# Artificial Neural Network Model

## Models of Artificial Neural Networks

There are various Artificial Neural Network Models. Main ones are

• Multilayer Perceptron – It is a feedforward artificial neural network model. It maps sets of input data onto a set of appropriate outputs.
• Radial Basis Function Network – A radial basis function network is an artificial neural network. It uses radial basis functions as activation functions.

Both of the above are being supervised learning networks used with 1 or more dependent variables at the output.

• The Kohonen Network – It is an unsupervised learning network used for clustering.

### 1. Multilayer Perceptron

As we saw above, A multilayer perceptron is a feedforward artificial neural network model. It maps sets of input data onto a set of appropriate outputs. In feed-forward neural networks, the movement is only possible in the forward direction.

An MLP consists of many layers of nodes in a directed graph, with each layer connected to the next one. Each neuron is a linear equation like linear regression as shown in the following equation

Linear Regression Equations

The equation is the transfer function in a neural network. This linear weight sum would be a threshold at some value so that output of neuron would be either 1 or 0.

The multilayer perceptron networks are suitable for the discovery of complex nonlinear models. On the possibility of approximating any regular function with a sum of sigmoid its power based.

MLP utilizes a supervised learning technique called backpropagation for training the network. This requires a known, desired output for each input value to calculate the loss function gradient.

MLP is a modification of the standard linear perceptron and can distinguish data that are not linearly separable.

### 2. Radial Basis Function Network

A Radial Basis Function (RBF) network is a supervised learning network like MLP which it resembles in some ways. But, RBF network works with only one hidden layer. It accomplishes this by calculating the value of each unit in the hidden layer for an observation. It uses the distance in space between this observation and the center of the unit. Instead of the sum of the weighted values of the units of the preceding level.

Unlike the weights of a multilayer perceptron. The centers of the hidden layer of an RBF network are not adjusted at the each iteration during learning.

In RBF network, hidden neurons share the space and are virtually independent of each other. This makes for faster convergence of RBF networks in the learning phase, which is one of their strong points.

Response surface of a unit of the hidden layer of an RBF network is a hypersphere. The response of the unit to an individual (xi) is a decreasing function G of the distance between the individual and its hypersphere.

As this function Γ generally a Gaussian function. The response surface of the unit, after the application of the transfer function, is a Gaussian surface. In other words, it is a ‘bell-shaped’ surface.

Learning of RBF involves determining the number of units in the hidden layer. Like a number of radial functions, their centers, radii, and coefficients.

### 3. The Kohonen Network

A self-organizing map (SOM) is a type of ANN that trained using unsupervised learning. It is also called as self-organizing feature map (SOFM). It produces a low-dimensional discretized representation of the input space of the training samples called a map.

The Finnish professor Teuvo Kohonen describes the model first as an ANN and it is sometimes called a Kohonen map or network.

The Kohonen network is the most common unsupervised learning network. It is also called self-adaptive or self-organizing network because of it ‘self-organizes’ input data.

Like any neural network, it is being made up of layers of units and connections between these units. The major difference from the rest of neural networks is that there is no variable that can predict.

The purpose of the network is to ‘learn’ the structure of the data so that it can distinguish clusters in them. By the following two levels the Kohonen network composed.

• Input layer with a unit for each of the n variables used in clustering
• Output layer – Its units are generally in a square or rectangular grid of l*m units. Each of these l*m units is connected to each of n units of the input layer.

The key related to Kohonen networks:

• For each individual, only one output unit (the ‘winner’) is activated – The Kohonen Net has a competitive layer of neurons. There is also an input layer. The input layer is fully connected to the competitive layer. The units in the competitive layer sum their weighted inputs to find a single winner.
• It adjusts the weight of the winner and its neighbors.
• The adjustment is such that two close placed output units correspond to two close placed individuals.
• At the output Groups (clusters) of units forms.

In the application phase, Kohonen network operates by representing each input individual by the unit of the network. The network which is closest to it in terms of a distance defined above. This unit will be the cluster of the individual.