## 4 Discussion  
Candidate classification with the features obtained by the proposed method on about 160 candidates per case automatically extracted from MRA images achieved an average AUC of 0.987. The classification using the features by the proposed method for about 3400 candidates per case automatically extracted from CT images yielded an average AUC of 0.969. These are acceptable performances for clinical purposes. In addition, these results were higher performance than the unsupervised feature extraction by CAE [14] from 3D image patch directly. In this method, latent variables extracted from the 3D image patch were only used as the features. This means that the proposed method can automatically learn the useful features for lesion recognition from lesion-free normal data, regardless of the type of image or lesion. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Num. FPs/Case** & **Proposed** & **[PERSON] et al. [20]** & **[PERSON] et al. [13]** \\ \hline
2.9 & 70.0 \% & – & 94.2\% \\
5.0 & 83.3 \% & 93.5\% & – \\
9.0 & 91.4 \% & 95.2\% & – \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of aneurysm candidate classification sensitivities; the classification with proposed unsupervised generated features and those by other supervised learnings. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Num. FPs/Case** & **Proposed** & **[PERSON] et al. [18]** & **[PERSON] et al. [21]** \\ \hline
4.8 & 46.3\% & 80.0\% & – \\
14.1 & 57.2\% & 90.0\% & – \\ ANODE score & 0.218 & – & 0.790 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of sensitivity and ANODE scores for lung nodule candidate classification; the classification with proposed unsupervised generated features and those by other supervised learnings. In this evaluation experiment, Ada-Boost, which builds an ensemble by a sequential selection of features, was used as the training method for the discriminator. As the proposed method is an unsupervised feature extraction method, there is no guarantee that all extracted features are helpful for the target recognition problem. Using a classifier learning method with feature selection was considered effective in maximizing the performance of the features obtained by the proposed method. The performances of both Ada-Boosted classifier ensembles were high, showing an AUC of more than 0.96. In this evaluation experiment, we used Ada-Boost, a simple learning method that happens to be one of the Boosting methods. However, using Gradient Boosting (which can learn discriminator ensembles with high discriminative performance) and other feature selection methods will also lead to the more effective use of features obtained via the proposed method. Differences in feature selection tendencies were found when comparing the AdaBoost learning of the aneurysm candidate classifier ensemble to the classifier for lung nodule candidates. MIP-2.5D latent variables were the most frequently selected for classifying cerebral aneurysm candidates, followed by the MinIP-2.5D latent variable set and the CentSE-2.5D latent variable set. On the other hand, the Mahalanobis distance on the MinIP-2.5D latent variable space was the most frequently selected for classifying lung nodule candidates. The second most frequently selected latent variable was the MinIP-2.5D latent variable set. The difference in selection trends indicates that the 2.5D images suitable for image analysis differ depending on the type of image and lesion type under consideration. On the other hand, it was not the case that only certain 2.5D image-derived features were not selected to an extreme degree. The results demonstrate the effectiveness of using multiple 2.5D types. In addition to latent variables, the Mahalanobis distance on the latent variable space and the pixel value statistics of different 2.5D images, \(\mathbf{d_{\hat{t}-\hat{t}}}\) also contributed to the classification of lesion candidates. They show the validity of not just using latent variables obtained by CAE as features but also extracting valuable features from them.