Abstract Spectral clustering has been playing a vital role in various research areas. Most traditional spectral clustering algorithms comprise two independent stages (i.e., first learning continuous labels and then rounding the learned labels into discrete ones), which may lead to severe information loss and performance degradation. In this work, we study how to achieve discrete clustering as well as reliably generalize to unseen data. We propose a unified spectral clustering scheme which jointly learns discrete clustering labels and robust out-ofsample prediction functions. Specifically, we explicitly enforce a discrete transformation on the intermediate continuous labels, which leads to a tractable optimization problem with a discrete solution. Moreover, to further compensate the unreliability of the learned labels, we integrate an adaptive robust module with `2,p loss to learn prediction function for unseen data. Extensive experiments conducted on various data sets have demonstrated the superiority of our proposal as compared to existing clustering approaches.