2.3.2 Mixture of probabilistic PCA

Tipping and Bishop (1999) extended the probabilistic PCA (section 2.1.2) to a mixture model. Different from the Gaussian mixture model, the probabilistic PCA extension needs only a set of q < d principal components. The rest of the density's variance is given by the noise $\sigma^{2}_{}$, which is the mean residual local variance. In the algorithm, the density (2.16) needs to be therefore replaced by the density used for probabilistic PCA. Apart from this substitution, the algorithm is identical to the classical Gaussian mixture model.