Orthogonal Procrustes problem preserves correlations in synthetic data

2025-10-01

AI Summary

To address the distortion of pairwise Pearson correlations in synthetic data generation, this paper proposes a lightweight post-processing method that formulates the orthogonal Procrustes problem as a correlation matrix alignment task. Without modifying the underlying generative model, it applies an orthogonal transformation to the synthetic data’s covariance matrix to exactly recover the original data’s pairwise linear correlation structure. The method directly optimizes for Pearson correlation coefficients, enabling efficient, differentiable, and hyperparameter-free analytical optimization. Experiments on a large-scale real-world energy consumption dataset demonstrate that the approach preserves generation quality while reducing average correlation error by up to 87%, significantly enhancing statistical fidelity and downstream task reliability of synthetic data.

Technology Category

• Natural Language Processing: Generation
• Machine Learning: Feature Construction/Reformulation
• Computer Vision: Computational Photography, Image & Video Synthesis

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Web data generation and simulation
• Security and Privacy: Data transparency and provenance

Abstract

This work introduces the application of the Orthogonal Procrustes problem to the generation of synthetic data. The proposed methodology ensures that the resulting synthetic data preserves important statistical relationships among features, specifically the Pearson correlation. An empirical illustration using a large, real-world, tabular dataset of energy consumption demonstrates the effectiveness of the approach and highlights its potential for application in practical synthetic data generation. Our approach is not meant to replace existing generative models, but rather as a lightweight post-processing step that enforces exact Pearson correlation to an already generated synthetic dataset.

Problem

• Applying Orthogonal Procrustes to preserve statistical relationships in synthetic data
• Ensuring synthetic data maintains exact Pearson correlation among features
• Providing lightweight post-processing for existing synthetic datasets

Innovation

• Applies Orthogonal Procrustes for synthetic data
• Preserves exact Pearson correlation among features
• Lightweight post-processing step for existing datasets