## 5 Conclusions  
In this paper, we presented three methods for hot-spot detection and Ki67 LI evaluation based on CNN classification. These methods were differentiated according to the data used, that is, Ki67 stain only or combination of Ki and H&E stains (HEKI). Our study shows that hot-spot areas can be detected by using the proposed methods, although some aspects make the HEKI Method 3 better suited for this purpose. Method 1 and Method 2 present a confusion matrix that provides worse results than the HEKI method since the confused values are more critical than those that appear in the former method. Moreover, Methods 1 and 2 cannot correctly differentiate lymphocyte regions, which is a key issue for avoiding false positive classifications.  
Method 3 (HEKI), based on combining both Ki67 and H&E, provided better characteristics for Ki67 hot-spot detection and Ki67 LI calculation. It included WSI registration, color deconvolution, and the creation of artificial image structures (HEKI) used for CNN classification. The average value of CNN accuracy for tile classification was 95%, which means that the proposal correctly dealt with the different types of data and their combinations. Moreover, this approach allowed us to create a tumor proliferation map and compute both automatic hot-spot detections and Ki67 LI.  
To establish a robust evaluation of the proposed methods, complete training and complex tests were performed. The database used contains 50 WSIs stained by Ki67 and 50 WSIs stained by H&E. The ground truth was created by four medical experts with extensive experience selecting hot-spot areas and evaluating the Ki67 LI. The Ki67 LI was evaluated using 1 FOV and 10 FOV, as there is neither a consensus among pathologists nor a standard protocol on how many FOVs to use.  
Method 3's results were compared with the medical diagnosis ground truth. The Bland-Altman analysis and [PERSON]'s \(\rho\) correlation coefficient confirmed the agreement between the medical and automatic diagnosis. In the Bland-Altman plot, only one point was observed to be out of range. The Bland-Altman analysis showed that the discrepancy between the automatic diagnosis and medical evaluation of Ki67 LI, based on 10 FOV, is only 0.25. [PERSON]'s \(\rho\) correlation coefficient was 0.89 and 0.92 compared to the manual calculations for 10 FOV and 1 FOV, respectively. All statistical tests confirmed the good level of agreement between the automatic and medical evaluation of Ki67 LI.  
Finally, we showed that automatic diagnosis based on CNN and data combinations from two types of staining can facilitate the development of an efficient tool to support Ki67 LI evaluations in breast cancer specimens.  
Conceptualization, [PERSON] and Z.S.-C.; methodology, G.B., Z.S.-C. and J.G.; investigation: [PERSON], [PERSON] and [PERSON], data curation: [PERSON] and [PERSON], formal analysis: [PERSON] and [PERSON]; writing--original draft preparation: [PERSON], [PERSON], and [PERSON]; writing--review and editing: [PERSON], supervision: [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was partially funded by the EU FP7 Program, AIDPATH project, grant number 612471, and partially funded by National Science Center (Poland) by grant UMO-2016/23/N/ST6/02076 and Junta de Comunidades de Castilla-La Mancha (Spain), with grant SBPLY/19/180501/000273.  
The authors declare no conflict of interest.