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We present an approach to activity discovery, the unsupervised identification and modeling of human actions embedded in a larger sensor stream. Activity discovery can be seen as the inverse of the activity recognition problem. Rather than learn models from hand-labeled sequences, we attempt to discover motifs, sets of similar subsequences within the raw sensor stream, without the benefit of labels or manual segmentation. These motifs are statistically unlikely and thus typically correspond to important or characteristic actions within the activity. The problem of activity discovery differs from typical motif discovery, such as locating protein binding sites, because of the nature of time series data representing human activity. For example, in activity data, motifs will tend to be sparsely distributed, vary in length, and may only exhibit intra-motif similarity after appropriate time warping. In this paper, we motivate the activity discovery problem and present our approach for efficient discovery of meaningful actions from sensor data representing human activity. We empirically evaluate the approach on an exercise data set captured by a wrist-mounted, three-axis inertial sensor. Our algorithm successfully discovers motifs that correspond to the real exercises with a recall rate of 96.3% and overall accuracy of 86.7% over six exercises and 864 occurrences.