Evaluation of a Quasi-fractal Dimension to Enhance Breast Cancer Detection in X-ray Mammograms using Support Vector Machine.

We previously introduced a quasi-fractal dimension (Q-FD) to enhance breast cancer detection in X-ray mammography. In the present study, we evaluated the usefulness of this image feature for differentiating between benign and malignant masses using a support vector machine (SVM) with various kernels. The kernel computes the inner product of the functions that embed the data into a feature space where the nonlinear pattern appears linear. Q-FD was calculated using the method previously reported from the database of X-ray mammograms produced by the Japan Society of Radiological Technology. In addition to Q-FD, the image features such as curvature (C) and eccentricity (E) were extracted. The conventional fractal dimension (C-FD) was also calculated using the box-counting method. First, we investigated the SVM performance in terms of accuracy, sensitivity and specificity in the task of differentiating between benign and malignant masses by taking 5 parameters (C, E, C-FD, Q-FD and age) as input features in SVM. When using the linear kernel, the best accuracy was obtained at a regularization parameter of 50. For the polynomial and radial basis function (RBF) kernels, the best accuracy was obtained when the degree of polynomial and the width of RBF were 1 and 1, respectively. The accuracies were 0.746±0.089, 0.731±0.095 and 0.734±0.086 for the linear, polynomial and RBF kernels, respectively, when using C, E, C-FD and age as input features in the SVM. When Q-FD was added to the above input features, the accuracies were significantly improved to 0.957±0.045, 0.950±0.045 and 0.949±0.052 for the linear, polynomial and RBF kernels, respectively. These results suggest that Q-FD is effective for discriminating between benign and malignant masses and SVM is highly recommended as a classifier for its simple utilization and good performance, especially when the training set size is small.