Orthogonal Procrustes problem preserves correlations in synthetic data

• URL: http://arxiv.org/abs/2510.02405v1
• Date: Thu, 02 Oct 2025 03:14:57 GMT
• Title: Orthogonal Procrustes problem preserves correlations in synthetic data
• Authors: Oussama Ounissi, Nicklas Jävergård, Adrian Muntean,
• Abstract summary: The proposed methodology ensures that the resulting synthetic data preserves important statistical relationships among features, specifically the Pearson correlation.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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