Breast cancer detection using deep convolutional neural networks and support vector machines

Thresholding method

Thresholding methods are the simplest methods for image segmentation. The image pixels are divided with respect to their intensity level. The most common type of thresholding method is the global threshold (Kaur & Kaur, 2014). This is done by setting an appropriate threshold value (T). This value of (T) will be constant for the whole image. On the basis of (T) the output image p(x, y) can be obtained from the original image q(x, y) as given in Eq. (1), (1)${\displaystyle p\left(x,y\right)=\left\{\begin{array}{c}1,ifq\left(x,y\right)>T\hfill \\ 0,ifq\left(x,y\right)<T\hfill \end{array}\right.}$

Region based segmentation method

The region-based segmentation is simpler than other methods. It divides the image into different regions based on predefined criteria (Khan, 2013). There are two main types for the region-based segmentation; (1) region growing and (2) region splitting and merging.

The region-growing algorithm has the ability to remove a region from an image based on some predefined criteria such as the intensity. Region growing is an approach to image segmentation in which neighbouring pixels are examined and joined to a region class where no edges are detected. It is also classified as a pixel-based image segmentation method as it involves the selection of initial seed point (Kaur & Goyal, 2015). It should be noted that the region splitting and merging method is the opposite of the region growing method as it works on the complete image (Kaur & Goyal, 2015).

In this manuscript, the region of interest (ROI) is extracted from the original mammogram image by two different methods. Deep convolutional neural network The first method is to determine the ROI by using circular contours. The tumors in the DDSM dataset are labelled with a red contour and accordingly, these contours are determined manually by examining the pixel values of the tumor and using them to extract the region. (Duraisamy & Emperumal, 2017) cropped the ROI manually from the dataset. The ROI is shown in Fig. 4B.

In the second method, the threshold and the region-based methods are used to determine the ROI. The tumor in the samples of the DDSM dataset (Heath et al., 2001) is labelled by a red contour as illustrated in Fig. 4A. The first step to extract the ROI is to determine the tumor region by a threshold value, which is a value determined with respect to the red color pixel. After some trials, the threshold was set to 76 for all the images regardless of the size of the tumor. Then, the biggest area within this threshold along the image was determined and the tumor was cropped automatically. Figure 4C shows the ROI extracted by the threshold and the region based method. The steps for the used method can be summarized as follows:

1. Convert the original mammogram grayscale image into a binary image using the threshold technique.

2. Binary image objects are labelled and the number of pixels are counted. All binary objects are removed except for the largest one, which is the tumor with respect to the threshold. The largest area is the area enclosed within the red contour labelled around the tumor.

3. After the algorithm checks all pixels in the binary image, the largest area pixels within the threshold are set to “1”, otherwise all other pixels are set to “0”.

4. The resulting binary image is multiplied with the original mammogram image to get the final image without taking in consideration the rest of the breast region or any other artifacts.

Deep convolutional neural network

DCNN has achieved success in image classification problems including image analysis as in (Han et al., 2015; Zabalza et al., 2016). A convolutional neural network (CNN) consists of multiple trainable stages stacked on top of each other, followed by a supervised classifier and sets of arrays named feature maps (LeCun, Kavukcuoglu & Farabet, 2010). There are three main types of layers used to build CNN architectures; (1) convolutional layer, (2) pooling layer, and (3) fully connected (fc) layer (Spanhol, 2016).

There are many CNN architectures such as CiFarNet (Krizhevsky, 2009; Roth et al., 2016), AlexNet (Krizhevsky, Sutskever & Hinton, 2012), GoogLeNet (Szegedy et al., 2015), the ResNet (Sun, 2016), VGG16, and VGG 19. However, the most commonly used architectures are the AlexNet, CiFarNet, and the Inception v1 (GoogleNet).

The AlexNet architecture achieved significantly better performance over the other deep learning methods for ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2012. This success has revived the interest in CNNs in computer vision. AlexNet has five convolution layers, three pooling layers, and two fully connected layers with approximately 60 million free parameters (Krizhevsky, Sutskever & Hinton, 2012). The AlexNet CNN architecture is shown in Fig. 5.

The layers of conv1-5 in Fig. 5 are the convolution layers. Each neuron in the convolution layers computes a dot product between their weights and the local region that is connected to the input volume (Krizhevsky, Sutskever & Hinton, 2012).

The pooling layers are pool1, pool2, and pool5 as shown in Fig. 5. These layers perform a down sampling operation along the spatial dimensions to reduce the amount of computation and improve the robustness (Suzuki et al., 2016; Krizhevsky, Sutskever & Hinton, 2012).

The layers of norm1-2 in Fig. 5 are the normalization layers. They perform a kind of lateral inhibition that is observed in the brain (Krizhevsky, Sutskever & Hinton, 2012).

Additionally, the fully connected layers are fc6, fc7, and fc8 as shown in Fig. 5. Neurons in the fully connected layer have full connections to all neurons in the previous layer, as in ordinary feedforward neural networks (Krizhevsky, Sutskever & Hinton, 2012; Deng et al., 2009).

Transfer learning

The DCNN is pre-trained firstly using the ImageNet dataset, which contains 1.2 million natural images for classification of 1,000 classes. Then, the last fully connected layer is replaced by a new layer for the classification of two classes; benign and malignant masses. Figure 5 shows the fine-tuning of the AlexNet to classify only two classes (Deng et al., 2009).

