In terms of machine learning-based power system dynamic stability assessment, it is feasible to collect learning data from massive synchrophasor measurements in practice. However, the fact that instability events rarely occur would lead to a challenging class imbalance problem. Besides, short-term feature extraction from scarce instability seems extremely difficult for conventional learning machines. Faced with such a dilemma, this paper develops a systematic imbalance learning machine for online short-term voltage stability assessment. A powerful time series shapelet (discriminative subsequence) classification method is embedded into the machine for sequential transient feature mining. A forecasting-based nonlinear synthetic minority oversampling technique is proposed to mitigate the distortion of class distribution. Cost-sensitive learning is employed to intensify bias toward those scarce yet valuable unstable cases. Furthermore, an incremental learning strategy is put forward for online monitoring, contributing to adaptability and reliability enhancement along with time. Simulation results on the Nordic test system illustrate the high performance of the proposed learning machine and of the assessment scheme.