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<span class="title_page">Theory</span>
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<div id="tab_space_lateral"><a href="#sub_1" class="lnk_text">Neural Networks</a></div>
<div id="tab_space_lateral"><a href="#sub_2" class="lnk_text">Kohonen Maps</a></div>
<div id="tab_space_lateral"><a href="#sub_3" class="lnk_text">Counterpropagation Artificial Neural Networs (CPANNs)</a></div>
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<span class="title_paragraph">_ Neural Networs</span>
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Artificial Neural networks (ANNs) can solve both supervised and unsupervised problems, such as clustering and modeling of qualitative responses (classification).
Basically, ANN is supposed to mimic the action of a biological network of neurons, where each neuron accepts different signals from neighbouring neurons.
Each neuron can give an output signal: the function which calculates the output vector from the input vector is composed of two parts;
the first part evaluates the net input and is a linear combination of the input variables, multiplied with coefficients called weights; the second part transfers the net input in a non-linear manner to the output vector.
Artificial neural networks can be composed of different numbers of neurons, placed into one or more layers.
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Among ANN learning strategies, Kohonen Maps and Counterpropagation Artificial Neural Networks are two of the most popular approaches.
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<span class="title_paragraph">_ Kohonen maps</span>
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Kohonen Maps are self-organising systems applied to the unsupervised problems (cluster analysis and data structure analysis).
In Kohonen maps similar input objects are linked to the topological close neurons in the network.
Basically, the neurons have as many weights as
the number of responses in the target vectors and learn to identify the location in the ANN that is most similar to the input vectors; the weights of the net are updated on the basis of the input object, i.e. the network is modified each time an object is introduced and all the objects are introduced for a certian number of times (epochs). An example of the structure of a Kohonen map with dimension 5x5, built for a dataset described by p variables is shown in the following picture.<BR>
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<center><img src="theory_kohonen.gif" width="350" height="264" border="1"></center>
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An useful paper on Kohonen maps is: <BR><BR>
Zupan J, Novic M, Ruisánchez I. (<strong>1997</strong>) Kohonen and counterpropagation artificial neural networks in analytical chemistry. <em>Chemometrics and Intelligent Laboratory Systems</em> <strong>38</strong> 1-23.<BR><BR>
The <strong>Kohonen and CPANN toolbox</strong> builds Kohonen maps in the same way as described in this paper. In order to use Kohonen maps, read <a href="kohonen.htm" class="lnk_text">how to build them by means of the <strong>Kohonen and CPANN toolbox</strong></a>.<BR>
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<span class="title_paragraph">_ Counterpropagation Artificial Neural Networks</span>
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Counterpropagation Artificial Neural Networks (CPANNs) are very similar to the Kohonen Maps and are essentially based on the Kohonen approach,
but combines characteristics from both supervised and unsupervised learning, i.e. CPANNs can be used to build both regression or classification models. CPANNs of the <strong>Kohonen and CPANN toolbox</strong> are able to build just classification models, where classification consists in finding a mathematical model
able to recognize the membership of each object (sample) to its proper class on the basis of a series of measurements (the classes must be defined a priori). To do so, an output layer is added to the Kohonen ANN:<BR>
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<center><img src="theory_cpann.gif" width="350" height="402" border="1">
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An useful paper on CPANNs is: <BR>
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Zupan J, Novic M, Ruisánchez I. (<strong>1997</strong>) Kohonen and counterpropagation artificial neural networks in analytical chemistry. <em>Chemometrics and Intelligent Laboratory Systems</em> <strong>38</strong> 1-23.<BR>
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The <strong>Kohonen and CPANN toolbox</strong> builds CPANNs in the same way as described in this paper. In order to build classification models by menas of CPANNs maps, read <a href="cpann.htm" class="lnk_text">how to do that with the <strong>Kohonen and CPANN toolbox</strong></a>.<BR>
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