## 1 Introduction  
The revolution of deep learning (DL) techniques, visible in many areas [1; 2; 3], has also reached medical diagnosis [4; 5]. In histopathology, the advances in digital pathology, image processing, and artificial intelligence techniques can be applied to cancer diagnosis [6; 7]. The quantification of cellular proliferation is one of the metrics used to study cell activity in oncology. In particular, the proliferative activity assessed by Ki67 immunohistochemistry (IHC) is an established prognostic and predictive biomarker that determines the choice of therapeutic protocols applied to breast cancer [8; 9]. Tumor regions that exhibit high proliferating activity are called hot-spots. Several standardization issues for both the planning process and the related quantification protocols must be solved prior to the implementation of quantification in regular practice [9; 10; 11; 12]. [PERSON] et al. [12] showed significant variations in Ki67 hot-spot scoring depending on the number of included tumor cells and the hot-spot's size, shape and location. There is a need to accurately measure the proportion of the Ki67 labeling index (Ki67 LI) [13; 14; 15], and digital image analysis methods may help with this task [16]. Several methods to automatically quantify the Ki67 index or detect hot-spots have been reported in the literature (see Table 1). Extant approaches are based on two main strategies: (I) machine learning with clustering, adaptive thresholding, and edge-based segmentation [9; 17; 18; 19; 20; 21; 22; 23; 24; 25] or (II) deep learning [26; 27; 28; 29]. Moreover, two main goals can be distinguished--(I) labeling index (LI) estimation or (II) hot-spot detection. The KI67 LI and hot-spots have been detected for tumors occurring in various organs including the breasts, brain, adrenal glands, and pancreas. Due to the large size of a single WSI (2-4 GB), in many research papers, the results are presented only for tissue micro arrays (TMAs) or small parts of tissue samples (sub-images). Table 1 shows the success in producing outcomes and implementing more advanced approaches. The drawback of methods based on classical machine learning is that they are parameter-dependent and cannot be easily tuned for non-homogeneous staining, which can vary in a range of hot-spot density values. Moreover, the methods described in the literature do not distinguish tumors from stromal tissues and, therefore, do not exclude nonepithelial cells that potentially express the biomarker--that is, proliferating Ki67-positive lymphocytes. Only cells that express cytokeratin should be eligible for the positive or negative detection of the biomarker concerned. Another aspect not considered in works focused on TMA or sub-images is the artifacts that occur on WSIs and how to process the WS to obtain the final evaluation. In this paper, we propose and compare three methods based on Deep Learning to detect and characterize Ki67 hot-spots in breast cancer WSIs. The proposed techniques solve the problem of handcrafted feature selection by using convolutional neural networks (CNNs) to automatically determine the best features to characterize the hot-spot regions. In the present work, we explore the possibility of using DL methods for extracting and combining information from KI67 and hematoxylin and eosin (H&E) stained slides. Three methods have been developed, as mentioned above. Method 1 is the simplest one, where a single CNN is used to process samples extracted from KI67-stained slides. Method 2 uses both Ki67 proliferation and tumor localization obtained by H&E analysis, where KI67 and consecutive H&E slides are processed by two independent CNNs. Method 3 is the most advanced one, where we combine Ki67 and H&E WSIs by means of color deconvolution to use the mutual information of both biomarkers in one CNN. This method achieved the best performance, with average accuracy of 95%, sensitivity of 77% and specificity of 98%.