A. Introduction to neural networks
B. ANN architectures
- Feedforward networks
- Feedback networks
- Lateral networks
C. Learning methods
- Supervised learning
- Unsupervised learning
- Reinforced learning
D. Learning rule on supervised learning
- Gradient descent,
- Widrow-hoff (LMS)
- Generalized delta
- Error-correction
E. Feedforward neural network with Gradient descent optimization
Introduction to neural networks
Definition: the ability to learn, memorize and still generalize, prompted research in algorithmic modeling of biological neural systems.
Human brain has the ability to perform tasks such as pattern recognition, perception and motor control much faster than any computer.
Biological neuron
Soma: Nucleus of neuron (the cell body) –
process the input
- Dendrites: long irregularly shaped filaments attached to the soma – input channels
- Axon: another type link attached to the soma – output channels
- Output of the axon: voltage pulse (spike) that lasts for a ms
- Firing of neuron – membrane potential
- Axon terminates in a specialized contact called the synaptic junction – the electrochemical contact between neurons
- The size of synapses are believed to be linked with learning
- Larger area: excitatory—smaller area: inhibitory
Artificial neuron model (McCulloh-Pitts model, 1949)
Qj : external threshold, offset or bias
wji : synaptic weights
xi : input
yj : output
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
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 the functional relationships between input and desired output vectors;
- Data mining, with the aim of discovering hidden patterns from data (knowledge discovery)
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
Feed Farword Networks
- 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.
•No feedback within the network
•The coupling takes place from one layer to the next
•The information flows, in general, in the forward direction
Feedback networks Elman Recurrent Network
The output of a neuron is either directly or indirectly fed back to its input via other linked neurons used in complex pattern recognition tasks, e.g., speech recognition etc.
Feedback networks Jordan Recurrent Network
Lateral Networks
•There exist couplings of neurons within one layer
•There is no essentially explicit feedback path amongst the different layers
•This can be thought of as a compromise between the forward and feedback network.
Learning methods
- Artificial neural networks work through the optimized weight values.
- The method by which the optimized weight values are attained is called
learning - In the learning process try to teach the network how to produce the
output when the corresponding input is presented - When learning is complete: the trained neural network, with the updated
optimal weights, should be able to produce the output within desired
accuracy corresponding to an input pattern.
Learning methods
- Supervised learning
- Unsupervised learning
- Reinforced learning
Classification of Learning Algorithms
Supervised learning
Supervised learning means guided learning by “teacher”; requires a training set which consists of input vectors and a target vector associated with each input vector.
Unsupervised learning
- The objective of unsupervised learning is to discover patterns or features in the input data with no help from a teacher, basically performing a clustering of input space.
- The system learns about the pattern from the data itself without a priori knowledge. This is similar to our learning experience in adulthood “For example, often in our working environment we are thrown into a project or situation which we know very little about. However, we try to familiarize with the situation as quickly as possible using our previous experiences, education, willingness and similar other factors”
- Hebb’s rule: It helps the neural network or neuron assemblies to remember specific patterns much like the memory. From that stored knowledge, similar sort of incomplete or spatial patterns could be recognized. This is even faster than the delta rule or the backpropagation algorithm because there is no repetitive presentation and training of input–output pairs.
Reinforced learning
•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
•A reward is given for a correct answer computed and a penalty for a wrong answer
Leaning algorithm in Supervised learning
- Gradient descent
- Widrow-hoff (LMS)
- Generalized delta
- Error-correction
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.
Where tp and fp are respectively the target and actual output for patterns p
The updated weights:
Analogy: Suppose we want to come down (descend) from a high hill (higher error) to a low valley (lower error). We move along the negative gradient or slopes. By doing so, we take the steepest path to the downhill valley steepest descent algorithm.
Widrow-hoff Least-Means-Square (LMS)
Assume that f = up The weights are updated using:
Generalized delta
Assume: Differentiable activation functions; such as sigmoid function The weights are updated using:
Error-correction
Assume that binary-valued functions are used, e.g the step function. The weights are updated using:
Weights are only adjusted when the neuron responds in error
Feedforward neural network with Gradient descent optimization
Functional Diagram of FFNN
Feedforward Operation
Input vector xj where j =1 to n (number of inputs)
Input weight matrix Wij where i = 1 to m (hidden neurons)
Backpropagation Operation
The backpropagation training algorithm is based on the principle of gradient descent and is given as half the square of the Euclidean norm of the output error vector.
One set of weight modifications is called an epoch, and many of these may be required before the desired accuracy of approximation is reached.
“This is the objective function for NN learning that need to be optimized by the optimization methods”
Optimization methods to carry out NN learning
- Local optimization, where the algorithm ends up in a local optimum without finding a global optimum. Gradient descent and scaled conjugate gradient are local optimizers.
- Global optimization, where the algorithm searches for the global optimum by with mechanisms that allow greater search space explorations. Global optimizers include Leapfrog, simulated annealing, evolutionary computing and swarm optimization.
“Local and global optimization techniques can be combined to form hybrid training algorithms”
Weight Adjustments/Updates
Two types of supervised learning algorithms exist, based on when/how weights are updated:
- Stochastic/Delta/(online) learning, where the NN weights are adjusted after each pattern presentation. In this case the next input pattern is selected randomly from the training set, to prevent any bias that may occur due to the sequences in which patterns occur in the training set.
- Batch/(offline) learning, where the NN weight changes are accumulated and used to adjust weights only after all training patterns have been presented.
Feedforward Neural Networks (effects of weight variations)
