We tackle the issue of generalized category discovery (GCD). GCD considers the open-world problem of automatically clustering a partially labelled dataset, in which the unlabelled data may contain instances from both novel categories and labelled classes. In this paper, we address the GCD problem with an unknown category number for the unlabelled data. We propose a framework, named CiPR, to bootstrap the representation by exploiting Cross-instance Positive Relations in the partially labelled data for contrastive learning, which have been neglected in existing methods. To obtain reliable cross-instance relations to facilitate representation learning, we introduce a semi-supervised hierarchical clustering algorithm, named selective neighbor clustering (SNC), which can produce a clustering hierarchy directly from the connected components of a graph constructed from selective neighbors. We further present a method to estimate the unknown class number using SNC with a joint reference score that considers clustering indexes of both labelled and unlabelled data, and extend SNC to allow label assignment for the unlabelled instances with a given class number. We thoroughly evaluate our framework on public generic image recognition datasets and challenging fine-grained datasets, and establish a new state-of-the-art. Code: https://github.com/haoosz/CiPR
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