Chunk-wise regularised PCA-based imputation of missing data

Standard multivariate techniques like Principal Component Analysis (PCA) are based on the eigendecomposition of a matrix and therefore require complete data sets. Recent comparative reviews of PCA algorithms for missing data showed the regularised iterative PCA algorithm (RPCA) to be effective. This paper presents two chunk-wise implementations of RPCA suitable for the imputation of tall data sets, that is, data sets with many observations. A chunk is a subset of the whole set of available observations. In particular, one implementation is suitable for distributed computation as it imputes each chunk independently. The other implementation, instead, is suitable for incremental computation, where the imputation of each new chunk is based on all the chunks analysed that far. The proposed procedures were compared to batch RPCA considering different data sets and missing data mechanisms. Experimental results showed that the distributed approach had similar performance to batch RPCA for data with entries missing completely at random. The incremental approach showed appreciable performance when the data is missing not completely at random, and the first analysed chunks contain sufficient information on the data structure.

Automated summary

Two chunk-wise implementations of RPCA suitable for tall data sets are proposed in this paper, with one for distributed computation and the other for incremental computation. Experimental results show that the distributed approach performs similarly to batch RPCA for data with completely random missing entries, while the incremental approach shows good performance for data with non-completely random missing entries if the first analyzed chunks contain sufficient information on the data structure.