## 4 Discussion
The PIRADS system, incorporated with DWI and dynamic enhanced imaging, may have the potential to serve as a tumor biomarker, and in fact, the PIRADS score shows a linear correlation with GS [34]. In conjunction with our results, PI-RADS may serve as an imaging biomarker for BCR following RP, as well as a scale for tumor visibility. Given the moderate predictive ability with an AUC of 0.656 for early BCR in using only the preoperative parameters as input data, our prediction algorithm may be helpful for preparing postoperative follow-up planning and aiding in the clinical management of patients with prostate cancer after RP in advance. Machine learning is the semi-automated extraction of knowledge and insight from data, allowing the training of algorithms that can discover and identify complex patterns and relationships within various parameters. In medicine, developed algorithms can be directly applied to patient care to improve the accuracy of predicting diseases and subsequent outcomes [35]. Recently, machine learning has been used to predict BCR using clinical and pathologic data and showed high predictive performance [16; 35]. Our models also showed promising results in terms of predicting early BCR using not only clinical and pathologic data but also imaging data. Although the diagnostic performance of our prediction model was lower than those of previous studies, it may result from a small population. However, the prediction model using our auto-encoder method showed a higher AUC as compared to MLP, KNN, and DT. Even in some cases, such as DT in the postoperative-parameters-only case, predictive performance could be found to be poorer than random prediction. The reason for this difference in performance is that the dataset we use is small and unbalanced. The general classification algorithm for the build of the predictive model conducts a training process to reduce the prediction error of the data used in the training. That means, in an unbalanced data set, training to predict all data as a class of large amounts of data tends to increase in terms of overall accuracy, rather than training to predict both classes. However, as a small number of data are incorrectly predicted, the precision and recall values are unbalanced, and the AUC value would be poor. In order to overcome a drawback of the classification algorithm, the under-sampling method is generally used. The under-sampling method randomly extracts data from large numbers of classes, matches the number of data from small numbers of classes, and then trains based on this data-set. In our study, if we want to show the good AUC value using the general prediction model, we have to use under-sampling when considering our small number of BCR patients, according to the general methodology that the number of two groups for training should be similar. However, if only 48 patients enrolled for training fit the 24 early BCR patients by under-sampling, it would be too small for a training prediction model. Or, if we do not adjust the number of the training dataset in our study, sensitivity and specificity would show very unbalanced performance and a subsequent poor AUC value. However, although our dataset is imbalanced, unlike classical classification methods, the auto-encodermethod can utilize most of our dataset without performance degradation in training. Thus, our method performed well with a small set of unbalanced data, as compared to conventional classification methods. Our study has several limitations. First, this study is a retrospective, single-institution investigation, and thus carries potential selection bias. Furthermore, the models were generated from information obtained from a small population. As a rule of thumb, at least 10 outcomes for each independent variable are required for a logistic regression or proportional hazards model [36; 37]. Nevertheless, we generated an acceptable prediction model using an auto-encoder that shows potential of dealing with small datasets.