Over the last few decades, psychologists have developed sophisticated formal models of human categorization using simple artificial stimuli. In this paper, we use modern machine learning methods to extend this work into the realm of naturalistic stimuli, enabling human categorization to be studied over the complex visual domain in which it evolved and developed. We show that representations derived from a convolutional neural network can be used to model behavior over a database of >300,000 human natural image classifications, and find that a group of models based on these representations perform well, near the reliability of human judgments. Interestingly, this group includes both exemplar and prototype models, contrasting with the dominance of exemplar models in previous work. We are able to improve the performance of the remaining models by preprocessing neural network representations to more closely capture human similarity judgments.