Probabilistic principal component analysis (PPCA) seeks a low dimensional
representation of a data set in the presence of independent spherical Gaussian
noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an
eigenvalue problem on the sample covariance matrix. In this paper we consider
the situation where the data variance is already partially explained by other
factors, e.g. covariates of interest, or temporal correlations leaving some
residual variance.