## 3 Results
### Would Image Clustering on Image Tile-Level Work for Such a Needle-in-Haystack-like Problem? The section above shows that standard CNN training methods do not work well with the needle-in-the-haystack problem (compare Figure 2A). At least not if all instances (hay and needles), which are assumed to be morphologically different, are given the same label. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Approach Used** & **Accuracy** & **F1-Score** & **Cohen’s Kappa** & **AUC** \\ \hline
**Standard CNN Bo2 No data set** & 0.468 & 0.379 & 0.126 & 0.626 \\
**Standard CNN Ce2 No dataset** & 0.328 & 0.255 & 0.044 & 0.642 \\
**MIL model on ResNet152 features** & 0.756 & 0.742 & 0.512 & 0.760 \\
**MIL model on HistoEncoder features** & 0.683 & 0.648 & 0.389 & 0.794 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: **Statistic evaluation of the classification models. ** Due to their architecture standard, CNN models could perform on central or peripheral tiles separately. MIL models had to perform on the combined dataset of central and border tumor tiles, as not all methods of image augmentation could be used with this approach. AUC: area under the receiver operator characteristics curve; CNN: convolutional neuronal network; Bo2 No: mapping of border tumor area tiles for their nodal status; Ce2 No: mapping of central tumor area tiles for their nodal status; MIL: multiple instance learning; ResNet152: residual neural network with 152 layers. Figure 1: **Region definition and distribution of informative tiles per case. (A) Sketch of WSI with annotated tumor region and border region. Based on a trained U-NET model the whole slide images are segmented into non-tumor (grey) and tumor (blue) tissue. The latter is subdivided based on the tumor content in each tile into tumor central (dashed line in magenta) and tumor border (dashed line in red). The tiles per region (exemplarily shown red dashed boxes) are then saved. For a graphic workflow of the tile preparations see Figure S3. (B) Boxplot for the frequency of meaningful instances per case. The MIL approach approach gives a class probability per instance or image tile. Per WSI, there are only a few instances with high class-probabilities. These few instances are the meaningful ones per case. The frequency of these meaningful instances per case is variable. The instances highly informative for nodal negativity are termed “low”, while those with significant relevance to nodal positivity are termed “high”. WSI: whole slide image; MIL: multi-instance learning. **  
This assumed morphological difference suggests cluster analysis methods as an alternative. However, plotting and subsequently analyzing the feature vectors per instance in the latent space shows no well-delineated groups. In 2-dimensional representation via Principal Component Analysis (PCA) or Uniform Manifold Approximation and Projection (UMAP), there is each time a point cloud where labeling based on the case label (nodal status) does not show well-delineated clusters with silhouette scores near 0, indicating significant overlap between the groups (Figure 2A). In conclusion, using the typical clustering methods for pre-defined groups is not promising. This also explains why the above-described CNN approaches cannot generate a clear separation. This haystack-like picture of feature vectors in the latent space appears regardless of whether models are trained completely from scratch on this data set, as in the section above, or whether pre-trained models are used. The silhouette score is with and without pre-training in the interval \([-0.1;\ 0.1]\), indicating again no cluster separation but huge cluster overlap. For the pre-trained models, it also makes no difference whether the models were pre-trained on standard data sets such as ImageNet [46], whether they were trained on other circumscribed histological data sets like the glomeruli data set from a previous publication, or whether they are models for feature extraction from histological images in general like the HistoEncoder model [36].