Classification of breast masses via nonlinear transformation of features based on a kernel matrix

We propose methods to perform a certain nonlinear transformation of features based on a kernel matrix, before the classification step, aiming to improve the discriminating power of the comparatively weak edge-sharpness and texture features of breast masses in mammograms, and seek better incorporation of features representing different radiological characteristics than shape features only. Kernel principal component analysis (KPCA) is applied to improve the discriminating power of each single feature in an expanded feature space and the discriminating capability of different feature combinations in other transformed, more informative, lower-dimensional feature spaces. A kernel partial least squares (KPLS) method is developed to derive score vectors for a shape feature set, and an edge-sharpness and texture feature set, respectively, with minimal covariance between each other, to help in achieving improved diagnosis using multiple radiological characteristics of breast masses. Fisher's linear discriminant analysis (FLDA) is employed to evaluate the classification capability of the transformed features. The methods were tested with a set of 57 regions in mammograms, of which 20 are related to malignant tumors and 37 to benign masses, represented using five shape features, three edge-sharpness features, and 14 texture features. The classification performance of the edge-sharpness and texture features, via KPCA transformation, was significantly improved from 0.75 to 0.85 in terms of the area under the receiver operating characteristics curve (Az). The classification performance of all of the shape, edge-sharpness, and texture features, via KPLS transformation, was improved from 0.95 to 1.0 in Az value.