Abstract—This paper investigates successful sub-bands of wave atom transform via classification of mammograms, when the coefficients of sub-bands are used as features. A computer-aided diagnosis system is constructed by using wave atom transform, support vector machine and k-nearest neighbor classifiers. Two-class classification is studied in detail using two data sets, separately. The successful sub-bands are determined according to the accuracy rates, coefficient numbers, and sensitivity rates. Keywords—Breast cancer, wave atom transform, SVM, k-NN. I. INTRODUCTION REAST cancer, a type of cancer which is a frequent cause of death, commonly occurs among women. Thus, its detection in early phases is crucial to fight the disease [1]. Another important thing about breast cancer is the classification of breast cancer as benign or malignant [2], [3]. Mammograms are the best available tools to accomplish these important goals. However, the process of diagnosis is a very difficult task. So, 10–30% of cancer cases are missed by radiologists [4]. Furthermore, non-cancerous lesions are misinterpreted. To avoid the risks mentioned above, computer- aided diagnosis (CAD) systems as a second opinion provider are aimed to aid the radiologists to reduce false positive and false negative rates [5]-[9]. In the present study, a mammogram classification system is constructed to investigate wave atom transform. The scope of the system is to analyze wave atom transform to take advantage of its property that is capturing both the coherence of the pattern along the oscillations and the pattern across the oscillations. Because of this property, wave atom transform generates coefficients that can be naturally arranged as two matrices (coefficients’ packets) for every scale. In order to explore the different aspects of this algorithm, the aim is to determine which packet will provide the maximum classification accuracy. The classification is performed in two successive stages: distinguishing between normal and abnormal regions, and classifying tumors as malignant or benign. To do so two different classifiers are employed (SVM, and k-NN). In summary; the investigation in this paper are explored in three: determination of the most successful packet and scale of the wave atom sub-bands, comparing the results using two different classifiers and test the results using two Nebi Gedik is with the Faculty of Marine Sciences at Karadeniz Technical University Trabzon, Turkey (phone: +90 462 377 8066, corresponding author, e-mail: ngedik@ktu.edu.tr). Ayten Atasoy is with the Faculty of Engineering at Karadeniz Technical University Trabzon, Turkey (e-mail: ayten@ktu.edu.tr) different databases. The remainder of the paper is organized as follows: Sections II and III include related works and a brief introduction of wave atom transform respectively. Materials and methods are described in Section IV, and the results and discussion are presented in Section V. Sections VI and VII contain the experiment and the conclusions. II. RELATED WORKS The diagnostic performance of CAD systems, particularly, depends on the feature extraction step which performs a key function. If the feature set has a high representational power, compactness and good discrimination ability, speed and classification accuracy of the CAD systems are greatly improved [10]. Therefore, in the literature, many studies have focused on this issue. Among the proposed feature extraction methods, multi-resolution analysis techniques such as contourlet, wavelet and curvelet transform draw attention. Liu et al. [11] propose a system that includes multi-resolution analysis to detect speculated lesions in digital mammograms. The system uses a linear phase non-separable two-dimensional wavelet transform to represent the mammograms. The feature set is composed using the coefficients of the wavelet pyramid at each resolution. A binary tree classifier is used to detect abnormalities. The results show that the system is capable of detecting abnormalities in different sizes at low false positive rates. Ferreira et al. [12] construct a system to extract and select the best features from the images to solve the difficulties of classifying them as benign, malignant or normal ones. The feature extraction process is performed using special sets of the coefficients after transforming the images in a wavelet basis. The results of the system are very promising. Ergin et al. [13] use a combination consisting of the histogram of oriented gradients (HOG), dense scale-invariant feature transform (DSIFT) and local configuration pattern (LCP) methods to classify breast cancer cases. These methods are able to extract the rotation- and scale-invariant features for all tissue types. The classification is made using support vector machine (SVM), k-nearest neighbor (k-NN), decision tree, and Fisher linear discriminant analysis (FLDA). Moayedi et al. [14] use the contourlet transform which is a powerful and developed version of Discrete Wavelet Transform. From the system, initially, regions of interest are obtained using a preprocessing step to remove the pectoral muscles. The feature extraction is performed utilizing the contourlet transform, and then feature set is created using the contourlet coefficients. A genetic algorithm is employed as feature selection to get most distinctive features. The Investigation of Wave Atom Sub-Bands via Breast Cancer Classification Nebi Gedik, Ayten Atasoy B World Academy of Science, Engineering and Technology International Journal of Biomedical and Biological Engineering Vol:11, No:9, 2017 552 International Scholarly and Scientific Research & Innovation 11(9) 2017 scholar.waset.org/1307-6892/10008417 International Science Index, Biomedical and Biological Engineering Vol:11, No:9, 2017 waset.org/Publication/10008417