Unpaired CCA finds shared patterns without matching data pairs
Unpaired Canonical Correlation Analysis
Machine Learning
Summary
Canonical Correlation Analysis (CCA) is a way to find common signals between two sets of data, but it normally requires the data to be paired up. The authors introduce Unpaired CCA (UCCA), a method that can find these shared relationships even when no pairs are given during training. They connect this problem to a well-known mathematical challenge and develop a practical approach to solve it. Their tests show UCCA works better than other methods for finding true correlations without paired samples.
What this means in practice
- •For machine learning engineers: Align datasets from different sources without requiring paired samples for training projections that maximize shared correlations.
- •For data integration teams: Combine unpaired multimodal data to uncover underlying relationships for improved joint analyses.
Authors
Nir Ben-Ari, Ronen Talmon, Uri Shaham
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.