# Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration

arXiv: https://arxiv.org/abs/2603.12351 · HTML: https://mlsanity.com/paper/2603.12351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Structural Learning and Integrative Decomposition of Multi-View Data](https://mlsanity.com/paper/1707.06573/) (2017)
- [Group Factor Analysis](https://mlsanity.com/paper/1411.5799/) (2014)
- [Data Integration Via Analysis of Subspaces (DIVAS)](https://mlsanity.com/paper/2212.00703/) (2022)
- [Generalized Integrative Principal Component Analysis for Multi-Type Data with Block-Wise Missing Structure](https://mlsanity.com/paper/1808.02193/) (2018)
- [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022)
- [Simultaneous Non-Gaussian Component Analysis (SING) for Data Integration in Neuroimaging](https://mlsanity.com/paper/2005.00597/) (2020)

## Abstract (arXiv)

Collecting multiple types of data on the same set of subjects is common in modern scientific applications including, genomics, metabolomics, and neuroimaging. Joint and Individual Variance Explained (JIVE) seeks a low-rank approximation of the joint variation between two or more sets of features captured on common subjects and isolates this variation from that unique to eachset of features. We develop an expectation-maximization (EM) algorithm to estimate a probabilistic model for the JIVE framework. The model extends probabilistic principal components analysis to multiple data sets. Our maximum likelihood approach simultaneously estimates joint and individual components, which can lead to greater accuracy compared to other methods. We apply ProJIVE to measures of brain morphometry and cognition in Alzheimer's disease. ProJIVE learns biologically meaningful courses of variation, and the joint morphometry and cognition subject scores are strongly related to more expensive existing biomarkers. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Code to reproduce the analysis is available on our GitHub page.