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

TL;DR

This paper introduces a Blockwise PCA Imputation framework that efficiently reduces dimensionality and imputes monotone missing data, significantly speeding up the process and improving convergence with certain imputation techniques.

Contribution

The proposed BPI framework enables faster dimensionality reduction and imputation for monotone missing data by applying PCA blockwise before imputation, adaptable to various imputation methods.

Findings

BPI significantly reduces imputation time.

BPI with MICE can lead to convergence issues in direct imputation.

Experiments validate BPI's efficiency and effectiveness.

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. To address this issue, 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 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. In addition, our experiments also show that while applying MICE imputation directly on missing data may not yield convergence, applying BPI with MICE for the data may lead to convergence.