Brain-imaging research has largely focused on localizing patterns of activity related to specific mental processes, but recent work has shown that mental states can be identified from neuroimaging data using statistical classifiers. We investigated whether this approach could be extended to predict the mental state of an individual using a statistical classifier trained on other individuals, and whether the information gained in doing so could provide new insights into how mental processes are organized in the brain. Using a variety of classifier techniques, we achieved cross-validated classification accuracy of 80% across individuals (chance = 13%). Using a neural network classifier, we recovered a low-dimensional representation common to all the cognitive-perceptual tasks in our data set, and we used an ontology of cognitive processes to determine the cognitive concepts most related to each dimension. These results revealed a small organized set of large-scale networks that map cognitive processes across a highly diverse set of mental tasks, suggesting a novel way to characterize the neural basis of cognition.