## 4 Modeling and Results
### Results of All Other Variants of the Investigated Smart System  
In this paper, also other existing approaches based on PNN are used that are implemented in the designed smart web service, in particular:  
* Classical PNN;
* Modified PNN;
* PNN-Logit system from [12] that used PNN-based dimensionality reduction;
* Modified PNN-Ito-Logit system proposed in [12] that used PNN-based dimensionality reduction;
* PNN-SVM system that used PNN-based dimensionality reduction;
* Modified PNN-Ito-SVM system that used PNN-based dimensionality reduction;
* PNN-SVM system proposed in [39]. The results of all studied approaches using the developed web service are summarized in Table 2.  
It should be noted that assessing the results of different systems adequately, additional modeling of PNN-Logit and PNN-Ito-Logit (approaches that used PNN for dimensionality reduction) systems was performed by replacing the Logistic regression with an SVM classifier. As a result, Table 2 presents two new systems for comparison, one of which demonstrated the highest accuracy among those considered. It indicates the effectiveness of using the SVM in all considered variants of the smart system in solving the stated task. Figure 10: Classes of the Ti-based alloy’s quality evaluation task for medical implants manufacturing. 4. Systems where PNN is used to reduce the dimension of the input data space of the task provide a slight increase in accuracy, although significantly reduce the duration of training procedures for such systems;
5. PNN-based systems for expanding the input data space of the task increased the accuracy of linear classifiers, which is fully justified by [PERSON]'s theorem. However, high enough accuracy is not obtained here;
6. The highest classification accuracy in solving the stated task is obtained using the improved system proposed in this paper. In particular, due to additional modeling of the attributes of the extended dataset based on the Ito Decomposition, it was possible to increase the system's accuracy by more than 6% compared to the existing implementation of the system. The last point provides a significant advantage when using the improved system to solve the classification tasks. In particular, a classification accuracy of 97% will ensure a proper assessment of Ti-based alloy's quality for the defect-free production of biocompatible titanium implants for various purposes. Among the disadvantages of the proposed approach that should be noted is a significant increase in the duration of the training procedure of the improved system compared to the basic option. This is due to the considerable increase in the number of attributes of the extended dataset, which is fed to the SVM classifier [53, 54]. However, the following should be noted here:  
* the improved system is based on preprocessing of data based on an Artificial Neural Network without training, which will eliminate this shortcoming in the case of processing small-sized and middle-sized datasets [55, 56];
* a linear SVM is selected as the basic classifier, which is quite fast [57]. The processing of nonlinear extended inputs also provides significantly higher classification accuracy than other kernels of this method. In addition, the optimal implementations of this method, which are laid down in the Scikit-learn library and its was used in this paper, provide high performance of this machine learning method;
* in Materials Science tasks, large datasets are challenging to collect [38, 58]. That is why combining the above methods will provide high-speed processing of available data. Figure 11: Total accuracy values for all investigated methods. In case it is necessary to process large datasets, the authors implemented other approaches in the designed smart web service, particularly the system based on PNN's dimensionality reduction, which will significantly reduce the computational load and the duration of the training procedure by the selected classifier.