# H&E Multi-Laboratory Staining Variance Exploration with Machine Learning
## 4 Discussion  
This study demonstrates the first results of the underlying structure between multiple laboratory stainings. The clustering section showcased that the stainings formed two primary clusters within different tissue types. The laboratories in these clusters maintain a similarity that steadily decreases as we approach each cluster's edges. Although clusters did form according to the best silhouette scores, the clustering effects were not as strong as expected, with average silhouette scores below 0.3. It is important to note that we only had a single example per tissue type per laboratory. Such limitations can make it more challenging to analyze the staining variance, since more examples from each laboratory may be needed to characterize any given laboratory more accurately. In contrast, the supervised approach showed good separability between laboratories. This result showed that laboratories have an effect, part of which can be predicted. We demonstrated that the tissue type affected the supervised results and cluster assignment. The large accuracy differences between tissue types were shown in the supervised approach. The same effect was shown in the unsupervised results where the rand index showed that laboratory assignment within clusters and between tissue types did not match, i.e., were slightly above the 50% chance level. It is important to note that we simultaneously analyzed the hematoxylin and eosin components in both machine learning approaches. Individual variation may exist in the two staining components whose impact and contribution to these results are yet undetermined. It therefore remains unclear if this effect would persist if the clustering and learning were to occur separately for hematoxylin and eosin. This novel study was designed as a proof-of-concept approach and an initial investigation into inter-laboratory staining variation. Consequently, additional limitations include the limited resolution, a fixed zoom level, and one region of interest per input sample. If these parameters are updated in future studies, we might obtain an even more adequate margin of error and resolution for the numerical results. Additionally, we note that the features and preprocessing pipeline focused on color-related information, not morphological information. Such an approach has the benefit of highlighting non-structural features but does not consider tissue morphology. Another approach could use active learning such that clustering labels are used as ground truth to a supervised learning set-up; in this way, it might be possible to investigate which features play a more critical role in the clustering result by modeling the clustering result itself with a classification algorithm. In conclusion, we investigated the impact and relationships of multi-laboratory H&E staining variance on different tissue types with machine learning methods. We hypothesized that individual laboratory stainings are consistent between tissue types and that \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tissue Type** & **KNN** & \
\begin{tabular}{c} **KNN** \\ **(Feature Selected)** \\ \end{tabular} &
\begin{tabular}{c} **Random Classifier** \\ \end{tabular} \\ \hline Kidney & 0.395 (0.010) & 0.706 (0.009) & 0.014 (0.001) \\ Skin & 0.553 (0.007) & 0.617 (0.009) & 0.014 (0.003) \\ Colon & 0.344 (0.007) & 0.513 (0.006) & 0.009 (0.002) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Cross-validation classification accuracy in predicting laboratory of origin of ROI tiles; standard deviation in parentheses. different staining approaches form subgroups with similar features. Our results showed that multi-laboratory staining varies between tissue types. Multiple laboratories did not appear to form strong clusters within each tissue type but were relatively well separated in the supervised approach. From a clinical perspective, we showed that only some of the laboratories were identified. According to the result, not all laboratory samples were distinct and were confused with other laboratories.