# Unpaired Canonical Correlation Analysis

arXiv: https://arxiv.org/abs/2610.09530 · HTML: https://mlsanity.com/paper/2610.09530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 78 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 11 of 11)

- [CSA: Data-efficient Mapping of Unimodal Features to Multimodal Features](https://mlsanity.com/paper/2410.07610/) (2024)
- [Toward Unpaired Multi-modal Medical Image Segmentation via Learning Structured Semantic Consistency](https://mlsanity.com/paper/2206.10571/) (2022)
- [Weakly Supervised Vision-and-Language Pre-training with Relative Representations](https://mlsanity.com/paper/2305.15483/) (2023)
- [mini-vec2vec: Scaling Universal Geometry Alignment with Linear Transformations](https://mlsanity.com/paper/2510.02348/) (2025)
- [Better Together: Leveraging Unpaired Multimodal Data for Stronger Unimodal Models](https://mlsanity.com/paper/2510.08492/) (2025)
- [SOTAlign: Semi-Supervised Alignment of Unimodal Vision and Language Models via Optimal Transport](https://mlsanity.com/paper/2602.23353/) (2026)
- [ContourDiff: Unpaired Medical Image Translation with Structural Consistency](https://mlsanity.com/paper/2403.10786/) (2024)
- [Towards Aligned Canonical Correlation Analysis: Preliminary Formulation and Proof-of-Concept Results](https://mlsanity.com/paper/2312.00296/) (2023)
- [Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data](https://mlsanity.com/paper/2502.18756/) (2025)
- [Unpaired Image-to-Image Translation for Segmentation and Signal Unmixing](https://mlsanity.com/paper/2505.20746/) (2025)
- [Continual Learning-Based Unified Model for Unpaired Image Restoration Tasks](https://mlsanity.com/paper/2507.19184/) (2025)

## Abstract (arXiv)

Canonical Correlation Analysis (CCA) is a fundamental method for multiview shared space learning. However, its strict reliance on paired data poses a significant limitation, as such data is often difficult to obtain or entirely unavailable. In this paper, we present Unpaired CCA (UCCA), a novel method that learns linear projections to maximize the correlation of the true underlying pairing without access to any paired samples during training. We first establish theoretical results connecting the Quadratic Assignment Problem (QAP) to CCA. Leveraging these theoretical insights, we derive a practical method to maximize correlation exclusively from unpaired data. To the best of our knowledge, UCCA is the first approach to learn maximally correlated projections in a strictly unpaired setting. We validate UCCA on real-world multi-modal datasets, demonstrating that it significantly outperforms recent unpaired alignment baselines in recovering the underlying true correlation. This work fills a critical gap between traditional statistical multiview learning and the growing field of unpaired data learning.