Single Imputation Via Chunk-Wise PCA

Abstract

The straightforward application of Principal Component Analysis (PCA) to incomplete data sets is not possible and practitioners often remove or ignore observations that contain at least one missing value. Three different strategies can be mainly distinguished to apply PCA on a data set with missing entries: (i) imputation of the missings prior to the application of PCA; (ii) obtain the PCA solution and ignore the missings; and (iii) obtain the PCA solution and deal explicitly with missings. Methods implementing the latter strategy have been reviewed and, among them, the iterative PCA (iPCA) approach has been shown to be preferable. This paper proposes a chunk-wise implementation of iPCA, suitable for tall data sets, that is, with many observations. In the proposed approach, each data chunk is imputed according to the insofar analyzed data. The proposed procedure is compared to the batch iPCA and to a naive implementation, which imputes each data chunk independently. In a series of experiments, we consider different data sets and missing data mechanisms.