In the era of large scientific data sets, there is an urgent need for methods to automatically prioritize data for review. At the same time, for any automated method to be adopted by scientists, it must make decisions that they can understand and trust. In this paper, we propose Discovery through Eigenbasis Modeling of Uninteresting Data (DEMUD), which uses principal components modeling and reconstruction error to prioritize data. DEMUD’s major advance is to offer domain-specific explanations for its prioritizations. We evaluated DEMUD’s ability to quickly identify diverse items of interest and the value of the explanations it provides. We found that DEMUD performs as well or better than existing class discovery methods and provides, uniquely, the first explanations for why those items are of interest. Further, in collaborations with planetary scientists, we found that DEMUD (1) quickly identifies very rare items of scientific value, (2) maintains high diversity in its selections, and (3) provides explanations that greatly improve human classification accuracy.