Principal component analysis-adaptive neuro-fuzzy inference systems (ANFISs) for the simultaneous spectrophotometric determination of three metals in water samples

Performance comparison of wavelet neural network and adaptive neuro-fuzzy inference system with small data sets

In this work, performance of wavelet neural network (WNN) and adaptive neuro-fuzzy inference system (ANFIS) models were compared with small data sets by different criteria such as second order corrected Akaike information criterion (AICc), Bayesian information criterion (BIC), root mean squared error (RMSE), mean absolute relative error (MARE), coefficient of determination (R²), external Q² function ( [Formula: see text] ) and concordance correlation coefficient (CCC). Another criterion was the over-fitting. Ten data sets were selected from literature and their data were divided into training, test, and validation sets. Network parameters were optimized for WNN and ANFIS models and the best architectures with the lowest errors were selected for each data set. A precise survey of the number of permitted adjustable parameters (NPAP) and the total number of adjustable parameters (TNAP) in WNN and ANFIS models was shown that 60% of the ANFIS models and 30% of the WNN models had over-fitting. As a rule of thumb, to avoid over-fitting it is suggested that the ratio of the number of observations in training set to the number of input neurons must be greater than 10 and 20 for WNN and ANFIS, respectively. The smaller ratio required in WNN indicates its flexibility vs. ANFIS that relates to differences in structure and connections in the both networks.

Application of the calibration surfaces method in quantitative analysis of water — ethanol — methanol mixture

The simple and quick calibration surfaces method has been applied to the quantitative analysis of water — ethanol — methanol mixtures. The refractive index, viscosity, boiling point, density, and position of the absorption band of the solvatochromic dye and the absorbance of the band corresponding to a particular wavelength were used as measured magnitudes which are functionally related to the quantitative composition of the mixture. The 3rd order surface equation was fitted to the experimental data via the multidimensional regression method. Various pairs of macroscopic features were tested to obtain the best results. To find the solution, the set of three equations were calculated, in which two equations were the mathematical description of particular macroscopic features; the third one resulted from the definition of mass fraction. The detection and determination limits as well as the error of the method were determined which proved that the refractive index and the density were the most adequate pair of macroscopic features.