these signals. If the accumulated signal exceeds a certain value (called threshold value), the soma of the neuron activates an electrical pulse which then is transmitted to the neurons connected to the current one.
• The axon transfers outgoing pulses.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Artificial Neuron Model

McCulloh-Pitts model, 1949

• Firing and the strength of the exiting signal are controlled by activation function (AF)

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Qj : external threshold, offset or bias

wji : synaptic weights

xi : input

yj : output

• Types of AF:
• Linear
• Step
• Ramp
• Sigmoid
• Hyperbolic tangent
• Gaussian

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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• ACTIVATION FUNCTION
• ACTIVATION LEVEL – DISCRETE OR CONTINUOUS
• HARD LIMIT FUCNTION (DISCRETE)
• • Binary Activation function
• • Bipolar activation function
• • Identity function
• SIGMOIDAL ACTIVATION FUNCTION (CONTINUOUS)
• • Binary Sigmoidal activation function
• • Bipolar Sigmoidal activation function

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Learning Algorithms

• A prescribed set of well-defined rules for the solution of a learning problem is called a learning algorithm.
• Basically, learning algorithms differ from each other in the way in which the adjustment Δwkj to the synaptic weight wkj is formulated.

Theoretically, a neural network could learn by:

• 1. Developing new connections.
• 2. Deleting existing connections.
• 3. Changing connecting weights, (and practically).
• 4. Changing the threshold values of neurons, (and practically).
• 5. Changing activation function, propagation function or output function.
• 6. Developing new neurons.
• 7. Deleting existing neurons.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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� Fundamentals on learning and training

• Learning is a process by which the free parameters (weights and biases) of a neural network are adapted through a continuing process of stimulation by the environment.
• This definition of the learning process implies the following sequence of events:
• 1. The neural network is stimulated by an environment.
• 2. The neural network is changed (internal structure) as a result of this stimulation.
• 3. The neural network responds in a new way to the environment.

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Department of Electrical and Electronics Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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� Setting the Weights

• The method of setting the values of the weights (training) is an important characteristic of different neural nets. different types of training:
• Supervised: in which the network is trained by providing it with input and matching output patterns.
• Unsupervised or Self-organization in which an output unit is trained to respond to clusters of pattern within the input, the system must develop its own representation of the input stimuli.
• Reinforcement learning, sometimes called reward-penalty learning, is a combination of the above two methods; it is based on presenting input vector x to a neural network and looking at the output vector calculated by the network. If it is considered "good," then a "reward" is given to the network in the sense that the existing connection weights are increased; otherwise the network is "punished," the connection weights decreased.

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Department of Electrical and Electronics Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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�Supervised learning network paradigms �

• Supervised Learning in Neural Networks: Perceptrons and Multilayer Perceptrons.
• Training set: A training set (named P) is a set of training patterns, which we use to train our neural net.
• Batch training of a network proceeds by making weight and bias changes based on an entire set (batch) of input vectors.
• Incremental training changes the weights and biases of a network as needed after presentation of each individual input vector. Incremental training is sometimes referred to as “on line” or “adaptive” training.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Topology

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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• Different NN types:
• Single-layer NNs, such as the Hopfield network
• Multilayer feedforward NNs, for example standard
• backpropagation, functional link and product unit networks
• Temporal NNs, such as the Elman and Jordan simple recurrent networks as well as time-delay neural networks
• Self-organizing NNs, such as the Kohonen self-organizing

feature maps and the learning vector quantizer

• Combined feedforward and self-organizing NNs, such as the

radial basis function networks

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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The ANN applications

• Classification, the aim is to predict the class of an input vector
• Pattern matching, the aim is to produce a pattern best associated with a

given input vector

• Pattern completion, the aim is to complete the missing parts of a given

input vector

• Optimization, the aim is to find the optimal values of parameters in an

optimization problem

• Control, an appropriate action is suggested based on given an input vectors
• Function approximation/times series modeling, the aim is to learn thefunctional relationships between input and desired output vectors;
• Data mining, with the aim of discovering hidden patterns from data (knowledge discovery)

