Counterpropagation ANN

Counterpropagation networks have been used in property prediction, QSAR, the prediction of retention indices, and Kovats indices in gas chromatography. " In the latter application these networks performed better than multilinear regression when the coefficient of determination (r ) was low but were worse when was high. Apparently, counterpropagation ANNs per-... 

Figure 9 A counterpropagation ANN has two layers of neurons one Kohonen and one output layer. In the Kohonen layer to which objects X, are input the most excited neuron is selected. Corrections of weights are made around the position of the excited neuron (bold arrow) in the Kohonen and in the output layer using equations (8) and (9), respectively...

By far the largest group of ANN applications in chemistry is dealing with various kinds of classification problems. In this group one can find simple one-object-to-one-class classifications to more complicated one-object-to several-classes problems. The classification problems can be solved either by error-backpropagation or by counterpropagation ANNs. 

Figure 17 The same counterpropagation ANN can serve as a direct or as an inverse model even in cases with a single-valued-output in the direct model. The direct model on the left yields for the input vector X = (0.8,0.2, 0.6) the response y = 0.9. The inverse model (right) does not provide unique responses (answers), but allows three output variables to be found within intervals (shaded areas on right). It has to be emphasized that in the inverse model not all combinations of output values are possible even if they are within the specified intervals...

Several nonlinear QSAR methods have been proposed in recent years. Most of these methods are based on either ANN or machine learning techniques. Both back-propagation (BP-ANN) and counterpropagation (CP-ANN) neural networks [33] were used in these studies. Because optimization of many parameters is involved in these techniques, the speed of the analysis is relatively slow. More recently, Hirst reported a simple and fast nonlinear QSAR method in which the activity surface was generated from the activities of training set compounds based on some predefined mathematical functions [34]. 

Another type of ANNs widely employed is represented by the Kohonen self organizing maps (SOMs), used for unsupervised exploratory analysis, and by the counterpropagation (CP) neural networks, used for nonlinear regression and classification (Marini, 2009). Also, these tools require a considerable number of objects to build reliable models and a severe validation. 

M-CASE/BAIA (see text). BP-ANN = three-layer feedforward artificial neural network trained by the backpropagation algorithm, PAAN = probabilistic artificial neural network, CPANN = counterpropagation artificial neural network. 

Counterpropagation (CPG) Neural Networks are a type of ANN consisting of multiple layers (i.e., input, output, map) in which the hidden layer is a Kohonen neural network. This model eliminates the need for back-propagation, thereby reducing training time. 

Hybrid networks combine the features of two or more types of ANN, the idea being to highlight the strengths and minimize the weaknesses of the different networks. Examples are the Hamming network, which has a perceptron-like and a Hopfield-like layei and the counterpropagation network, which has a Kohonen layer and a Grossberg outstar layer. 

To provide you with a solid basis for deciding whether or not a given ANN is appropriate for your intended use, we describe briefly in this section many of the types of ANNs that have appeared in the literature in the past few years. For each network we focus on strengths and weaknesses, some practical aspects of operation, and a literature review of the chemical applications. We do not delve into detailed mathematical descriptions of networks, since these can be found in any number of texts. In particular we call attention to Ref. 19, which offers step-by-step developments of equations and detailed numerical examples for backpropagation, biassociative memory, counterpropagation, Hopfield, and Kohonen self-organizing map networks. Adaptive resonance theory networks are reviewed in detail in Ref. 27. 

Heteroassociative networks termed counterpropagation can accept continuous inputs and outputs. They are two-layer ANNs (disregarding the... 

ANN = artificial neural network CPG = counterpropagation 3D-MoRSE = 3D molecular representation of structures based on electron diffraction FREL = fragment reduced to an environment that is limited. 

ANN = artificial neural networks CP ANN = counterpropagation artificial neural networks EBP ANN = error-back-propagation artificial neural network XOR = exclusive-or logical operation. 

Once clusters of classes which correspond to the expectations are confirmed by the Kohonen ANN, the clas.sification problem (described in Section 5.1) can be solved by error-backpropagation or counterpropagation training in which each... 

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