False positive (FP) marks represent an obstacle for effective use of computer-aided detection (CADe) of breast masses in mammography. Typically, the problem can be approached either by developing more discriminative features or by employing different classifier designs. In this paper, the usage of support vector machine (SVM) classification for FP reduction in CADe is investigated, presenting a systematic quantitative evaluation against neural networks (NNet), k-nearest neighbor classification (k-NN), linear discriminant analysis (LDA) and random forests (RF). A large database of 2516 film mammography examinations and 73 input features was used to evaluate the classifiers for their performance on correctly diagnosed exams as well as false negatives. Further, classifier robustness was investigated using varying training data and feature sets as input. The evaluation was based on the mean exam sensitivity in 0.05 to 1 false positives on the free-response receiver operating characteristic curve (FROC), incorporated into a 10-fold cross validation framework. It was found that SVM classification using a Gaussian kernel offered significantly increased detection performance (P = 0.0002) compared to the reference methods. Varying training data and input features, SVMs showed improved exploitation of large feature sets. It is concluded that with SVM-based CADe a significant reduction of false positives is possible outperforming other state-of-the-art approaches for breast mass CADe.