An empirical framework for customer churn prediction modeling is presented in this work. This task represents a very interesting business analytics challenge, given its highly class imbalanced nature, and the presence of noisy variables that adversely affect the prediction capabilities of classification models. In this work, two SVM-based techniques are compared: Support Vector Data Description (SVDD), and standard two-class SVMs. The proposed methodology involves the comparison of these two methods under different conditions of class imbalance and using different subsets of variables. Feature ranking is performed via the Fisher Score Criterion, while the class imbalance problem is dealt with through resampling techniques, namely random undersampling and SMOTE oversampling. Experiments on four customer churn prediction datasets show the advantages of SVDD: it outperforms standard SVM in terms of predictive performance, demonstrating the importance of techniques that take the class imbalance problem into account.