Symmetry-Preserving Optimization of Differentially Private Machine Learning Based on Feature Importance

Symmetry plays a critical role in preserving the structural balance and statistical integrity of datasets, particularly in privacy-preserving machine learning. Differential privacy introduces random noise to individual data points to ensure privacy while maintaining the overall symmetry of statistical distributions. However, excessive noise can reduce the utility of data, model accuracy, and computational efficiency. This study proposes a symmetry-preserving optimization framework for differentially private machine learning by integrating feature importance and t-SNE (t-distributed Stochastic Neighbor Embedding), UMAP (Uniform Manifold Approximation and Projection), and PCA (Principal Component Analysis), respectively. Feature importance derived from a random forest selects high-value features to improve data relevance. At the same time, t-SNE preserves geometric symmetry by retaining local and global structures more effectively than PCA or UMAP. Therefore, t-SNE is the best feature extraction method for dimensionality reduction in the proposed scheme. Experimental results demonstrate that the t-SNE method significantly enhances model performance under differential privacy, showing improved accuracy and reduced computational time compared to PCA and UMAP while preserving the underlying symmetry of the data distributions.