coeff = ppca (Y, K) fits a probabilistic principal component analysis (PPCA) model with K components to the $N\; \times \; P$ data matrix Y (rows are observations, columns are variables) and returns the $P\; \times$K matrix coeff of orthonormal principal component coefficients, ordered by decreasing component variance. Y may contain NaN values marking missing observations; the model is fitted by an expectation-maximization algorithm that accounts for them. K must be a positive integer smaller than $P$.

[coeff, score, pcvar, mu, v, S] = ppca (…) returns further outputs:

score

The $N\; \times$K principal component scores (the data projected onto the components; missing entries are reconstructed from the model before projection).

pcvar

A $$K × 1 vector of the principal component variances (the variance explained by each component).

mu

A $1\; \times \; P$ vector of the estimated mean of Y.

v

The estimated residual (isotropic noise) variance.

S

A structure with the fitted model details: the loadings W, the expected scores Xexp, the reconstruction Recon, the number of iterations NumIter, and the root-mean-square residual RMSResid.

Name/Value pairs control the fit:

'W0'

A $P\; \times$K initial value for the loadings used by the expectation-maximization algorithm (missing-data case).

'Options'

A structure of algorithm options, as returned by statset, whose MaxIter, TolFun, and TolX fields set the maximum number of iterations and the convergence tolerances of the expectation-maximization algorithm.

When Y has no missing values the model is fitted directly from the eigendecomposition of its covariance matrix; coeff, pcvar, and v are then the principal component directions, the leading variances, and the mean of the trailing variances, respectively.

See also: pca, pcacov, pcares, factoran, barttest

Source Code: ppca