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

arXiv: https://arxiv.org/abs/2305.06042 · HTML: https://mlsanity.com/paper/2305.06042/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 8 of 8)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [MIDA: Multiple Imputation using Denoising Autoencoders](https://mlsanity.com/paper/1705.02737/) (2017)
- [Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning](https://mlsanity.com/paper/1912.06989/) (2019)
- [Multiple imputation for continuous variables using a Bayesian principal component analysis](https://mlsanity.com/paper/1401.5747/) (2014)
- [EPEM: Efficient Parameter Estimation for Multiple Class Monotone Missing Data](https://mlsanity.com/paper/2009.11360/) (2020)
- [Missing Data Estimation in High-Dimensional Datasets: A Swarm Intelligence-Deep Neural Network Approach](https://mlsanity.com/paper/1607.00136/) (2016)

## Built on by (most cited first, 2 of 2)

- [Principal Components for Neural Network Initialization](https://mlsanity.com/paper/2501.19114/) (2025)
- [Imputation using training labels and classification via label imputation](https://mlsanity.com/paper/2311.16877/) (2023)

## Abstract (arXiv)

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.