## 4 Experiments
### Analysis of Our pCR Prediction Model  
We evaluated the effectiveness of the proposed pCR prediction method by examining two major factors: MRI feature vector extraction and pCR classification. Recall that for effective pCR classification, we suggest using multi-parametric MRI embedding as an input to a random forest classifier.  
In the proposed pCR prediction method, we generate multi-parametric MRI embedding by concatenating MSFI embedding and radiomics features extracted from given MRI sequences, {T2, DWI/ADC, and CE}, and applying kernel PCA. To check the impact of multi-parametric MRI embedding, we apply nine different input vectors to a random forest classifier by combining a feature vector of {radiomics features, MSFI embedding, concatenation of both} and a dimension reduction method of {No dimension reduction, PCA, and Kernel PCA}.  
Table 3 presents the pCR prediction performance of random forest classifiers using nine input vectors. We observe, among various input vectors, that with the input vector obtained by concatenating MSFI embedding and radiomics features and then applying kernel PCA, that is, our multi-parametric MRI embedding, random forest classifier achieved the highest AUC of 0.837.  
From this, we observe that MSFI embedding extracts novel volumetric features that cannot be found in the pool of radiomics features. At the same time, radiomics features explain some essential characteristics of rectal cancer that MSFI embedding cannot represent. Thus, multi-parametric MRI embedding succeeds in capturing more diverse features from the given MRI sequences. We also observe that kernel PCA can extract discriminative features for pCR prediction from MSFI embedding and radiomics features.  
Then, we compare the effectiveness of MSFI embedding and radiomics features. In Table 3, MSFI embedding shows a lower AUC than the radiomics features when used as the input to the random forest classifier. However, while we use 3D-ResNet only for MSFI embedding extraction, it should be noted that its pCR classification performance has already reached 0.807 just as (B4) in Section 4.4. Recall that the random forest classifier on radiomics features is known to be highly effective in pCR prediction for rectal cancer [8].  
Given three MRI sequences, {T2, DWI/ADC, and CE}, we can obtain multi-parametric MRI embedding by concatenating MSFI embedding and radiomics features and performing kernel PCA. Through this novel embedding, we aim to show the effectiveness of our random forest classifier by comparing it with various classification models.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Feature Vector** & **No Dimension Reduction** & **PCA** & **Kernel PCA** \\ \hline MSFI embedding & 0.776 & 0.739 & 0.732 \\ Radiomics features & 0.811 & 0.754 & 0.819 \\ Concatenation of both & 0.796 & 0.746 & 0.837 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of pCR prediction performance of various combinations of feature vectors and dimension reduction methods. Three types of feature vectors, {radiomics features, MSFI embedding, concatenation of both}, and three dimension reduction methods, {No dimension reduction, PCA, and Kernel PCA}, are considered. The pCR classification model is fixed to a random forest.  
Table 4 presents the AUC of six pCR classifiers built on multi-parametric MRI embedding: logistic regression, xgboost, lightgbm, random forest, MLP, and an ensemble of all the classifiers. The random forest classifier outperforms all the other classifiers, including the ensemble, demonstrating an AUC of 0.837.