# Automatic Breast Tumor Screening of Mammographic Images with Optimal Convolutional Neural Network
Traditional ML methods have fewer parameters that can easily be optimized by the gradient descent optimization or back-propagation algorithms through training with small-to-medium-sized datasets [21; 22]. Through a series of convolutional and pooling processes, the multilayer CNN can enhance and extract the desired object at different scales and different levels from low-level features (extract object's edge) to high-level information (extract object's shape) for detecting nonlinear features, which can increase nonlinearity and obtain feature representation. Then, the pooling process with maximum pooling (MP) is used to reduce the sizes of feature maps for obtaining abstract features. Thus, in contrast to the traditional machine-learning method, CNN-based methods can learn to extract the feature patterns from the raw data and improve the classification accuracy significantly. However, small- or medium-sized datasets are insufficient to train a deep-learning-based CNN. For example, from the existing literature [23; 24; 25; 26], such as AlexNet (eight-layer CNN) [25] and ZFnet [26], it can be observed that the deep-learning-based CNN requires several convolutional-pooling layers and fully connected layers for the large-scale image classification (ImageNet image database [27; 28]). This CNN can learn to optimize features during the training stage, process large inputs with sparsely connected weights, adapt to different sizes of 2D images, and reduce error rates. Furthermore, this approach demonstrates greater computational efficiency compared with the traditional fully connected multilayer perceptron (MLP) networks. Despite its many advantages, however, a deep-learning-based CNN presents several drawbacks and limitations, such as the number of convolutional-pooling layers' determination, the number of convolutional windows and pooling windows, the sizes of convolutional window assignment (3 \(\times\) 3, 5 \(\times\) 5, 7 \(\times\) 7, 9 \(\times\) 9, 11 \(\times\) 11), the high computational complexity and large-scale dataset requirement for training the CNN-based classifier, and the poor suitability for real-time applications. Additionally, multi-convolutional-pooling processes with different sizes of convolution masks will result in a very large information loss for feature extraction, and this will result in increased complexity levels. The multilayer CNN must be performed with a graphics processing unit (GPU) to speed up the training and classification tasks by making use of a large amount of training and testing data. Therefore, to simplify the image processing and classification tasks, this study aimed to design a suitable number of convolutional-pooling layers and a classification layer that is capable of increasing the identification accuracy of image classification, to facilitate automatic breast tumor screening. As observed from Figure 1, we utilized a multilayer classifier, consisting of a fractional-order convolutional layer, two convolutional-pooling layers, a flattening layer, and a multilayer classifier in the classification layer. In the first convolutional layer, a 2D spatial convolutional process with two 3 \(\times\) 3 fractional-order convolutional masks was used to perform the enhancement task and to remove unwanted noise from the original mammography image, to distinguish the edges and shapes of the object. In the second and third convolutional layers, sixteen 3 \(\times\) 3 kernel convolutional windows were used to subsequently enhance and sharpen the feature patterns twice; hence, the tumor contour could easily be highlighted and distinguished for feature pattern extraction. Consequently, two MP processes were used to reduce the dimensions of the feature patterns, which conducted network training to avoid failing in overfitting problems [29; 30]. In the classification layer, a multilayer classifier with an input layer, two hidden layers, and an output layer is implemented to perform the pattern recognition task, which separates tumor-free feature patterns from tumor feature patterns.