The main question about the spiked Wigner model is: how large should the signal-to-noise ratio λ > 0 be in order to achieve constant correlation withx?

Compared with conventional minimization problems (e.g., empirical risk minimization), min-max optimization has aricher mathematical structure, thus being able tomodel more sophisticated learning problems thatemergefrom ever-emerging applications.

Inspecific,wepropose a novel method, namely, SVD-Dictionary enhancement, to build two separated spaces based on the sorted singular values. Concretely, the eigenvectors corresponding to larger singular values are used to build the generalization space in which localization isperformed, asthese eigenvectors generally suppress certain variations (e.g., the variation of styles) and contain intrinsical characteristics of objects.