Cross validation genetic algorithm

Fig. 1. Statistical classification strategy (SCS) a schematic road map of how the SCS method is developed for individual databases. GA ORS, genetic algorithm based optimal region selection LDA, linear discriminant analysis LOO, leave-one-out (method of cross-validation) coeff, coefficients.

Another application of GAs was published by Aires de Sousa et al. they used genetic algorithms to select the appropriate descriptors for representing structure-chemical shift correlations in the computer [69]. Each chromosome was represented by a subset of 486 potentially useful descriptors for predicting H-NMR chemical shifts. The task of a fitness function was performed by a CPG neural network that used the subset of descriptors encoded in the chromosome for predicting chemical shifts. Each proton of a compound is presented to the neural network as a set of descriptors obtaining a chemical shift as output. The fitness function was the RMS error for the chemical shifts obtained from the neural network and was verified with a cross-validation data set. 

For the architecture search by means of cross-validation, only data about catalysts from the first to the sixth generation of the genetic algorithm and about the 52 catalysts with manually designed composition were employed, thus altogether data about 604 catalytic materials. Data about catalysts from the seventh generation were completely excluded and left out for vaUdating the search results. To use as much information as possible from the employed data, cross-validation was applied as the extreme 604-fold variant, i.e., leave-one-out validation. The set of architectures within which the search was performed was delimited by means of the heuristic pyramidal condition the number of neurons in a subsequent layer must not increase the number of neurons in a previous layer. This condition in particular implies ... 

Figure 8.3. Mean absolute errors and mean squared errors of approximations computed for materials from the seventh generation of the genetic algorithm by MLPs with one-hidden-layer architectures fulfilling 7 S bh S 14, trained with all the data considered during the architecture search. For comparison, average cross-validation error values of the involved architectures are recalled from Figure 8.1.

Table 8.2. Results of quantitatively checking whether the order of errors of approximations computed by the trained mnltilayer perceptrons for catal3dic materials from the seventh generation of the genetic algorithm correlates with the order of the mean cross-validation errors of their architectures.

Figure 11.11 Flow chart for the self-consistent construction of a CE Hamiltonian, (a) Initial input data from DFT and information about all possible clusters on a lattice L form the initial setup, (b) Some clusters C are chosen and the CE sum is fitted to the energies of the input structures

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