# Shared Independent Component Analysis for Multi-Subject Neuroimaging

arXiv: https://arxiv.org/abs/2110.13502 · HTML: https://mlsanity.com/paper/2110.13502/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 65 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 8 of 8)

- [Machine Learning for Neuroimaging with Scikit-Learn](https://mlsanity.com/paper/1412.3919/) (2014)
- [Faster independent component analysis by preconditioning with Hessian approximations](https://mlsanity.com/paper/1706.08171/) (2017)
- [Group Factor Analysis](https://mlsanity.com/paper/1411.5799/) (2014)
- [Modeling Shared Responses in Neuroimaging Studies through MultiView ICA](https://mlsanity.com/paper/2006.06635/) (2020)
- [Independent Vector Analysis: Identification Conditions and Performance Bounds](https://mlsanity.com/paper/1303.7474/) (2013)
- [mvlearn: Multiview Machine Learning in Python](https://mlsanity.com/paper/2005.11890/) (2020)
- [A Convolutional Autoencoder for Multi-Subject fMRI Data Aggregation](https://mlsanity.com/paper/1608.04846/) (2016)
- [Beyond Pham's algorithm for joint diagonalization](https://mlsanity.com/paper/1811.11433/) (2018)

## Built on by (most cited first, 6 of 6)

- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Multi-View Independent Component Analysis with Shared and Individual Sources](https://mlsanity.com/paper/2210.02083/) (2022)
- [Latent Processes Identification From Multi-View Time Series](https://mlsanity.com/paper/2305.08164/) (2023)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Diff-CA: Separating Common and Salient Factors with Diffusion Models](https://mlsanity.com/paper/2606.06120/) (2026)
- [Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms](https://mlsanity.com/paper/2502.20115/) (2025)

## Abstract (arXiv)

We consider shared response modeling, a multi-view learning problem where one wants to identify common components from multiple datasets or views. We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear transform of shared independent components contaminated by additive Gaussian noise. We show that this model is identifiable if the components are either non-Gaussian or have enough diversity in noise variances. We then show that in some cases multi-set canonical correlation analysis can recover the correct unmixing matrices, but that even a small amount of sampling noise makes Multiset CCA fail. To solve this problem, we propose to use joint diagonalization after Multiset CCA, leading to a new approach called ShICA-J. We show via simulations that ShICA-J leads to improved results while being very fast to fit. While ShICA-J is based on second-order statistics, we further propose to leverage non-Gaussianity of the components using a maximum-likelihood method, ShICA-ML, that is both more accurate and more costly. Further, ShICA comes with a principled method for shared components estimation. Finally, we provide empirical evidence on fMRI and MEG datasets that ShICA yields more accurate estimation of the components than alternatives.