# Angle-Based Joint and Individual Variation Explained arXiv: https://arxiv.org/abs/1704.02060 ยท HTML: https://mlsanity.com/paper/1704.02060/ ## Key facts - Cited by 30 papers in the map (data through 14 Oct 2026). - First posted on arXiv 7 Apr 2017. ## Built on by (most cited first, 30 of 30) - [sJIVE: Supervised Joint and Individual Variation Explained](https://mlsanity.com/paper/2102.13278/) (2021) - [Double InfoGAN for Contrastive Analysis](https://mlsanity.com/paper/2401.17776/) (2024) - [Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matrices](https://mlsanity.com/paper/2411.17054/) (2024) - [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024) - [A spectral method for multi-view subspace learning using the product of projections](https://mlsanity.com/paper/2410.19125/) (2024) - [Representation Retrieval Learning for Heterogeneous Data Integration](https://mlsanity.com/paper/2503.09494/) (2025) - [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022) - [Robust SVD Made Easy: A fast and reliable algorithm for large-scale data analysis](https://mlsanity.com/paper/2402.09754/) (2024) - [Contrastive Learning on Multimodal Analysis of Electronic Health Records](https://mlsanity.com/paper/2403.14926/) (2024) - [Discovering Common Information in Multi-view Data](https://mlsanity.com/paper/2406.15043/) (2024) - [Multiple Augmented Reduced Rank Regression for Pan-Cancer Analysis](https://mlsanity.com/paper/2308.16333/) (2023) - [Learning Joint and Individual Structure in Network Data with Covariates](https://mlsanity.com/paper/2406.08776/) (2024) - [Rethinking LoRA for Data Heterogeneous Federated Learning: Subspace and State Alignment](https://mlsanity.com/paper/2602.01746/) (2026) - [Double-matched matrix decomposition for multi-view data](https://mlsanity.com/paper/2105.03396/) (2021) - [Multimodal Understanding Through Correlation Maximization and Minimization](https://mlsanity.com/paper/2305.03125/) (2023) - [D-CDLF: Decomposition of Common and Distinctive Latent Factors for Multi-view High-dimensional Data](https://mlsanity.com/paper/2407.00730/) (2024) - [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025) - [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025) - [Anchor PCA](https://mlsanity.com/paper/2606.06233/) (2026) - [Joint estimation of high-dimensional spiked covariance matrices via a partially shared subspace](https://mlsanity.com/paper/2607.08123/) (2026) - [Non-Euclidean Analysis of Joint Variations in Multi-Object Shapes](https://mlsanity.com/paper/2109.02230/) (2021) - [IGCN: Integrative Graph Convolution Networks for patient level insights and biomarker discovery in multi-omics integration](https://mlsanity.com/paper/2401.17612/) (2024) - [Joint Linked Component Analysis for Multiview Data](https://mlsanity.com/paper/2406.11761/) (2024) - [Empirical Bayes Linked Matrix Decomposition](https://mlsanity.com/paper/2408.00237/) (2024) - [Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration](https://mlsanity.com/paper/2603.12351/) (2026) - [Enhancing Spectral Embedding through Robust and Flexible Knowledge Transfer in Electronic Health Records](https://mlsanity.com/paper/2606.11570/) (2026) - [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (2026) - [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026) - [FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data](https://mlsanity.com/paper/2608.10857/) (2026) - [JIVEAdapter: A Multi-Task Additive Low-Rank Adapter via Joint and Individual Variation Explained (JIVE)](https://mlsanity.com/paper/2610.07036/) (2026) ## Abstract (arXiv) Integrative analysis of disparate data blocks measured on a common set of experimental subjects is a major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there is a strong desire to integrate the multiple genomic data sets in The Cancer Genome Atlas to characterize the common and also the unique aspects of cancer genetics and cell biology for each source. In this paper we introduce Angle-Based Joint and Individual Variation Explained capturing both joint and individual variation within each data block. This is a major improvement over earlier approaches to this challenge in terms of a new conceptual understanding, much better adaption to data heterogeneity and a fast linear algebra computation. Important mathematical contributions are the use of score subspaces as the principal descriptors of variation structure and the use of perturbation theory as the guide for variation segmentation. This leads to an exploratory data analysis method which is insensitive to the heterogeneity among data blocks and does not require separate normalization. An application to cancer data reveals different behaviors of each type of signal in characterizing tumor subtypes. An application to a mortality data set reveals interesting historical lessons. Software and data are available at GitHub .