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112 changes: 59 additions & 53 deletions src/lab/exp7/Tutorial.html
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Expand Up @@ -7,24 +7,30 @@
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Expand All @@ -41,11 +47,11 @@
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Expand All @@ -54,7 +60,7 @@
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<h2 class="text-h2-lightblue" style=" margin-bottom: 20px; margin-top: 10px; "><a href="http://vlab.co.in/ba_labs_all.php?id=2" class="sidebar-a" >Computer Science & Engineering</a> &rarr;<a href="../Experiments.html" class="sidebar-a" >Artificial Neural Networks Virtual Lab</a>&nbsp&rarr;<a href="../Experiments.html" class="sidebar-a" >List Of Experiments</a><br/></h2>

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<a href="Objective.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Objective</h3></a><a href="Tutorial.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Tutorial</h3></a><a href="Illustration.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Illustration</h3></a><a href="Procedure.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Procedure</h3></a><a href="Experiment.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Experiment</h3></a><a href="Observations.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Observations</h3></a><a href="Assignment.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Assignment</h3></a><a href="References.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">References</h3></a><a href="Feedback.html?domain=Computer Science&lab=Artificial Neural Networks Virtual Lab" class="sidebar-a" > <h3 class="text-h3-darkblue" style="margin-top: 2px;">Feedback</h3></a> </div>

