## 5 Discussion  
This is the first study that fully exploits both radiomics features and a deep embedding network of multi-parametric MRI to predict pCR after nCRT in patients with locally advanced rectal cancer. We demonstrated the superiority of the proposed method by analyzing its pCR prediction performance and comparing it with competing baselines based on a large cohort of 912 rectal cancer patients. Before analyzing the pCR prediction performance of our method, we showed that the average pCR prediction performance was the highest (AUC = 0.819) when using various features from the entire multi-parametric MRI (Table 2). Given multi-parametric MRI, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Classifier** & **Logistic Regression** & **Xgboost** & **Lightgbm** & **Random Forest** & **MLP** & **Ensemble** \\ \hline AUC & 0.804 & 0.783 & 0.792 & **0.837** & 0.798 & 0.819 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of pCR prediction performance of various classifiers built on multi-parametric MRI embedding. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**pCR Prediction Method** & **AUC** & **F1-Score** & **Specificity** & **Sensitivity** \\ \hline (B1) SVM classifier (input = radiomics features) [46] & 0.799 & 0.53 & 0.45 & 0.67 \\ (B2) RF classifier (input = radiomics features) [8] & 0.811 & 0.63 & 0.56 & 0.74 \\ (B3) MLP classifier (input = radiomics features) [25] & 0.763 & 0.54 & 0.49 & 0.62 \\ (B4) 3D-CNN classifier (input = MRI images) [18] & 0.807 & 0.63 & 0.59 & 0.68 \\ Proposed Method & 0.837 & 0.65 & 0.60 & 0.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of pCR prediction performance with competing baselines. we generated radiomics features and MSFI embedding and merged them through kernel PCA to obtain multi-parametric MRI embedding. The multi-parametric MRI embedding exhibited higher pCR prediction performance than radiomics features or MSFI embedding (Table 3). This means that some tumor characteristics that are highly relevant to pCR prediction are captured by either radiomics features or MSFI embedding but not both. It also indicates that MSFI embedding can represent novel volumetric features of tumors in multi-parametric MRI. Given multi-parametric MRI embedding, we demonstrated that a random forest classifier was the most effective pCR prediction model (Table 4), as suggested in our method. Then, we confirmed that our method outperformed four competing baselines in terms of overall prediction performance (AUC = 0.837 and F1-score = 0.65) for pCR after nCRT for locally advanced rectal cancer (Table 5). The 3740 radiomics features and 512 features in MSFI embedding are not equally important to the pCR prediction. Using kernel PCA, we performed non-linear dimensionality reduction over the vector of 4252 features to obtain a low-dimensional embedding that maximizes the variance. In our experiments, we selected 150 as the optimal number of components through hyperparameter tuning. Instead of tuning the output dimension manually, advanced feature selection techniques [50] that automatically determine the optimal number of features can be used. To explore non-linear combinations of features, we can also consider performing kernel PCA by fixing the variance threshold instead of specifying the number of components. Our MRI data is heterogeneous as it was acquired from different patients using MRI scanners of various vendors, as stated in Appendix A. Due to the lack of a standardized signal intensity scale, heterogeneous MRI images are not directly comparable [31]. To deal with such heterogeneity, we used pyradiomics, the most widely used tool for reliable radiomics feature extraction. During preprocessing, we applied voxel size resampling and signal intensity normalization implemented in pyradiomics because these two techniques have been known to improve the robustness of radiomics features [32; 33]. We used the preprocessed MRI data as an input to 3D-CNN for MSFI embedding to improve the robustness of MSFI embedding.