An automated computer-assisted medical diagnosis that combines latest medical approaches and the advanced machine learning algorithms is a very crucial multidisciplinary technology, generating correct and noninvasive diagnoses of multiple diseases like breast cancer. The work proposed in this article focuses on the development of a biomedical computer-assisted diagnosis model that can classify digital mammography as normal (healthy) or abnormal, and further, as malignant or benign.The proposed approach employs the discrete Chebyshev transform to extract the features. Then, the kernel principal component analysis technique is used to extract the discriminating features from the original feature vector. Subsequently, an optimized kernel extreme learning machine is proposed as a classifier to detect the tumors present in the mammographic images. Because the efficiency of the proposed classifier depends on its characteristic kernel variable, the main idea of the present work is to choose the most appropriate features from the downsized feature set and simultaneously obtain the optimized value of the aforementioned parameter. To validate the efficiency of the proposed work, the proposed scheme is performed on two publicly available data sets, namely the Mammographic Image Analysis Society data set and the INbreast data set. From the experimental analysis and its results, it is showed that for both normal-abnormal and malignant-benign classification, the proposed approach results in accuracy of 100% for the first data set. However, in the case of malignant-benign classification, the proposed approach gives an accuracy of 99.93% for the second data set. Further, it is also observed that the proposed approach exhibits highest performance as compared to that of the other approaches.Additionally, the ANOVA test is evaluated to demonstrate that the achievement of the proposed approach is significantly good than that of the other existing approaches.