Linear networks, artificial neural

In the last few decades, several methods for the training of various types of predicting functions [117] were developed using inferential statistics. Most important ene linear models, artificial neural networks, support vector machines, classification and regression trees emd the method of k nearest neighbors. 

Aptula et al. used multiple linear regression to investigate the toxicity of 200 phenols to the ciliated protozoan Tetrahymena pyriformis Using their MLR model, they then predicted the toxicity of another 50 phenols. Here we present a comparative study for the entire set of 250 phenols, using multiple linear regression, artificial neural networks, and SVM regression methods. Before computing the SVM model, the input vectors were scaled to zero mean and unit variance. The prediction power of the QSAR models was tested with complete cross-validation leave-5%-out (L5%0), leave-10%-out (L10%O), leave-20%-out (L20%O), and leave-25%-out (L25%0). The capacity parameter C was optimized for each SVM model. 

Woodruff and co-workers introduced the expert system PAIRS [67], a program that is able to analyze IR spectra in the same manner as a spectroscopist would. Chalmers and co-workers [68] used an approach for automated interpretation of Fourier Transform Raman spectra of complex polymers. Andreev and Argirov developed the expert system EXPIRS [69] for the interpretation of IR spectra. EXPIRS provides a hierarchical organization of the characteristic groups that are recognized by peak detection in discrete ames. Penchev et al. [70] recently introduced a computer system that performs searches in spectral libraries and systematic analysis of mixture spectra. It is able to classify IR spectra with the aid of linear discriminant analysis, artificial neural networks, and the method of fe-nearest neighbors. 

Aqueous solubility is selected to demonstrate the E-state application in QSPR studies. Huuskonen et al. modeled the aqueous solubihty of 734 diverse organic compounds with multiple linear regression (MLR) and artificial neural network (ANN) approaches [27]. The set of structural descriptors comprised 31 E-state atomic indices, and three indicator variables for pyridine, ahphatic hydrocarbons and aromatic hydrocarbons, respectively. The dataset of734 chemicals was divided into a training set ( =675), a vahdation set (n=38) and a test set (n=21). A comparison of the MLR results (training, r =0.94, s=0.58 vahdation r =0.84, s=0.67 test, r =0.80, s=0.87) and the ANN results (training, r =0.96, s=0.51 vahdation r =0.85, s=0.62 tesL r =0.84, s=0.75) indicates a smah improvement for the neural network model with five hidden neurons. These QSPR models may be used for a fast and rehable computahon of the aqueous solubihty for diverse orgarhc compounds. 

In recent years there has been much activity to devise methods for multivariate calibration that take non-linearities into account. Artificial neural networks (Chapter 44) are well suited for modelling non-linear behaviour and they have been applied with success in the field of multivariate calibration [47,48]. A drawback of neural net models is that interpretation and visualization of the model is difficult. Several non-linear variants of PCR and PLS regression have been proposed. Conceptually, the simplest approach towards introducing non-linearity in the regression model is to augment the set of predictor variables (jt, X2, ) with their respective squared terms (xf,. ..) and, optionally, their possible cross-product... 

Several additional instrumental techniques have also been developed for bacterial characterization. Capillary electrophoresis of bacteria, which requires little sample preparation,42 is possible because most bacteria act as colloidal particles in suspension and can be separated by their electrical charge. Capillary electrophoresis provides information that may be useful for identification. Flow cytometry also can be used to identify and separate individual cells in a mixture.11,42 Infrared spectroscopy has been used to characterize bacteria caught on transparent filters.113 Fourier-transform infrared (FTIR) spectroscopy, with linear discriminant analysis and artificial neural networks, has been adapted for identifying foodbome bacteria25,113 and pathogenic bacteria in the blood.5... 

In the last decades not only thousands of chemical descriptors but also many advanced, powerful modeling algorithms have been made available, The older QSAR models were linear equations with one or a few parameters. Then, other tools have been introduced, such as artificial neural network, fuzzy logic, and data mining algorithms, making possible non linear models and automatic generation of mathematical solutions. 

Artificial neural network Multiple linear regression (Statistica)... 

Compared with the artificial neural network (ANN) approach used in previous work to predict CN12 the linear regression model by QSAR is as good or better and easier to implement. The predicted CN values, some of which are tabulated in Table 1, will be employed below to evaluate the different catalytic strategies to optimize the fuel. 

Also nonlinear methods can be applied to represent the high-dimensional variable space in a smaller dimensional space (eventually in a two-dimensional plane) in general such data transformation is called a mapping. Widely used in chemometrics are Kohonen maps (Section 3.8.3) as well as latent variables based on artificial neural networks (Section 4.8.3.4). These methods may be necessary if linear methods fail, however, are more delicate to use properly and are less strictly defined than linear methods. 

Models of the form y =f(x) or v =/(x1, x2,..., xm) can be linear or nonlinear they can be formulated as a relatively simple equation or can be implemented as a less evident algorithmic structure, for instance in artificial neural networks (ANN), tree-based methods (CART), local estimations of y by radial basis functions (RBF), k-NN like methods, or splines. This book focuses on linear models of the form... 

M. Blanco, J. CoeUo, H. Iturriaga, S. Maspoch and J. Pages, NIR calibration in non-linear systems different PLS approaches and artificial neural networks, Chemom. Intell. Lab. Syst, 50, 75-82 (2000). 

Traditional regression-type models have been linear and quadratic regression models. Linear and quadratic regression models unfortunately impose further constraints upon the nature of the process nonlinearity as such, these models are limited in the range of their applicability. A relatively new nonlinear regression-type model—the Artificial Neural Network (ANN)—is not as limited, and is worthy of additional discussion. 

The method of Lydersen [28] is a GCM of this type to estimate the critical temperature, Tc. Other approaches to non-linear GCMs include the model of Lai et al. [29] for the boiling point, Tby and the ABC approach [30] to estimate a variety of thermodynamic properties. Further, artificial neural networks have been used to construct nonlinear models for the estimation of the normal boiling point of haloalkanes [31] and the boiling point, critical point, and acentric factor of diverse fluids [32]. 

---