As a problem of high practical appeal but many outstanding challenges, computer-based face recognition remains a topic of extensive research attention. In this paper we are specifically interested in the task of identifying a person using multiple images both in training and as a query. Thus, a novel method is proposed which advances the state-of-the-art in set-based face recognition. The introduced approach is based on a previously described invariant in the form of generic shape-illumination effects. The contributions include (i) an analysis of the computational demands of the original method and a demonstration of its practical limitations, (ii) a novel representation of personal appearance in the form of linked mixture models in image and pose-signature spaces, and (iii) an efficient (in terms of storage needs and matching time) manifold re-illumination algorithm based on the aforementioned representation. An evaluation and comparison of the proposed method with the original generic shape-illumination algorithm shows that comparably high recognition rates are achieved on a large data set (1.5% error on 700 face sets containing 100 individuals and extreme illumination variation) with a dramatic improvement in matching speed (over 700 times for sets containing 1600 faces) and storage requirements (independent of the number of training images). Theoretical and empirical findings of the present work are used to identify and discuss avenues for future research.