# Breast Cancer Image Classification Using Phase Features and Deep Ensemble Models
## 1 Introduction  
Breast cancer detection and treatment are major priorities in both basic and clinical medicine, as it is one of the leading causes of mortality among women worldwide [1]. Furthermore, in recent years, the mortality rate has increased by 130% in females and 648% in males [2]. Approximately 2.3 million women are diagnosed with breast cancer worldwide each year, making it the most frequently diagnosed cancer among women worldwide [3, 4]. Several studies indicate that the survival rate for this disease is higher when detected in its initial stages [5]. Thus, the need for auxiliary tools motivates the development of image processing and pattern recognition techniques for the detection of breast cancer. The extraction of useful features from medical images and the use of artificial intelligence techniques for pattern classification have been intensively investigated for this purpose. Texture-based features such as fractal dimension [6], gray local covariance matrix (GLCM) [7], and local binary patterns (LBPs) [8] have been considered for this problem. These features are often extracted from a region of interest (ROI), which is typically the portion of the image where the potential cancer lesion is located. Conventional techniques used to classify these features are usually based on conventional machine learning (ML) methods considering binary and multiclass classification [9; 10; 11; 12; 13; 14; 15]. Due to the need to develop automated systems for the detection and classification of cancer in mammograms, different artificial intelligence strategies have been explored. CNN, which can be used for feature extraction, classification, and image segmentation, have emerged as an attractive strategy for mammography image classification. Several existing CNN-based methods have achieved similar effectiveness to that of expert radiologists in controlled conditions. The effectiveness of a CNN model strictly depends on the availability of a large number of annotated training images and adequate data balancing. These requirements are not always feasible, so data augmentation is commonly employed to reduce model overfitting [16; 17; 18; 19; 20]. However, augmented data can misrepresent real mammography images, potentially leading to poor generalization of extracted features to clinical data. Recently, a proposed scheme combines multiple CNN architectures with machine learning strategies for breast cancer classification [21; 22; 23]. This strategy uses various CNN models as features extractors, which are then classified using different classifiers. This hybrid approach allows exploiting the advantages of CNN-based features while benefiting from the effectiveness of traditional ML algorithms for both binary and multiclass classification. Various hybrid systems combine convolutional neural networks (CNNs) with recurrent neural network (RNN) modules, such as bidirectional long short-term memory (BLSTM) layers, for feature extraction and classification [24]. Other methods integrate CNN architectures with Transformer encoders and specialized convolutional modules for binary classification [25]. An approach that combines stereoscopic attention mechanisms with Transformer-based feature fusion has also been explored to enhance lesion localization and classification in automated breast ultrasound (ABUS) images [26]. Additional strategies apply bio-inspired optimization algorithms [27] or combine CNN-derived features with texture-based descriptors using ensemble classifiers [28]. It is noteworthy that several existing methods based on CNN or hybrid-CNN have achieved high performance in breast cancer detection. However, these methods typically require data augmentation and specialized procedures for parameter optimization. These requirements increase computational costs and implementation complexity, additionally increasing the risk of overfitting and sensitivity to initial values.