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

Monotone missing data is a common problem in data analysis. However,imputation combined with dimensionality reduction can be computationallyexpensive, especially with the increasing size of datasets. To address thisissue, we propose a Blockwise principal component analysis Imputation (BPI)framework for dimensionality reduction and imputation of monotone missing data.The framework conducts Principal Component Analysis (PCA) on the observed partof each monotone block of the data and then imputes on merging the obtainedprincipal components using a chosen imputation technique. BPI can work withvarious imputation techniques and can significantly reduce imputation timecompared to conducting dimensionality reduction after imputation. This makes ita practical and efficient approach for large datasets with monotone missingdata. Our experiments validate the improvement in speed. In addition, ourexperiments also show that while applying MICE imputation directly on missingdata may not yield convergence, applying BPI with MICE for the data may lead toconvergence.