Can Synthetic Data Preserve Manifold Properties?

Machine learning has shown remarkable performance in modeling large datasets with complex patterns. As the amount of data increases, it often leads to high-dimensional feature spaces. This data may contain confidential information that must be safeguarded against disclosure. One way to make the data accessible could be by using anonymization. An alternative is to use synthetic data that mimics the behavior of the original data. GANs represent a prominent approach for generating synthetic samples that faithfully replicate the distributional characteristics of the original data. In scenarios involving high-dimensional data, preserving the geometric properties, structural integrity, and relative positioning of data points is paramount, as neglecting such information may compromise utility. This research aims to investigate the manifold properties of synthetically generated data and introduces a novel framework for producing privacy-preserving synthetic data while upholding the manifold structure of the original data. While existing studies predominantly focus on privacy preservation within GANs, the critical aspect of preserving the manifold structure of data remains unaddressed. Our novel approach adeptly addresses both privacy concerns and manifold structure preservation, distinguishing it from prior research endeavors. Comparative assessments against baseline models are conducted using metrics such as Maximum Mean Discrepancy (MMD), Fréchet Inception Distance (FID), and F1-score. Additionally, the privacy risk posed by the models is evaluated through data reconstruction attacks. Results demonstrate that the proposed framework exhibits diminished vulnerability to privacy breaches while more effectively preserving the intrinsic structure of the data.