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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ANN architectures

• Neural Networks are known to be universal function

approximators

• Various architectures are available to approximate any nonlinear function
• Different architectures allow for generation of functions of

different complexity and power

• Feedforward networks
• Feedback networks
• Lateral networks

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Feedforward Networks

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Network size: n x m x r = 2x5x1

Wmn: input weight matrix

Vrm: output weight matrix

No feedback within the network

•The coupling takes place from one layer to the next

•The information flows, in general, in the forward

direction

• Input layer: Number of neurons in this layer corresponds to the number of inputs to the neuronal network. This layer consists of passive nodes, i.e., which do not take part in the actual signal modification, but only transmits the signal to the following layer.
• Hidden layer: This layer has arbitrary number of layers with arbitrary number of neurons. The nodes in this layer take part in the signal modification, hence, they are active.
• Output layer: The number of neurons in the output layer corresponds to the number of the output values of the neural network. The nodes in this layer are active ones.

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Leaning algorithm in Supervised learning

• Gradient descent
• Widrow-hoff (LMS)
• Generalized delta
• Error-correction

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Gradient Descent

• Gradient descent (GD)…(not the first but used most)
• GD is aimed to find the weight values that minimize Error
• GD requires the definition of an error (or objective) function to measure the neuron's error in approximating the target.

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Where tp and fp are respectively the target and actual output for patterns p

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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The updated weights:

Widrow-hoff�Least-Means-Square (LMS)

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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What is Backpropagation?

• Back-propagation is the essence of neural net training.
• It is the method of fine-tuning the weights of a neural net based on the error rate obtained in the previous epoch (i.e., iteration).
• Proper tuning of the weights allows you to reduce error rates and to make the model reliable by increasing its generalization.
• Backpropagation is a short form for "backward propagation of errors."
• It is a standard method of training artificial neural networks. This method helps to calculate the gradient of a loss function with respects to all the weights in the network.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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How Backpropagation Works: Simple Algorithm

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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• Inputs X, arrive through the preconnected path
• Input is modeled using real weights W. The weights are usually randomly selected.
• Calculate the output for every neuron from the input layer, to the hidden layers, to the output layer.
• Calculate the error in the outputs
• Error_B= Actual Output – Desired Output Travel back from the output layer to the hidden layer to adjust the weights such that the error is decreased.
• Keep repeating the process until the desired output is achieved

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Department of Electrical and Electronics Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Why We Need Backpropagation?

• Most prominent advantages of Backpropagation are:
• Backpropagation is fast, simple and easy to program
• It has no parameters to tune apart from the numbers of input
• It is a flexible method as it does not require prior knowledge about the network
• It is a standard method that generally works well
• It does not need any special mention of the features of the function to be learned.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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What is Reinforcement Learning

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• Reinforcement Learning is defined as a Machine Learning method that is concerned with how software agents should take actions in an environment.
• Reinforcement Learning is a part of the deep learning method that helps you to maximize some portion of the cumulative reward.
• This neural network learning method helps you to learn how to attain a complex objective or maximize a specific dimension over many steps.

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Characteristics of Reinforcement Learning

• There is no supervisor, only a real number or reward signal
• Sequential decision making
• Time plays a crucial role in Reinforcement problems
• Feedback is always delayed, not instantaneous
• Agent's actions determine the subsequent data it receives

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Reinforcement Learning vs. Supervised Learning

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Applications of Reinforcement Learning

• Robotics for industrial automation.
• Business strategy planning
• Machine learning and data processing
• It helps you to create training systems that provide custom instruction and materials according to the requirement of students.
• Aircraft control and robot motion control

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Multilayer Perception Model

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Multilayer Perception Model

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Radial Basis functions

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Hopfield Networks

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Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Hopfield Network Algorithm

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Associative Memories

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Pattern Association

Department of Electrical and Electronics Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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Hetero Associative Memory

Department of Instrumentation and Controls Engineering, BVCOE, New Delhi Subject: NEURO & FUZZY SYSTEMS

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