Neural network computed mapping

Rassokhin, D., Lobanov, V. S., and Agrafiotis, D. K. (2000) Nonlinear mapping of massive data sets by fuzzy clustering and neural networks../. Comput. Chem. 21, 1-14. 

The profits from using this approach are dear. Any neural network applied as a mapping device between independent variables and responses requires more computational time and resources than PCR or PLS. Therefore, an increase in the dimensionality of the input (characteristic) vector results in a significant increase in computation time. As our observations have shown, the same is not the case with PLS. Therefore, SVD as a data transformation technique enables one to apply as many molecular descriptors as are at one s disposal, but finally to use latent variables as an input vector of much lower dimensionality for training neural networks. Again, SVD concentrates most of the relevant information (very often about 95 %) in a few initial columns of die scores matrix. 

So far, we have seen that given a neural architecture, the neural network may be trained to arrive at colors that are approximately constant. Evolution is also able to find a solution to the problem of color constancy. One of the remaining questions is about how a computational color constancy algorithm is actually mapped to the human visual system. Several researchers have looked at this problem and have proposed possible solutions. 

We can sum up what one can do with a neural network. In principle, neural networks are universal approximators and can compute any computable function. In practice, neural networks are especially useful for classification and function approximation/mapping problems that have plenty of training data available and can tolerate some imprecision but that resist the easy application of hard and fast rules. 

Kireev, D.B. (1995). ChemNet A Novel Neural Network Based Method for Graph/Property Mapping. J. Chem.lnf.Comput.Sci., 35,175-180. 

Maggiora, G.M., Elrod, D.W and Trenary, R.G. (1992). Computational Neural Networks as Model Free Mapping Devices. J.Chem.Inf.Comput.ScL, 32,732-741. 

Nonlinear PCA To address the nonlinearity in the identity mapping of multivariate data, a nonlinear counterpart of the PCA can be used (see Section 3.6.1). As the versions of NLPCA make use of the neural network (NN) concept to address the nonlinearity, they suffer from the known overparameterization problem in the case of noise corrupted data. Data with small SNR will also give rise to extensive computations during the training of the network. Shao et al. [266] used wavelet filtering to pre-process the data followed by IT-net to detect the non-conforming trends in an industrial spray drier. 

Self-organizing maps (SOMs) are one manifestation of neural network approaches to clustering. They have been extensively used in many fields of computational medicinal chemistry [51]. SOMs consist of a grid of neural elements, each containing a vector of a certain dimension. The map is trained by presenting a series of new data objects to the... 

In direct inverse control, (Figure 12.2), the neural network is used to compute an inverse model of the system to be controlled ]Levin et al., 1991 Nordgren and Meckl, 1993]. In classical linear control techniques, one would find a linear model of the system then analytically compute the inverse model. Using neural networks, the network is trained to perform the inverse model calculations, that is, to map system outputs to system inputs. Biomedical applications of this type of approach include the control of arm movements using electrical stimulation [Lan et al., 1994] and the adaptive control of arterial blood pressure [Chen et al, 1997]. 

Artificial neural networks (ANNs) are a non-linear function mapping technique that was initially developed to imitate the brain from both a structural and computational perspective. Its parallel architecture is primarily responsible for its computational power. The multilayer perceptron network architecture is probably the most popular and is used here. 

R. Kocjancic and J. Zupan,/. Chem. Inf. Comput. Set, 37,985 (1997). Application of Feed-Forward Artificial Neural Network as a Mapping Device. 

The use of ANN is highly developed due their great advantage compared with traditional computing systems. ANNs have a flexible structiue, capable to make a nonlinear mapping between input and output data sets. In fact, multilayer perceptrons, one of the more extended neural network architectures, are imiversal approximators for complex problems [12]. The apphcation of this is reflected in the hteratiue devoted to prediction of many physical and chemical parameters, such as nanofluids density [14], density of binary mixtures of ionic hquids [15], electrical percolation temperatiue [16], molecular diffusivity of nonelectrolytes [17], vegetable oils viscosity [18], esters flash point prediction [12], polarity parameter in binary mixed solvents systems [19], etc. 

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