Machine perception often requires a large amount of user-annotated data which is time-consuming, difficult, or expensive to collect. Perception systems should be easy to train by regular users, and this is currently far from the case. Our previous work, tracking-based semi-supervised learning , helped reduce the labeling burden by using tracking information to harvest new and useful training examples. However,  was designed for offline use; it assumed a fixed amount of unlabeled data and did not allow for corrections from users. In many practical robot perception scenarios we A) desire continuous learning over a long period of time, B) have a stream of unlabeled sensor data available rather than a fixed dataset, and C) are willing to periodically provide a small number of new training examples. In light of this, we present group induction, a new mathematical framework that rigorously encodes the intuition of  in an alternating optimization problem similar to expectation maximization (EM), but with the assumption that the unlabeled data comes in groups of instances that share the same hidden label. The mathematics suggest several improvements to the original heuristic algorithm, and make clear how to handle user interaction and streams of unlabeled data. We evaluate group induction on a track classification task from natural street scenes, demonstrating its ability to learn continuously, adapt to user feedback, and accurately recognize objects of interest.