To retrain the AlexNet after fine-tuning the fully connected layer to two classes, some parameters must be set; the iteration number and the primary learning rate are set to 10⁴ and 10⁻³, respectively. Whereas, the momentum is set to 0.9 and the weight decay is set to 5 × 10⁻⁴. These configurations are to ensure that the parameters are fine-tuned for medical breast cancer diagnosis. Other parameters are set to default values. The optimization algorithm used is the Stochastic Gradient Descent with Momentum (SGDM).

The confusion matrix

The confusion matrix is a specific table visualizing the performance of the classifier.

Usually, in the field of machine learning a confusion matrix is known as the error matrix.

An image region is said to be positive or negative, depending on the data type. Furthermore, a decision for the detected result can be either correct (true) or incorrect (false). Therefore, the decision will be one of four possible categories: true positive (TP), true negative (TN), false positive (FP), and false negative (FN). The correct decision is the diagonal of the confusion matrix. Table 1 provides an example of the confusion matrix for two classes classification.

The accuracy

Accuracy is the measure of a correct prediction made by the classifier. It gives the ability of performance of the whole classifier. The accuracy is defined as in Eq. (2). (2)${\displaystyle \text{accuracy}=\frac{TP+TN}{TN+FP+FN+TP}}$

The Receiver operating characteristic (ROC)

The ROC analysis is a well-known evaluation method for detecting tasks. Firstly, a ROC analysis was used in medical decision-making; consequently, it was used in medical imaging.

The ROC curve is a graph of operating points which can be considered as a plotting of the true positive rate (TPR) as a function of the false positive rate (FPR).

The TPR and the FPR are also called sensitivity (recall) and specificity, respectively. They are defined as in Eqs. (3) and (4). (3)${\displaystyle \text{sensitivity}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}}$ (4)${\displaystyle \text{specificity}=\frac{TN}{TN+FP}}$

The Area under the ROC curve (AUC)

The AUC is used in the medical diagnosis system and it provides an approach for evaluating models based on the average of each point on the ROC curve. For a classifier performance the AUC score should be always between ‘0’ and ‘1’, the model with a higher AUC value gives a better classifier performance.

Precision

Precision is the ratio of correctly predicted positive observations to the total predicted positive observations. High precision relates to the low FPR. The precision is calculated using the following equation, (5)${\displaystyle \text{Precision}=\frac{TP}{TP+FP}}$

F1 score

F1 score is the weighted average of precision and recall. It is used as a statistical measure to rate the performance of the classifier. Therefore, this score takes both false positives and false negatives into account. F1 score is defined as in Equation (6) (6)${\displaystyle \mathrm{F}1\text{score}=\frac{2\text{ * Recall * Precision}}{\text{Recall}+\text{Precision}}}$

DCNN architecture

The Alexnet DCNN architecture is used in this manuscript after fine-tuning to classify two classes instead of 1,000 classes. A conventional DCNN consists of a convolutional layer, a pooling layer, and a fully connected (fc) layer. The DCNN architecture is formed by stacking all these layers together. Figure 6 shows a complete description of each layer in the AlexNet architecture.

In the convolutional layer number (1) as an example, the output of this layer is calculated using Equation (7). The output is equals to 55 × 55 × 96, which indicates that the size of the feature map is 55 × 55 in width and in height. In addition, the number of feature maps is 96. (7)${\displaystyle \text{The output size of the conv layer}=\left(\frac{input-filtersize}{Stride}\right)+1.}$

On the other hand, the output size of the pooling layer is calculated using Eq. (8). (8)${\displaystyle \text{The output size of the pool layer}=\left(\frac{outputofconv-poolsize}{Stride}\right)+1.}$

DCNN-based SVM Architecture

The DCNN based SVM architecture is shown in Fig. 7. It consists of five stages of convolutional layers, ReLU activations, pooling layers, followed by three fully connected (fc) layers. The last fully connected layer is connected to SVM classifier to obtain better accuracy.

Data augmentation

Generally, training on a large number of training samples performs well and give high accuracy rate. However, the biomedical datasets contain a relatively small number of samples due to limited patient volume. Accordingly, data augmentation is a method for increasing the size of the input data by generating new data from the original input data. There are many strategies for data augmentation; the one used here in this manuscript is the rotation. Each original image is rotated by 0, 90, 180, and 270 degrees. Therefore, each image is augmented to four images.

CBIS-DDSM Dataset

For this dataset, the samples were only enhanced and the features were extracted using the DCNN. This is because that the samples of this dataset were already segmented.

Data augmentation was applied to all the mass samples in this dataset as well to increase the training samples. The samples were augmented to four images using the rotation technique. When using the DCNN for feature extraction and classification the accuracy became 73.6%. Additionally, when classifying the features extracted from the DCNN using the SVM the accuracy with medium Gaussian kernel function reached 87.2% as illustrated in Table 6. The AUC was 0.94 (94%). The ROC curve is shown in Fig. 9.

By comparing to other researches results, either when using the AlexNet architecture with or other DCNN architectures, the results of the new proposed methods achieved the highest results. This is clear in Tables 7 and 8.

In Table 7, some of the previous work using the AlexNet architecture is shown. On the other hand, Table 8 shows a comparative view of several mass detection methods based on DCNN, including the newly proposed method.