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Hundreds of thousands of deaths each year in the world are caused by breast cancer (BC). An early-stage diagnosis of this disease can positively reduce the morbidity and mortality rate by helping to select the most appropriate treatment options, especially by using histological BC images for the diagnosis.

The present study proposes and evaluates a novel approach which consists of 24 deep hybrid heterogenous ensembles that combine the strength of seven deep learning techniques (DenseNet 201, Inception V3, VGG16, VGG19, Inception-ResNet-V3, MobileNet V2 and ResNet 50) for feature extraction and four well-known classifiers (multi-layer perceptron, support vector machines, K-nearest neighbors and decision tree) by means of hard and weighted voting combination methods for histological classification of BC medical image. Furthermore, the best deep hybrid heterogenous ensembles were compared to the deep stacked ensembles to determine the best strategy to design the deep ensemble methods. The empirical evaluations used four classification performance criteria (accuracy, sensitivity, precision and F1-score), fivefold cross-validation, Scott–Knott (SK) statistical test and Borda count voting method. All empirical evaluations were assessed using four performance measures, including accuracy, precision, recall and F1-score, and were over the histological BreakHis public dataset with four magnification factors (40×, 100×, 200× and 400×). SK statistical test and Borda count were also used to cluster the designed techniques and rank the techniques belonging to the best SK cluster, respectively.

Results showed that the deep hybrid heterogenous ensembles outperformed both their singles and the deep stacked ensembles and reached the accuracy values of 96.3, 95.6, 96.3 and 94 per cent across the four magnification factors 40×, 100×, 200× and 400×, respectively.

The proposed deep hybrid heterogenous ensembles can be applied for the BC diagnosis to assist pathologists in reducing the missed diagnoses and proposing adequate treatments for the patients.

Histopathology biopsy imaging is currently the gold standard for the diagnosis of breast cancer in clinical practice. Pathologists examine the images at various magnifications to identify the type of tumor because if only one magnification is taken into account, the decision may not be accurate. This study explores the performance of transfer learning and late fusion to construct multi-scale ensembles that fuse different magnification-specific deep learning models for the binary classification of breast tumor slides.

Three pretrained deep learning techniques (DenseNet 201, MobileNet v2 and Inception v3) were used to classify breast tumor images over the four magnification factors of the Breast Cancer Histopathological Image Classification dataset (40×, 100×, 200× and 400×). To fuse the predictions of the models trained on different magnification factors, different aggregators were used, including weighted voting and seven meta-classifiers trained on slide predictions using class labels and the probabilities assigned to each class. The best cluster of the outperforming models was chosen using the Scott–Knott statistical test, and the top models were ranked using the Borda count voting system.

This study recommends the use of transfer learning and late fusion for histopathological breast cancer image classification by constructing multi-magnification ensembles because they perform better than models trained on each magnification separately.

The best multi-scale ensembles outperformed state-of-the-art integrated models and achieved an accuracy mean value of 98.82 per cent, precision of 98.46 per cent, recall of 100 per cent and F1-score of 99.20 per cent.