Probabilistic Principal Component Analysis
Probabilistic principal component analysis (PPCA) was introduced in  as a probabilistic version of standard PCA based on the assumption of a Gaussian distribution. PPCA can be implemented using singular value decomposition as described in detail on this extract of my master thesis found below. The following repository contains a Python implementation of PPCA:PPCA on GitHub
-  Tipping, Michael E., and Christopher M. Bishop. 1Probabilistic Principal Component Analysis. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 61, no. 3 (1999): 611–22.
The full mathematical background is decribed in this excerpt from my master thesis:thesis2017-ppca-excerpt