# Unsupervised discovery of the shared and private geometry in multi-view data

arXiv: https://arxiv.org/abs/2408.12091 · HTML: https://mlsanity.com/paper/2408.12091/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 83 references that are in the map.
- First posted on arXiv 22 Aug 2024.

## Builds on (most cited first, 30 of 30)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Disentangling factors of variation in deep representations using adversarial training](https://mlsanity.com/paper/1611.03383/) (2016)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Joint Embedding of Words and Labels for Text Classification](https://mlsanity.com/paper/1805.04174/) (2018)
- [A Sober Look at the Unsupervised Learning of Disentangled Representations and their Evaluation](https://mlsanity.com/paper/2010.14766/) (2020)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Deep Variational Canonical Correlation Analysis](https://mlsanity.com/paper/1610.03454/) (2016)
- [Multi-View Fusion of Sensor Data for Improved Perception and Prediction in Autonomous Driving](https://mlsanity.com/paper/2008.11901/) (2020)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Population Transformer: Learning Population-level Representations of Neural Activity](https://mlsanity.com/paper/2406.03044/) (2024)
- [Visualizing the PHATE of Neural Networks](https://mlsanity.com/paper/1908.02831/) (2019)
- [Isometric Autoencoders](https://mlsanity.com/paper/2006.09289/) (2020)
- [Drop, Swap, and Generate: A Self-Supervised Approach for Generating Neural Activity](https://mlsanity.com/paper/2111.02338/) (2021)
- [Seeing the forest and the tree: Building representations of both individual and collective dynamics with transformers](https://mlsanity.com/paper/2206.06131/) (2022)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [LDLE: Low Distortion Local Eigenmaps](https://mlsanity.com/paper/2101.11055/) (2021)
- [Parallel Transport Unfolding: A Connection-based Manifold Learning Approach](https://mlsanity.com/paper/1806.09039/) (2018)
- [Multi-modal Gaussian Process Variational Autoencoders for Neural and Behavioral Data](https://mlsanity.com/paper/2310.03111/) (2023)
- [Multi-view Data Visualisation via Manifold Learning](https://mlsanity.com/paper/2101.06763/) (2021)
- [Revisiting Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2312.13455/) (2023)
- [A probabilistic framework for task-aligned intra- and inter-area neural manifold estimation](https://mlsanity.com/paper/2209.02816/) (2022)
- [Disentangled Representation Learning with the Gromov-Monge Gap](https://mlsanity.com/paper/2407.07829/) (2024)

## Built on by (most cited first, 1 of 1)

- [Coupled Transformer Autoencoder for Disentangling Multi-Region Neural Latent Dynamics](https://mlsanity.com/paper/2510.20068/) (2025)

## Abstract (arXiv)

Studying complex real-world phenomena often involves data from multiple views (e.g. sensor modalities or brain regions), each capturing different aspects of the underlying system. Within neuroscience, there is growing interest in large-scale simultaneous recordings across multiple brain regions. Understanding the relationship between views (e.g., the neural activity in each region recorded) can reveal fundamental insights into each view and the system as a whole. However, existing methods to characterize such relationships lack the expressivity required to capture nonlinear relationships, describe only shared sources of variance, or discard geometric information that is crucial to drawing insights from data. Here, we present SPLICE: a neural network-based method that infers disentangled, interpretable representations of private and shared latent variables from paired samples of high-dimensional views. Compared to competing methods, we demonstrate that SPLICE 1) disentangles shared and private representations more effectively, 2) yields more interpretable representations by preserving geometry, and 3) is more robust to incorrect a priori estimates of latent dimensionality. We propose our approach as a general-purpose method for finding succinct and interpretable descriptions of paired data sets in terms of disentangled shared and private latent variables.