# Group Factor Analysis

arXiv: https://arxiv.org/abs/1411.5799 · HTML: https://mlsanity.com/paper/1411.5799/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2014.

## Built on by (most cited first, 15 of 15)

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- [Variational Bayes for high-dimensional proportional hazards models with applications within gene expression](https://mlsanity.com/paper/2112.10270/) (2021)
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- [Calibrated Multimodal Representation Learning with Missing Modalities](https://mlsanity.com/paper/2511.12034/) (2025)
- [A hierarchical Bayesian model to find brain-behaviour associations in incomplete data sets](https://mlsanity.com/paper/2103.06845/) (2021)
- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Encoding Domain Information with Sparse Priors for Inferring Explainable Latent Variables](https://mlsanity.com/paper/2107.03730/) (2021)
- [Variational Interpretable Learning from Multi-view Data](https://mlsanity.com/paper/2202.13503/) (2022)
- [Identifying latent disease factors differently expressed in patient subgroups using group factor analysis](https://mlsanity.com/paper/2410.07890/) (2024)
- [Factor Analysis with Correlated Topic Model for Multi-Modal Data](https://mlsanity.com/paper/2504.18914/) (2025)
- [Multi-context principal component analysis](https://mlsanity.com/paper/2601.15239/) (2026)
- [Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration](https://mlsanity.com/paper/2603.12351/) (2026)
- [The Trade-off Between Covariate Dependence and Latent Structure in Representation Learning](https://mlsanity.com/paper/2608.16245/) (2026)

## Abstract (arXiv)

Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also naturally extends canonical correlation analysis to more than two sets, in a way that is more flexible than previous extensions. Our solution is formulated as variational inference of a latent variable model with structural sparsity, and it consists of two hierarchical levels: The higher level models the relationships between the groups, whereas the lower models the observed variables given the higher level. We show that the resulting solution solves the group factor analysis problem accurately, outperforming alternative factor analysis based solutions as well as more straightforward implementations of group factor analysis. The method is demonstrated on two life science data sets, one on brain activation and the other on systems biology, illustrating its applicability to the analysis of different types of high-dimensional data sources.