Low rank approximation techniques are widespread in pattern recogni- tion research — they include Latent Semantic Analysis (LSA), Proba- bilistic LSA, Principal Components Analysus (PCA), the Generative As- pect Model, and many forms of bibliometric analysis. All make use of a low-dimensional manifold onto which data are projected. Such techniques are generally “unsupervised,” which allows them to model data in the absence of labels or categories. With many practi- cal problems, however, some prior knowledge is available in the form of context. In this paper, I describe a principled approach to incorpo- rating such information, and demonstrate its application to PCA-based approximations of several data sets.