A novel way to learn and track simultaneously the appearance of a previously non-seen face without intrusive techniques can be found in this article. The presented approach has a causal behaviour: no future frames are needed to process the current ones. The model used in the tracking process is refined with each input frame thanks to a new algorithm for the simultaneous and incremental computation of the singular value decomposition (SVD) and the mean of the data. Previously developed methods about iterative computation of SVD are taken into account and an original way to extract the mean information from the reduced SVD of a matrix is also considered. Furthermore, the results are produced with linear computational cost and sublinear memory requirements with respect to the size of the data. Finally, experimental results are included, showing the tracking performance and some comparisons between the batch and our incremental computation of the SVD with mean information.