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distinguish breast cancer images into three categories: normal, in situ carcinoma and invasive carcinoma. By using multiple threshold values, binary images were generated for the feature extraction and training tasks. Zhang et al.  used a set of parallel SVM classifiers and a set of artificial neural networks (ANN) to create a strong cascade classifier. In their research, the SVM and ANN classifiers were considered as weak classifiers that could be combined together to create a final, strong classifier. A breast cancer image was only rejected if it was rejected by the majority of SVM and ANN classifiers. In this algorithm, training features extracted by the Curvelet transform and local binary pattern (LBP) methods were used to train the set of SVM classifiers. Similarly, Zhang et al.  presented an ensemble of a single-class kernel principal component analyses models trained using different characteristic features from each breast cancer class. This ensemble method achieved high-classification accuracy for classifying benign and malignant lesions from breast cancer histopathological images. Inter-estingly, Dimitropoulos et al.  used the Grassmannian vector of local aggregated descriptor (VLAD) method to extract local features of breast cancer tumors and present them as a set of multidimensional spatially-evolving signals that can be e ciently modeled through a higher-order linear dynamical systems analysis. Although they did not use deep learning models, their method is one of the state-of-the-art methods for detecting breast cancers.
Sparse representation [45,47,51,52], developed from the Z-Guggulsterone of sparse coding, has attracted much attention from researchers in the fields of face recognition, object detection, and cancer detection. Helal et al.  used a sparse representation-based classifier to classify benign and malignant breast lesions. In this type of representation, a breast cancer sample can be su ciently represented by training samples from the same subject. Then, this breast cancer sample is clas-sified based on the least representation residual computed by the sparse representation coe cients and training samples. Thus, this method can considerably improve the effectiveness of breast cancer detection. Similarly, Nayak et al.  used a method of sparse feature learning and classification to decompose whole slide images of histology sections into distinct patches. These patches were then classified into tumor types. Kong et al.  also proposed a method of jointly sparse dis-criminant analysis to discriminate the category of the breast cancer types. This method was used to extract the key factors in breast cancer, which are helpful for improving the accuracy in diagnosis and prediction.
Recently, deep learning networks have been developed to extract the most discriminative features and to improve the effectiveness of medical image analysis. There are two advantages regarding the use of deep learning networks for feature extraction. First, we can automatically extract more complex feature sets by using deep feature learning models than those that we may have using other machine learning tools. Second, joint and hierarchal learning features can be extracted from different layers of a deep learning network. As a result, deep learning networks are also e ciently used in the feature selection step. However, deep learning networks are still a drawback for H&E breast tissue biopsy classification. Training a deep learning network for recognizing an entire H&E breast tissue biopsy image is extremely time-consuming because of the huge number of training parameters. To deal with this drawback, Spanhol et al.  trained his deep learning network on the dataset of 32 × 32 and 64 × 64 pixels patches collected from original H&E breast tissue biopsy images. The resulting H&E breast tissue biopsy image was classified based on the sum of patch probabilities or the highest patch probability. Spanhol et al.  also proved that the feature extraction task was more di cult if the deep learning network was trained on breast tissue images at higher magnifications. This is because only nuclei edges were extracted from images at high magnifications and the most useful features were not found by the deep learning network. Similarly, Ciresan et al.  used convolutional neural networks (CNN) to detect mitosis in each of the patches extracted from H&E stained breast biopsy slides. The advantage of this deep learning model is to detect nuclei in different sizes. Cruz-Roa et al.  also divided the breast histology slide into 100 × 100 patches in which his deep learning network could detect invasive carcinoma regions. Han et al.  used a deep learning model to identify eight classes of breast cancer. With the application of deep learning models, Euclidean distances among samples in the same class were minimized whereas the Euclidean distance between two arbitrary samples that belonged to two different classes was maximized. Similarly, Song et al.  combined a convolution neural network with a Fisher feature layer to encode the local features of breast cancer tumors in a higher discriminative space where breast cancer types were distinguished effectively. Interestingly, Chen et al.  proposed an architecture of deep cascaded networks to quickly retrieve the mitosis candidates while preserving a high sensitivity. The retrieved candidates were then classified by the second deep convolutional neural network which can discriminate mitoses from hard mimics more precisely. Therefore, this approach achieved high performance of classifying breast cancer images.