# Multi-View Independent Component Analysis with Shared and Individual Sources

arXiv: https://arxiv.org/abs/2210.02083 · HTML: https://mlsanity.com/paper/2210.02083/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 96 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Learning Robust Representations via Multi-View Information Bottleneck](https://mlsanity.com/paper/2002.07017/) (2020)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [Trivializations for Gradient-Based Optimization on Manifolds](https://mlsanity.com/paper/1909.09501/) (2019)
- [Causal Discovery with General Non-Linear Relationships Using Non-Linear ICA](https://mlsanity.com/paper/1904.09096/) (2019)
- [Deep Variational Canonical Correlation Analysis](https://mlsanity.com/paper/1610.03454/) (2016)
- [Modeling Shared Responses in Neuroimaging Studies through MultiView ICA](https://mlsanity.com/paper/2006.06635/) (2020)
- [Faster ICA under orthogonal constraint](https://mlsanity.com/paper/1711.10873/) (2017)
- [Independent Vector Analysis: Identification Conditions and Performance Bounds](https://mlsanity.com/paper/1303.7474/) (2013)
- [Shared Independent Component Analysis for Multi-Subject Neuroimaging](https://mlsanity.com/paper/2110.13502/) (2021)
- [Common and Distinct Components in Data Fusion](https://mlsanity.com/paper/1607.02328/) (2016)
- [A Searchlight Factor Model Approach for Locating Shared Information in Multi-Subject fMRI Analysis](https://mlsanity.com/paper/1609.09432/) (2016)

## Built on by (most cited first, 7 of 7)

- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [MultiView Independent Component Analysis with Delays](https://mlsanity.com/paper/2312.00484/) (2023)
- [Provable Subspace Identification of Nonlinear Multi-view CCA](https://mlsanity.com/paper/2602.23785/) (2026)
- [FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data](https://mlsanity.com/paper/2608.10857/) (2026)
- [Foundations of Independent Component Analysis](https://mlsanity.com/paper/2608.13229/) (2026)

## Abstract (arXiv)

Independent component analysis (ICA) is a blind source separation method for linear disentanglement of independent latent sources from observed data. We investigate the special setting of noisy linear ICA where the observations are split among different views, each receiving a mixture of shared and individual sources. We prove that the corresponding linear structure is identifiable, and the source distribution can be recovered. To computationally estimate the sources, we optimize a constrained form of the joint log-likelihood of the observed data among all views. We also show empirically that our objective recovers the sources also in the case when the measurements are corrupted by noise. Furthermore, we propose a model selection procedure for recovering the number of shared sources which we verify empirically. Finally, we apply the proposed model in a challenging real-life application, where the estimated shared sources from two large transcriptome datasets (observed data) provided by two different labs (two different views) lead to recovering (shared) sources utilized for finding a plausible representation of the underlying graph structure.