Optimized Nonlinear Random Projection for High-Dimensional Data Representation

We introduce a novel Nonlinear Hybrid Random Projection (NHRP) method for dimensionality reduction in high-dimensional (HD) data analysis. HD data, characterized by the curse of dimensionality, poses substantial challenges for traditional machine learning algorithms. NHRP integrates Normal Random Projection (RP) and Plus-Minus One RP through nonlinear transformations, to capture complex data structures while maintaining computational efficiency. NHRP inherits JL-type distance-preservation bounds from its constituent RP matrices under mild smoothness conditions. Simulation study demonstrates that NHRP achieves superior performance in preserving pairwise distances and data structure integrity compared to existing random projection methods. Real-world dataset application shows significant improvements in both computational efficiency and representational accuracy, making NHRP a promising approach for various domains.