Blockwise Principal Component Analysis for monotone missing data imputation and dimensionality reduction

Tu T. Do, Anh M. Vu, Tuan L. Vo, Hoang Thien Ly, Thu Nguyen, Steven Hicks, Pål Halvorsen, Michael Riegler, Binh T. Nguyen

Abstract: Monotone missing data is a common problem in data analysis. However, imputation combined with dimensionality reduction can be computationally expensive, especially with the increasing size of datasets. We propose a Blockwise Principal Component Analysis Imputation (BPI) framework for dimensionality reduction and imputation of monotone missing data to address this issue. The framework conducts Principal Component Analysis on the observed part of each monotone block of the data and then imputes on merging the obtained principal components using a chosen imputation technique. BPI can work with various imputation techniques and can significantly reduce imputation time compared to conducting dimensionality reduction after imputation. This makes it a practical and efficient approach for large datasets with monotone missing data. Our experiments validate the improvement in speed while achieving an accuracy that is comparable to the common strategy of imputation prior to dimensional reduction.