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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">MOLMAP modeling </a></div>
<div id="tab_space_lateral"><a href="#sub_2" class="lnk_text">Kohonen Maps</a></div>
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<span class="title_paragraph">_ MOLMAP modeling</span>
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A new method for the study of molecule chemical information organized into three-way data structures (MOLMAP) was recently proposed in literature (Zhang 2007 and Zhang 2005, see the references below). Basically, MOLMAP molecular fingerprints are calculated by projecting bond properties of molecules into Kohonen networks and used to generate molecular descriptors for QSAR modeling. The input of the MOLMAP approach is a three-way data matrix: molecules on the first mode, molecule bonds on the second mode and bond properties on the last mode. The data array is unfolded and used to train a Kohonen map; after the training phase, each slice of the original data array (representing a single molecule) is submitted to the trained map and a score vector is built on the basis of the activated neurons. This score vectors can be thought as the pattern of neurons that are activated by the bonds existing in the molecule and considered as a fingerprint of molecule features. <BR>
The MOLMAP approach has been used for QSAR modeling and chemo-informatic studies of molecular reactivity; but the <strong>MOLMAP multiway toolbox </strong>has been built in order to apply the <a href="molmap_modeling.htm" class="lnk_text">MOLMAP approach</a> for the classification of three-way (multiway) datasets. <BR>
The MOLMAP approach requires two major steps: a) generation of MOLMAP scores by means of <a href="#sub_2" class="lnk_text">Kohonen Maps</a> and b) development of predictive classification models which use MOLMAP scores as independent variables. In the <strong>MOLMAP multiway toolbox</strong>, this second step is <strong>not</strong> calculated , but you can apply the classification method you prefer on the MOLMAP score matrix produced by the toolbox. In order to better understand the MOLMAP approach for the classification of multiway data, read: <BR>
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Ballabio D, Consonni V, Todeschini R. (<strong>2007</strong>) Classification of multiway analytical data based on MOLMAP approach. <em>Analytica Chimica Acta </em> <strong>in press</strong>, doi:10.1016/j.aca.2007.10.029
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Original papers on MOLMAP molecular descriptors are:
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Zhang QY, Aires-de-Sousa J. (<strong>2005</strong>) Structure-Based Classification of Chemical Reactions without Assignment of Reaction Centers. <em>Journal of Chemical Information and Modeling</em> <strong>45</strong> 1775-1783.
<p>Zhang QY, Aires-de-Sousa J. (<strong>2007</strong>) Random Forest Prediction of Mutagenicity from Empirical Physicochemical Descriptors. <em>Journal of Chemical Information and Modeling</em> <strong>47</strong> 1-8.<BR>
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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.</p>
<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>
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