Neural network calibration models

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... 

A. Bos, M. Bos and W.E. Van der Linden, Artificial neural networks as a multivariate calibration tool modeling the ion-chromium nickel system in x-ray fluorescence spectra. Anal. Chim. Acta, 277 (1993) 289-295. 

For PyMS to be used for (1) routine identification of microorganisms and (2) in combination with ANNs for quantitative microbiological applications, new spectra must be comparable with those previously collected and held in a data base.127 Recent work within our laboratory has demonstrated that this problem may be overcome by the use of ANNs to correct for instrumental drift. By calibrating with standards common to both data sets, ANN models created using previously collected data gave accurate estimates of determi-nand concentrations, or bacterial identities, from newly acquired spectra.127 In this approach calibration samples were included in each of the two runs, and ANNs were set up in which the inputs were the 150 new calibration masses while the outputs were the 150 old calibration masses. These associative nets could then by used to transform data acquired on that one day to data acquired at an earlier data. For the first time PyMS was used to acquire spectra that were comparable with those previously collected and held in a database. In a further study this neural network transformation procedure was extended to allow comparison between spectra, previously collected on one machine, with spectra later collected on a different machine 129 thus calibration transfer by ANNs was affected. Wilkes and colleagues130 have also used this strategy to compensate for differences in culture conditions to construct robust microbial mass spectral databases. 

How can we fine-tune the model Well, remember that we have prepared a different set of samples to validate the model. You can use this set to evaluate which model predicts best. If you have a sufficient number of samples, it would be even better to prepare a small testing or "control set (different from the calibration and validation sets and without a too large number of samples) to visualise which model seems best and, then, proceed with the validation set. This strategy has to be applied when developing artificial neural networks (see Chapter 5). 

It is worth comparing briefly the PLS (Chapter 4) and ANN models. The ANN selected finally uses four neurons in the hidden layer, which is exactly the same number of latent variables as selected for PLS, a situation reported fairly frequently when PLS and ANN models perform similarly. The RMSBC and RMSBP were slightly higher for PLS, 1.4 and L5pgmU respectively, and they were outperformed by the ANN (0.7 and 0.5pgnil respectively). The best predictive capabilities of the neural network might be attributed to the presence of some sort of spectral nonlinearities in the calibration set and/or some spectral behaviour not easy to account for by the PLS linear models. 

E. Richards, C. Bessant and S. Saini, Optimisation of a neural network model for calibration of voltametric data, Chemom. Intell. Lab. Syst., 61(1-2), 2002, 35 49. 

Using artificial neural networks to develop calibration models is also possible. The reader is referred to the literature [68-70] for further information. Neural networks are commonly utilized when the data set maintains a large degree of nonlinearity. Additional multivariate approaches for nonlinear data are described in the literature [71, 72],... 

Frake and co-workers " extensively evaluated numerous chemometric techniques for the NIRS prediction of mass median particle size determination of lactose monohydrate. Models evaluated in zero order (untreated) and second derivative were MLR, PLS (partial least squares), and ANN (artificial neural network). The researchers concluded that there is more than one way to treat data and achieve a good calibration model. The group also confirms previous observations that derivitization of data does not remove particle size effects (previously thought to contribute to baseline shift). 

Eden Prairie, MN), DICKEY-john OmegAnalyzerG (DICKEY-john Corp, Auburn, IL), Perten DA 7200 (Perten Instruments Inc., Springfield, IL), Bruker Optics/ Cog-nis QTA (Brucker Optics Inc., Billerica, MA), and an ASD LabSpec Pro (Analytical Spectral Devices Inc., Boulder, CO) for 18 amino acids. Partial least squares (PLS) and support vector machines (SVM) regression models performed significantly better than artificial neural networks (ANN). They used a calibration data set of 526 samples... 

Multivariate Calibration Model for a Voltammetric Electronic Tongue Based on a Multiple Output Wavelet Neural Network... 

The complexity of the signals gathered from the sensor array, perhaps having nonlinear characteristics, and the unknown relationship between the analytes and the sensors response make the neural networks an ideal candidate for the construction of calibration models. 

Gutes, A., Cespedes, F., Cartas, R., Alegret, S., del Valle, M., Gutierrez, J.M., Munoz, R. Multivariate calibration model from overlapping voltammetric signals employing wavelet neural networks. Chemometr. Intell. Lab. Syst. 83,169-179 (2006)... 

Unlike MLR, PCR and PLS, the neural network does not start by assuming a particular type of mathematical relationship between the input and output variables. For this reason, it is particularly useful when the underlying mathematical model is unknown or uncertain. For example, it is appropriate in multivariate calibration when the analytes Interfere with each other strongly. Neural networks find application in many other areas, for example classification, pattern recognition and process control. 

Using artificial neural networks (ANN) Ivanduc et al. compared those results with multi-linear regression (MLR or MRA) results and found that, in this case, the neural network approach offers only slightly better results, both for calibration and cross validation. Apparently the same conclusion concerning prediction of C NMR chemical shifts of alkanes was reached by Svozil et al. [88] indicating, according to Ivanciuc, that the relationship between the path counts and CSS has a small non-linear character and the ANN model could not provide much better result than the MLR model ... 

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