# Prediction of Glioma Grades Using Deep Learning with Wavelet Radionic Features
## 4 Results  
### Data Exploration  
Grade II and Grade III MRI brain tumors of 121 patients were segmented by the GrowCut algorithm. 744 radiomic features of the 3D images were detected in low sub-band and high sub-band filters with Wavelet Transform method. Since the data of 121 patients were not normally distributed, the statistical significance of the data was tested with the Mann-Whitney U, which is a non-parametric test. As a result of the Mann-Whitney U test, 126 radiomic features with significant statistical properties were determined. The feature distribution of 8 sub-band groups is as follows. For LLH 18 radiomic features, for LHL 19 radiomic features, for LHH 14 radiomic features, for LLL 20 radiomic features, for HLL 11 radiomic features, for HLH 19 radiomic features, for HHL 13 radiomic features, and for HHH 12 \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Optimizer & Stochastic gradient descent \\ Epsilon & 0.00000001 \\ Elastic regularization & 0.001 \\ Learning rate & 0.005 \\ Loss & Cross-entropy \\ Epoch & 10 \\ Mini-batch & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DNN hyper-parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wavelet Sub-Bands** & **Weight/Biases** & **Memory Workload** & **Training Samples** \\ \hline HHH & 43.202 & 516.0 KB & 784 \\ HHL & 43.402 & 518.5 KB & 821 \\ HLH & 44.602 & 533.6 KB & 772 \\ HLL & 43.002 & 513.5 KB & 790 \\ LHH & 43.602 & 521.0 KB & 812 \\ LHL & 44.602 & 533.6 KB & 826 \\ LLH & 44.402 & 531.1 KB & 816 \\ LLL & 44.802 & 536.1 KB & 837 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computational Complexity of Classification Method. radiomic features were selected with the non-parametric Mann-Whitney U test. A total of 126 radiomic features, namely first-order features (\(n=14\)) and texture features (\(n=112\)). First-order features show that the Energy feature creates a statistically significant difference between Grade II and Grade III. In the HLL, HHL, LLH, LLH, and HHH filter groups, the radiomic features of the GLCM matrix group did not show a statistically significant difference between Grade II and Grade III. Radiomic features belonging to the GLSZM matrix group in the LLL and HLH filter groups showed the highest statistically significant difference between Grade II and Grade III. Among the 3D wavelet low-pass filter groups (LLH, LHL, LHH, LLL), the maximum statistically significant difference belonged to 20 radiomic features, especially in the LLL filter group. On the other hand, the maximum statistically significant difference among the high-pass filter groups belonged to 19 radiomic features, especially in the HLH filter group. The statistically significant differences of selected wavelet first-order features and texture features of Grade II and Grade III tumor images as evaluated by the Mann-Whitney U test are provided in Appendix A.  
First-order features for LLH show that Energy (\(p=0.004\)) and Total Energy (\(p=0.007\)) create a statistically significant difference between Grade II and Grade III. There was no significant difference between GLCM features and tumor grades for LLH. We found 5 statistically significantly different features for LLH in GLDM, 5 features for LLH in GLRLM, 5 features for LLH in GLSZM, and 1 feature for LLH in NGTDM between Grade II and Grade III (\(p<0.05\)). For the LLH GLSZM and LHL GLSZM groups, Gray Level Non-Uniformity differed the most significantly (\(p=0.000\)) between Grade II and Grade III. Two statistically significantly different features for LHL GLCM, 5 features for LHL GLDM, 4 features for LHL GLRLM, 5 features for LHL GLSZM, and 1 feature for LHL NGTDM were determined between Grade II and Grade III (\(p<0.05\)). Coarseness, Energy, and Total Energy differed significantly between Grades II and III (\(p<0.005\)) in all wavelet filter groups (LLH, LHL, LHH, LLL, HLL, HLH, HHL, HHH). Only one radiomic feature, Dependence Non-Uniformity (\(p=0.000\)), differed significantly between Grade II and Grade III in all filter groups.