## 2 State-of-the-Arts
The authors [29] used the feedforward neural network approach to predict material properties. They perform the feature selection procedure and use this neural network type to solve prediction tasks based on a significantly reduced dimension preprocessed dataset. The advantage of this step is to increase the prediction accuracy and, in part, the speed of the training procedure. However, the iterative nature of the training algorithm requires significant time to implement this model. In [12], the authors solved the task of predicting the properties of titanium alloys using a hybrid scheme. It involves a combination of PNN and machine learning algorithms. This approach is due to the very low accuracy of classification using existing machine learning methods [14]. One of the reasons for this is that the dataset used contains many independent attributes that can reduce the accuracy of the classifier [30]. Therefore, the authors proposed an approach to reduce data dimensionality with their subsequent classification. The paper's main idea is to use the Probabilistic Neural Network as a tool for data preprocessing, mainly to reduce the dimension of the input data space of the task. In this case, it was implemented through the outputs of the summation layer of the PNN. It forms a vector of probabilities of belonging of each observation to each of the predefined classes of the task. Thus, the study's main goal was to transform the vectors of the entire dataset and replace the original dataset with the resulting dataset. Further classification based on the new dataset was performed using Logistic Regression. The flowchart of the proposed approach is shown in Figure 2[12]. Figure 1: Topology of the classical PNN. As a result of experimental research, the authors found that the classification based on the initial and modified datasets differs significantly. In particular, in the first case, the accuracy was close to 64% (logit classifier) and 88% (classical PNN classifier), and in the second--90% (PNN + logit classifier). That is, the proposed hybrid PNN-Logit scheme provided an increase in accuracy by 24% compared to the logit classifier and an increase of 2% compared to the classical PNN classifier  
The advantage of this approach, in addition to a significant increase in accuracy, is a significantly smaller dimension of the input data space required for the effective operation of the classifier based on machine learning [31]. However, if there are a small number of predefined classes of the task (e.g., 2 or 3), the probability vector of each class will contain a small number of elements (e.g., 2 or 3). It may undermine the proposed approach's effectiveness, particularly accuracy. To increase the hybrid system's accuracy for intellectual data analysis of the problem with a few labeled classes, the authors in [12] proposed a modification of this approach. The modified PNN-Logit schema also uses a PNN-based preprocessing procedure. However, the main difference of this scheme was the nonlinear expansion of the input data space instead of reducing the dimensionality, as in the previous case. The method was to use the outputs of the PNN summation layer to replace the initial dataset and further expand the new dataset space using Ito decomposition [32]. Further classification of the dataset expanded in this way was carried out using Logistic Regression. The flowchart of the proposed approach is shown in Figure 3[12]. Ito decomposition (Kolmogorov-Gabor Polynomial) is increasingly used to approximate nonlinear dependences with high accuracy [33; 34; 35]. For the classification problem, such an approach is substantiated by [PERSON]'s theorem [36]. It was the main reason for its use to modify the scheme from Figure 2[37]. Mathematically, Ito decomposition can be represented as follows,  
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