Abstract: We tackle the problem of discovering novel classes in an image collection given labelled examples of other classes. This setting is similar to semi-supervised learning, but significantly harder because there are no labelled examples for the new classes. The challenge, then, is to leverage the information contained in the labelled images in order to learn a general-purpose clustering model and use the latter to identify the new classes in the unlabelled data. In this work we address this problem by combining three ideas: (1) we suggest that the common approach of bootstrapping an image representation using the labeled data only introduces an unwanted bias, and that this can be avoided by using self-supervised learning to train the representation from scratch on the union of labelled and unlabelled data; (2) we use rank statistics to transfer the model's knowledge of the labelled classes to the problem of clustering the unlabelled images; and, (3) we train the data representation by optimizing a joint objective function on the labelled and unlabelled subsets of the data, improving both the supervised classification of the labelled data, and the clustering of the unlabelled data. We evaluate our approach on standard classification benchmarks and outperform current methods for novel category discovery by a significant margin.