![bodyof an artificial neuron then sums the weighted inputs, bias and “processes”
the sum with a transfer function. At the end an artificial neuron passes the
processed information via output(s). Benefit of artificial neuron model
simplicity can be seen in its mathematical description below:
..(1)
Where:
• xi(k) is input value in discrete time k where i goes from 0 to m,
• wi(k) is weight value in discrete time k where i goes from 0 to m,
• b is bias,
• F is a transfer function,
• yi(k) is output value in discrete time k.
As seen from a model of an artificial neuron and its equation (1) the major
unknown variable of our model is its transfer function. Transfer function defines
the properties of artificial neuron and can be any mathematical function. We
chooseit on the basis of problem that artificial neuron (artificial neural network)
needs to solve.
y(k) = F[∑ {𝒙𝒊 ( 𝒌). 𝒘𝒊 ( 𝒌)} + 𝒃]𝒎
𝒊=𝟎](https://image.slidesharecdn.com/comparativestudyofansandbnsandmathematicalmodelingofaneuron-180202051639/85/Comparative-study-of-ANNs-and-BNNs-and-mathematical-modeling-of-a-neuron-4-320.jpg)
Comparative study of ANNs and BNNs and mathematical modeling of a neuron
- 1. ANALOGY BETWEEN ANs AND BNs It is known very well that the study of ANNs is inspired from the working of human brain. In this context, it is quite necessary to draw an analogy between ANN and BNN as the former closely resembles the latter and provides a better insight for the improvement so as to establish a closer correlation between the two. BIOLOGICAL NEURON STRUCTURE Biological Neurons have the following parts : Soma Dendrites Synapse Axon Biological neurons have three main parts: a central cell body, called the soma, and two different types of branched, tree like structures that extend from the soma, called dendrites and axons. Information from other neurons, in the form of electrical impulses, enters the dendrites at connection points called synapses. The information flows from the dendrites to the soma where it is processed. Theoutput signal, a train of impulses, is then sent down the axon to the synapse of other neurons. ARTIFICIAL NEURON Artificial neurons also have the following components that are equivalent to biological neurons : Node Input Weight Output The main bodyof an artificial neuron is called a node or unit. They are physically connected to one another by wires that resemble the connections between biological neurons. The arrangement and connections of the neurons which make up the network has three layers : The inputlayer, which is the only layer exposed to external signals. The input layer transmits signals to the neurons in the next layer, which is called a hidden layer. The hidden layer extracts relevant features or patterns from the received signals. Thosefeatures or patterns that are considered important in the hidden layer stage are then directed to the output layer, which is the final layer of the network.
- 2. FUNCTIONS Dendrites provide input signals to the cells. A synapse is able to increase or decrease the strength of the connection. This is where information is stored. The axon sends output signal to another cell. The axon terminals merge with the dendrites of the other cells. The brain is made up of a great number of neurons (about 1011 ), each of which is connected to many other components (about 104 ) and performs some relatively simple computation, whose nature is unclear, in slow fashion connections. The artificial neuron receives inputs in its input nodes analogous to the electrochemical impulses the dendrites of biological neurons receive from another neuron. The artificial signals can be changed by altering weights in a manner similar to the physical changes that occur in the synapses. The output nodes of the artificial neuron correspond to output signals sent out from biological neuron over its axon. Artificial neurons are connected randomly or uniformly, and all neurons perform the same computation. Each connection has a numerical weight associated with it. Each neuron’s output is a single numerical activity which is computed as a monotonic function of the sum of the products ofthe activity of the input neurons with their correspondingconnection weights. LEARNING They learn from past experience to improve their own performance levels. Learning in biological systems involves adjustments to the synaptic connections that exist between the neurons. They also learn from past experience to improve their own performance levels. This is true of artificial neurons as well.
- 3. INFORMATION TRANSMISSION Information transmission from one biological neuron to another involves in the form of electrical signals. In artificial neurons, electrical signals are also used in information transmission. MATHEMATICAL MODELLING OF A NEURON: As is evident from the above comparative study of biological and artificial neuron chiefly in regard to structural and functional perspectives, in a nutshell, we can draw an analogous mapping between biological neurons and their artificial counterparts, as summarised in the following table: BIOLOGICAL NEURON ARTIFICIAL NEURON Neuron Processing Element Dendrites Combining Function Cell Body Transfer Function Axons Element Output Synapses Weights In case of biological neuron information comes into the neuron via dendrite, soma processes the information and passes it on via axon. In case of artificial neuron the information comes into the bodyof an artificial neuron via inputs that are weighted (each input can be individually multiplied with a weight). The
- 4. bodyof an artificial neuron then sums the weighted inputs, bias and “processes” the sum with a transfer function. At the end an artificial neuron passes the processed information via output(s). Benefit of artificial neuron model simplicity can be seen in its mathematical description below: ..(1) Where: • xi(k) is input value in discrete time k where i goes from 0 to m, • wi(k) is weight value in discrete time k where i goes from 0 to m, • b is bias, • F is a transfer function, • yi(k) is output value in discrete time k. As seen from a model of an artificial neuron and its equation (1) the major unknown variable of our model is its transfer function. Transfer function defines the properties of artificial neuron and can be any mathematical function. We chooseit on the basis of problem that artificial neuron (artificial neural network) needs to solve. y(k) = F[∑ {𝒙𝒊 ( 𝒌). 𝒘𝒊 ( 𝒌)} + 𝒃]𝒎 𝒊=𝟎