## 3 Results
### Would Image Clustering on Image Tile-Level Work for Such a Needle-in-Haystack-like Problem?
In each case, the silhouette score is again in the range \([-0.1;\ 0.1]\). To sum it up, the information-bearing instances, the needles to stay with the image, are not morphologically distinct enough to stand out. Figure 2: **L-space analysis. ** Based on a PCA analysis of MIL results, for each instance a feature vector is plotted in 2D. (**A**) Instances from the entire data set, comprising the training and validation set, are plotted. The nodal status (nodal negative (N\(-\)) or positive (N\(+\))) is used as a label. The silhouette score, as a clustering metric, is 0.008, which indicates a high overlap of the clusters based on the case labels. (**B**) Instances from the training set (**B1**) and the validation set (**B2**) are plotted. The label used involves the information gained concerning the nodal status. The MIL model produces a pseudo-probability per instance for the nodal status, which ranges between 0 and 1. For this plot, this range is stretched between \(-1\) (low probability for nodal positivity and vice versa, therefore highly predictive for nodal negativity; here called “low”) and +1 (high probability for nodal positivity; here called “high”). For (**B1**) the silhouette score is 0.008 and respectively for (**B2**) \(-0.082\). PCA: principal component analysis; MIL: multi-instance learning. Does Supervised Training on Case-Level (So-Called Bag-Level) Work with a Needle-in-Haystack-like Problem? In the methods discussed earlier, we demonstrated that addressing the data sparsity issue for cases by analyzing image tiles alone is not a viable solution. So, we need to train on the case level with, alas, only a limited data set size. After splitting the data set into training and testing sets, training a MIL model shows again that the overall data set size is too small, and the model quickly over-fits. There are approaches on the model and the data side to overcome such a data sparsity scenario: On the model side, reducing the number of trainable parameters to reduce the memorization potential is a well-known approach. However, with 10,293 trainable parameters, the used MIL model is already small in contrast to, e.g., the ResNet152 model [20, 21, 28] used for feature generation that has 58,149,955 trainable parameters. A reduction of trainable parameters does not avoid over-fitting in our scenario as tested for a reduction from, e.g., 31,023 to 10,293 trainable parameters (for the features produced by the pre-trained ResNet12 model). Training a MIL model using the random query approach for data augmentation, a maximum accuracy of 0.762 and 0.721 can be achieved for the validation set, based on features from ResNet152 and HistoEncoder, respectively (compare Table 2). Per instance per bag, the N+ probability can be calculated. By doing so, image tiles can be found being informative for nodal negativity, henceforth termed \"low\" for being predictive for N\(-\) and, respectively, adding low risk for N+. If not, a tile might be informative for N+, henceforth termed \"high\" for being highly predictive for N+ (compare B in Figure 1). A mean 17.339% of the image tiles in nodal positive cases are informative for nodal positivity (N+). However, in nodal negative cases (N\(-\) cases), there are still 4.494% tiles with high probability values for nodal positivity. In summary, the predictive reliability of the used MIL model for the feature vectors per tile produced by a pre-trained network (either ResNet or HistoEncoder) is better than for models trained on the noisy tile-level (compare Section 3.1 above). Of note, in the penultimate layer, the MIL model also summarizes the given information or respectively the fed in feature vectors in its own feature vector. Visualizing the distribution of these feature vectors again in the latent space by PCA reveals a much clearer separation for the trained classes (visualized in B1 with the class labels and in B2 with the class pseudo-probabilities (in analogy to Figure 2) in Figure 3).