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.

Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation techniques. Meanwhile, the data nowadays tends toward high-dimensional. Therefore, in this work, we propose Principal Component Analysis Imputation (PCAI), a simple but versatile framework based on Principal Component Analysis (PCA) to speed up the imputation process and alleviate memory issues of many available imputation techniques, without sacrificing the imputation quality in term of MSE. In addition, the frameworks can be used even when some or all of the missing features are categorical, or when the number of missing features is large. Next, we introduce PCA Imputation - Classification (PIC), an application of PCAI for classification problems with some adjustments. We validate our approach by experiments on various scenarios, which shows that PCAI and PIC can work with various imputation algorithms, including the state-of-the-art ones and improve the imputation speed significantly, while achieving competitive mean square error/classification accuracy compared to direct imputation (i.e., impute directly on the missing data).