Neural network image classifiers informed by factor analyzers

The paper develops an approach to probability informing deep neural networks, that is, improving their resuits by using various probability models within architectural elements. We introduce factor analyzers with additive-impulse noise as such a model. The identifiability of the model is proved. The relationship between the parameter estimates by the methods of least squares and maximum likelihood is established, which actually means that the estimates of the parameters of the factor analyzer obtained within the informed block are unbiased and consistent. A mathematical model is used to create a new architectural element that implements the fusion of multiscale image features to improve classification accuracy in the case of a small volume of training data. This problem is typical for various applied tasks, including remote sensing data analysis. Various widely-used neural network classifiers (EfficientNet, MobileNet, Xception), both with and without a new informed block, are tested. It is demonstrated that on the open datasets UC Merced (remote sensing data) and Oxford Flowers (flower images), informed neural networks achieve a significant increase in accuracy for this class of tasks: the largest improvement in Top-1 Accuracy was 6.67% (mean accuracy without informing equals 87.3%), while Top-5 Accuracy increased by 1.49% (mean base accuracy value is 96.27%).