Accelerating Parametric Nonlinear Dimension Reduction via Representative Selection

Abstract

High-dimensional data continues to pose fundamental challenges across scientific and engineering disciplines, including computational complexity, the curse of dimensionality, and the difficulty of extracting meaningful representations. A prior thesis proposed a two-phase dimensionality reduction framework in which clustering-based representative selection was followed by standard UMAP training, demonstrating significant gains in computational efficiency while preserving embedding quality. We extend that foundational work to parametric non-linear dimensionality reduction methods. Specifically, we investigate parametric UMAP and autoencoders as the second phase of the pipeline. Parametric approaches offer several advantages over their non-parametric counterparts: they learn an explicit mapping function that can be applied to unseen data without retraining, they integrate naturally with deep learning workflows, and they enable end-to-end optimization with task-specific objectives. We evaluate the proposed two phases parametric dimension reduction framework on high-dimensional benchmark datasets, comparing it against the original parametric methods in terms of embedding quality, computational efficiency, generalization to new data, and downstream classification performance. The results demonstrate that combining representative selection with parametric embedding models yields a scalable, transferable, and efficient dimensionality reduction pipeline suitable for real-world, large-scale applications.