Probabilistic Principal Component Analysis

@article{Tipping1999ProbabilisticPC,
  title={Probabilistic Principal Component Analysis},
  author={Michael E. Tipping and Charles M. Bishop},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  year={1999},
  volume={61}
}
Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. We demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model that is closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively… 
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