In shear wave absolute vibro-elastography (S-WAVE), a steady-state multi-frequency external mechanical excitation is applied to tissue, while a time-series of ultrasound radio-frequency (RF) data are acquired. Our objective is to determine the potential of S-WAVE to classify breast tissue lesions as malignant or benign. We present a new processing pipeline for feature-based classification of breast cancer using S-WAVE data, and we evaluate it on a new data set collected from 40 patients. Novel bi-spectral and Wigner spectrum features are computed directly from the RF time series and are combined with textural and spectral features from B-mode and elasticity images. The Random Forest permutation importance ranking and the Quadratic Mutual Information methods are used to reduce the number of features from 377 to 20. Support Vector Machines and Random Forest classifiers are used with leave-one-patient-out and Monte Carlo cross-validations. Classification results obtained for different feature sets are presented. Our best results (95% confidence interval, Area Under Curve = 95%±1.45%, sensitivity = 95%, and specificity = 93%) outperform the state-of-the-art reported S-WAVE breast cancer classification performance. The effect of feature selection and the sensitivity of the above classification results to changes in breast lesion contours is also studied. We demonstrate that time-series analysis of externally vibrated tissue as an elastography technique, even if the elasticity is not explicitly computed, has promise and should be pursued with larger patient datasets. Our study proposes novel directions in the field of elasticity imaging for tissue classification.