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<h1 class="text-h2-lightblue">Competitive learning neural networks</h1><div class="content" id="experiment-article-section-2-content">
<h3>CLFFNN - An Introduction</h3>
<p>
In this experiment we consider pattern recognition tasks that a network
of the type shown in Fig. 1 below can perform. The network consists
of an input layer of linear units. The output of each of these units is
given to the units in the second layer (output layer) with
given to the units in the second layer (output layer) with
(adjustable) feedforward weights. The output functions of the units
in the second layer are either linear or nonlinear depending on the
task for which the network is to be designed. The output of each unit
Expand All @@ -117,11 +123,11 @@ <h3>CLFFNN - An Introduction</h3>
in the output layer, and hence such networks are called competitive
learning neural networks. Different choices of the output functions
and interconnections in the feedback layer of the network can be used
to perform different pattern recognition tasks. For example, if the
weights loading to the unit with the largest output for a given input are adjusted,
the resulting network performs pattern clustering or grouping, provided the
feedback connections in the output layer are all inhibitory.
The unit with largest output for a given input is called winner, and
to perform different pattern recognition tasks. For example, if the
weights loading to the unit with the largest output for a given input are adjusted,
the resulting network performs pattern clustering or grouping, provided the
feedback connections in the output layer are all inhibitory.
The unit with largest output for a given input is called winner, and
the learning law is called winner-take-all learning.
</p>
<p>
Expand All @@ -133,7 +139,7 @@ <h3>CLFFNN - An Introduction</h3>
</p>
<h3>Analysis of feature mapping network</h3>
<p>
There are situations where it is difficult to group the input patterns into distinct groups.
There are situations where it is difficult to group the input patterns into distinct groups.
The patterns may form a continuum in feature space, and it is this kind of
information that may be needed in some applications. For example,
it may be of interest to know how close a given input is to some of
Expand All @@ -152,13 +158,13 @@ <h3>Analysis of feature mapping network</h3>
input values to a line or a plane of the output units [Kohonen, 1982b;
Kohonen, 1989.]
The inputs to a feature mapping network could be N-dimensional
patterns, applied one at a time, and the network is to be trained to map the similarities
of the input patterns in the weights leading to the neighbouring units.
patterns, applied one at a time, and the network is to be trained to map the similarities
of the input patterns in the weights leading to the neighbouring units.
Another type of input is shown in Figure 2, where
the inputs are arranged in a 2-D array so that the array represents
the input pattern space as in the case of a textured image. At any
given time only a few of the input units may be turned on, and hence
only the corresponding links are activated.
only the corresponding links are activated.
</p>
<p>
<!--Figure HERE -->
Expand All @@ -172,10 +178,10 @@ <h3>Analysis of feature mapping network</h3>
are set to random initial values. When an input vector \(x\) is applied,
the winning unit \(k\) in the output layer is identified such that
<ol><ol><ol>
<p>
||<b>x</b> - <b>w</b>\(_k\) || \(\le\) ||<b>x</b> - <b>w</b>\(_i\) || \(\forall\) \(i \qquad(1)\)
<p>
||<b>x</b> - <b>w</b>\(_k\) || \(\le\) ||<b>x</b> - <b>w</b>\(_i\) || \(\forall\) \(i \qquad(1)\)
</p>
<p>
<p>
where <b>w</b>\(_i\) is the weight vector leading to the unit \(i\) in the output layer.
</p>
</ol></ol></ol>
Expand All @@ -185,17 +191,17 @@ <h3>Analysis of feature mapping network</h3>
using the expression
</p>
<ol><ol><ol>
<p>
\( \Delta{w_m} = \eta{*}\lambda{(k,m)(x-w_m)} \qquad(2)\)
<p>
\( \Delta{w_m} = \eta{*}\lambda{(k,m)(x-w_m)} \qquad(2)\)
</p>
</ol></ol></ol>
<p>
The neighbourhood function \( \lambda(k, m)~\) is maximum for \(m = k.~\) A suitable
choice for \( \lambda(k, m)~\) is a Gaussian function of the type
</p>
<ol><ol><ol>
<p>
\( \lambda(k,m) = ({1/}\sqrt{2\pi}\sigma) * exp(-||\)<b>r</b>\(_k\)-<b>r</b>\(_m||)^2/2\sigma^2 \qquad(3)\)
<p>
\( \lambda(k,m) = ({1/}\sqrt{2\pi}\sigma) * exp(-||\)<b>r</b>\(_k\)-<b>r</b>\(_m||)^2/2\sigma^2 \qquad(3)\)
</p>
</ol></ol></ol>
<p>
Expand All @@ -213,16 +219,16 @@ <h3>Following is an algorithm for implementing the self-organizing feature map l
random values. Initialize the size of the neighbourhood region \( R(0)\). </p>
<li><p>Present a new input <b><i>a</i></b>.</p>
<li><p>Compute the distance \(d_i\) between the input and the weight on each output
unit \(i\) as
\( d_i = \sum\limits_{j=1}^M [a_j(t)-w_{ij}(t)]^2 ,\) \(for\) \(i = 1,2.. N,~\)
where \(a_i(t)\) is the input to the \(j^{th}\) input unit at time \(t\) and \(w_{ij}\)
unit \(i\) as
\( d_i = \sum\limits_{j=1}^M [a_j(t)-w_{ij}(t)]^2 ,\) \(for\) \(i = 1,2.. N,~\)
where \(a_i(t)\) is the input to the \(j^{th}\) input unit at time \(t\) and \(w_{ij}\)
is the weight on the \(j^{th}\) input unit to the \(i^{th}\) output unit.
<li><p>
Select the output unit \(k\) with minimum distance
\( k =\) index of \([\min(d_i)]\) over \(i\)
</p>
<li><p>Update weight to node \(k\) and its neighbours \(w_{ij}(t+1) = w_{ij}(t) + \eta(t)(a_j(t)- w_{ij}(t))\)
for \( i\) \( \epsilon\) \(R_k(t)\) \(and\) \(j=1,2...M, ~ \) where \(\eta(t)\) is the learning rate parameter
<li><p>Update weight to node \(k\) and its neighbours \(w_{ij}(t+1) = w_{ij}(t) + \eta(t)(a_j(t)- w_{ij}(t))\)
for \( i\) \( \epsilon\) \(R_k(t)\) \(and\) \(j=1,2...M, ~ \) where \(\eta(t)\) is the learning rate parameter
\( (0 \lt \eta(t) \lt 1) \) that decreases with time.</p>
<li><p>Repeat steps 2 to 5 for all inputs several times</p>
</li></li></li></p></li></li></li></ol></ol></ol>
Expand All @@ -234,9 +240,9 @@ <h3>Following is an algorithm for implementing the self-organizing feature map l




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