Unpaired Canonical Correlation Analysis
stat.ML, cs.LG
Submitted: 2026-10-07
Updated: 2026-10-07
Comments: Accepted to NeurIPS 2026
Code: https://github.com/shaham-lab/UCCA
Project page: https://shaham-lab.github.io/UCCA_page
License: http://creativecommons.org/licenses/by/4.0/
The gist: Canonical Correlation Analysis (CCA) is a fundamental method for multiview shared space learning.
Terminology
Abstract
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.
Sources
- Unpaired Image-to-Image Translation for Segmentation and Signal Unmixing
- Weakly Supervised Vision-and-Language Pre-training with Relative Representations
- ContourDiff: Unpaired Medical Image Translation with Structural Consistency
- Towards Aligned Canonical Correlation Analysis: Preliminary Formulation and Proof-of-Concept Results
- mini-vec2vec: Scaling Universal Geometry Alignment with Linear Transformations
- Better Together: Leveraging Unpaired Multimodal Data for Stronger Unimodal Models
- Continual Learning-Based Unified Model for Unpaired Image Restoration Tasks
- CSA: Data-efficient Mapping of Unimodal Features to Multimodal Features
- SOTAlign: Semi-Supervised Alignment of Unimodal Vision and Language Models via Optimal Transport
- Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data
- Toward Unpaired Multi-modal Medical Image Segmentation via Learning Structured Semantic Consistency
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