Discrete Nonnegative Spectral Clustering
Spectral clustering has been playing a vital role in various research areas. Most traditional spectral clustering algorithms comprise two independent stages (e.g., first learning continuous labels and then rounding the learned labels into discrete ones), which may cause unpredictable deviation of resultant cluster labels from genuine ones, thereby leading 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 novel spectral clustering scheme which deeply explores cluster label properties, including discreteness, nonnegativity, and discrimination, as well as learns robust out-of-sample 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. Besides, we preserve the natural nonnegative characteristic of the clustering labels to enhance the interpretability of the results. Moreover, to further compensate the unreliability of the learned clustering labels, we integrate an adaptive robust module with $\ell _{2,p}$  loss to learn prediction function for grouping unseen data. We also show that the out-of-sample component can inject discriminative knowledge into the learning of cluster labels under certain conditions. Extensive experiments conducted on various data sets have demonstrated the superiority of our proposal as compared to several existing clustering approaches.