Roles of nodes in a social network (SN) represent their functions, responsibilities or behaviors within the SN. Roles typically evolve over time, making role analytics a challenging problem. Previous studies  either neglect role transition analysis or perform role discovery and role transition learning separately, leading to inefficiencies and limited transition analysis.  We propose a novel dynamic non-negative matrix factorization (DyNMF) approach to simultaneously discover roles and learn role transitions. DyNMF explicitly models temporal information by introducing a role transition matrix and clusters nodes in SNs from two views: the current view and the historical view. The current view captures structural information from the current SN snapshot and the historical view captures role transitions by looking at roles in past SN snapshots. DyNMF efficiently provides more effective analytics capabilities, regularizing roles by temporal smoothness of role transitions and reducing  uncertainties and inconsistencies between snapshots. Experiments on both synthetic and real-world SNs demonstrate the advantages of DyNMF in discovering and predicting roles and role transitions.