## 3 Methodology
### The Well Sequence
The significance value in Table 10 is 0.04639, which is less than 0.05, giving evidence that there is a significant difference among all variants of PSONN with a 95% confidence level. According to this, the variants of PSONN are significantly distinct from each other. Figure 40 represents the graph of one-way ANOVA results, which conclude that KN-PSONN significantly outperforms all other variants of PSONN. Figure 41 represents the results of multicomparisons of PSONN variants through post hoc [PERSON]'s test. The resultant graph depicts that KN-PSONN variant is significantly different from all other variants. According to the results of Figure 39, KN-PSONN is proved statistically different from all other approaches of PSONN with 95% confidence level. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Relation** & **Sum of Squares** & **df** & **Mean Square** & **F** & **Significance** \\ \hline Testing Accuracy & Among groups & 1318.2 & 6 & 219.697 & 2.3676 & 0.04639 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: One way ANOVA Test Results of PSO variants. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sr. No**} & \multirow{2}{*}{**Data Sets**} & \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**BPA**} & **PSONN** & **SO-PSONN** & **H-PSONN** & **TO-PSONN** & **WE-PSONN** & **KN-PSONN** \\ \cline{3-10}  & & & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** \\ \hline
1 & Diabetes & 2-Class & 65.3\% & 69.1\% & 69.1\% & 71.6\% & 73.3\% & 74.1\% & **78.5\%** \\
2 & Heart & 2-Class & 68.3\% & 72.5\% & 67.5\% & 72.5\% & 77.5 & 77.5\% & 79\% \\
3 & Wine & 3-Class & 62.1\% & 61.1\% & 66.6\% & 67.4\% & 69.4\% & 69.6\% & 72\% \\
4 & Seed & 3-Class & 70.56\% & 77.77\% & 84.44\% & 77.7\% & 88.88\% & 91.11\% & **93\%** \\
5 & vertebral & 2-Class & 84.9\% & 92.8\% & 92.8\% & 92.8\% & 94.64\% & 94.64\% & 96\% \\
6 & Blood Tissue & 2-Class & 73.4\% & 78.6\% & 78.66\% & 70\% & 82.66\% & 84\% & **87\%** \\
7 & Memo Graphy & 2-Class & 71.26\% & 76.66\% & 63\% & 85\% & 88.88\% & 96.66\% & **98\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of 10-fold classification rates of ANN-training methods in for seven data sets for accuracy. Figure 41: Multicomparison post hoc Tukey test graph of all PSO-based initialization approaches and BPA. Figure 40: Box plot visualization of the results achieved by the training of FFNN for all PSO-based initialization approaches and BPA for given data set of classification problem. Figure 39: Classification Testing Accuracy Results. ### NN Classifications with DE-Based Initialization Approaches

The proposed approaches DE-KN, DE-TO, and DE-WE and family of low-discrepancy sequences are extremely suitable for tackling the global optimization problems. A comparative study for real-world benchmark data sets problem is tested for the training of neural network. We have performed experiments using seven benchmark data sets (diabetes, heart, wine, seed, vertebral, blood tissue, and mammography) exerted from the world-famous machine-learning repository of UCI. Training weights are initialized within the interval \([-50,50]\). Accuracy of the feed-forward neural network is tested in the form of root mean squared error (RMSE)

Discussion

Multilayer feed-forward neural network is trained with a backpropagation algorithm, standard DE, DE-S, and DE-H and proposed DE-TO, DE-KN, and DE-WE. For this goal, we have prepared the multilayer feed-forward neural network utilizing the process of weight optimization. The performance of the DE, DE-S, DE-H, DE-TO, DE-KN, and DE-WE and state-of-the-art NN algorithms are examined on 10 well-known data sets which have been taken directly from the worldwide UCI repository of machine learning.