In this paper, we propose Discriminative Neural Clustering (DNC) that formulates data clustering with a maximum number of clusters as a supervised sequence-to-sequence learning problem. Compared to traditional unsupervised clustering algorithms, DNC learns clustering patterns from training data without requiring an explicit definition of a similarity measure. An implementation of DNC based on the Transformer architecture is shown to be effective on a speaker diarisation task using the challenging AMI dataset. Since AMI contains only 147 complete meetings as individual input sequences, data scarcity is a significant issue for training a Transformer model for DNC. Accordingly, this paper proposes three data augmentation schemes: sub-sequence randomisation, input vector randomisation, and Diaconis augmentation, which generates new data samples by rotating the entire input sequence of L2-normalised speaker embeddings. Experimental results on AMI show that DNC achieves a reduction in speaker error rate (SER) of 29.4% relative to spectral clustering.