# Generalized Integrative Principal Component Analysis for Multi-Type Data with Block-Wise Missing Structure

arXiv: https://arxiv.org/abs/1808.02193 · HTML: https://mlsanity.com/paper/1808.02193/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2018.

## Built on by (most cited first, 5 of 5)

- [sJIVE: Supervised Joint and Individual Variation Explained](https://mlsanity.com/paper/2102.13278/) (2021)
- [Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices](https://mlsanity.com/paper/2105.10360/) (2021)
- [Prediction approaches for partly missing multi-omics covariate data: A literature review and an empirical comparison study](https://mlsanity.com/paper/2302.03991/) (2023)
- [Imputation of missing values in multi-view data](https://mlsanity.com/paper/2210.14484/) (2022)
- [Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration](https://mlsanity.com/paper/2603.12351/) (2026)

## Abstract (arXiv)

High-dimensional multi-source data are encountered in many fields. Despite recent developments on the integrative dimension reduction of such data, most existing methods cannot easily accommodate data of multiple types (e.g., binary or count-valued). Moreover, multi-source data often have block-wise missing structure, i.e., data in one or more sources may be completely unobserved for a sample. The heterogeneous data types and presence of block-wise missing data pose significant challenges to the integration of multi-source data and further statistical analyses. In this paper, we develop a low-rank method, called Generalized Integrative Principal Component Analysis (GIPCA), for the simultaneous dimension reduction and imputation of multi-source block-wise missing data, where different sources may have different data types. We also devise an adapted BIC criterion for rank estimation. Comprehensive simulation studies demonstrate the efficacy of the proposed method in terms of rank estimation, signal recovery, and missing data imputation. We apply GIPCA to a mortality study. We achieve accurate block-wise missing data imputation and identify intriguing latent mortality rate patterns with sociological relevance.