Fast variational PCA for functional analysis of dynamic image sequences

Principal component analysis (PCA) is a well-known algorithm used in many areas of science. It is usually taken as the golden standard for dimensionality reduction. However, PCA usually does not provide information about uncertainty of its results, thus preventing further investigation of model structure. A full Bayesian treatment is not feasible. Recently, variational PCA (VPCA) was proposed as an approximate Bayesian solution of the problem. In this paper, we summarise the iterative solution to the PCA problem arising from a variational approach. A new model with orthogonality restrictions is constructed in order to overcome its limitations. Notably, a highly efficient computational algorithm for variational PCA is revealed. It is applied in the analysis of functional medical images, yielding solution in a fraction of the time needed by the conventional technique.