Images, as high-dimensional data, usually embody large variabilities. To classify images for versatile applications, an effective algorithm is necessarily designed by systematically considering the data structure, similarity metric, discriminant subspace, and classifier. In this paper, we provide evidence that, besides the Fisher criterion, graph embedding, and tensorization used in many existing methods, the correlation-based similarity metric embodied in supervised multilinear discriminant subspace learning can additionally improve the classification performance. In particular, a novel discriminant subspace learning algorithm, called correlation tensor analysis (CTA), is designed to incorporate both graph-embedded correlational mapping and discriminant analysis in a Fisher type of learning manner. The correlation metric can estimate intrinsic angles and distances for the locally isometric embedding, which can deal with the case when Euclidean metric is incapable of capturing the intrinsic similarities between data points. CTA learns multiple interrelated subspaces to obtain a low-dimensional data representation reflecting both class label information and intrinsic geometric structure of the data distribution. Extensive comparisons with most popular subspace learning methods on face recognition evaluation demonstrate the effectiveness and superiority of CTA. Parameter analysis also reveals its robustness.