Missing values in principal component analysis

Calculation schemes for principal component analysis are considered for the case when some matrix elements are missing. Iterative solutions are proposed—either a set of multilinear regression problems or as singular-value decomposition problems with iterative imputation of missing values. If mean values are subtracted from the data matrix, they should also be included in the iteration scheme. Test calculations using Matlab show that the regression approach is somewhat faster than the imputation approach. The results with a substantial amount of missing data are different and superior to those obtained with the naive NIPALS algorithm in common use in chemometrics.