OPTIMIZING DIMENSIONALITY REDUCTIONAND VISUALIZATION THROUGH ENHANCED CLUSTERING AND OPTIMAL TRANSPORTATION

Abstract

Dimensionality reduction (DR) is essential for analyzing and visualizing high-dimensional data by producing low-dimensional representations that preserve meaningful structure. Among non-linear DR methods, t-distributed Stochastic Neighbor Embedding (t-SNE) is widely used for its strong local structure preservation and clear visual clustering. However, t-SNE suffers from sensitivity to initialization, high computational cost, and reliance on the Kullback–Leibler (KL) divergence, which emphasizes local neighborhoods while neglecting global structure and ranking relationships. This work introduces a unified set of improvements that enhance t-SNE’s initialization, similarity modeling, and loss formulation. We first propose Centroid t-SNE (ct-SNE), which initializes embeddings using cluster centroids to improve stability, convergence, and visual clarity. Weighted Centroid t-SNE (wct-SNE) further accounts for cluster size imbalance, yielding more representative and balanced embeddings. To move beyond pairwise similarities, we introduce Triplet t-SNE (Tt-SNE), which models three-way relationships to capture richer structural information that pairwise methods may miss. To address the locality bias of KL divergence, we propose two enhanced losses: the KL–Wasserstein loss, which integrates optimal transport to preserve both local and global geometry, and the Max-Deviation KL loss, which incorporates ranking-based deviations to better reveal hierarchical and manifold structures. To reduce the computational cost of Wasserstein distances, we further introduce the Hybrid Merging Wasserstein (HW) measure, combining semantically guided projections derived from a novel Linear Merging Projection (LMP) with randomized directions. This hybrid strategy achieves improved structural preservation while remaining computationally efficient. Extensive experiments show that the proposed methods outperform existing DR techniques in clustering quality, robustness, and visualization fidelity. Together, these contributions form a scalable and interpretable framework for dimensionality reduction that balances local and global structure while remaining practical for large-scale, high-dimensional data.

Date of Award	2026
Original language	American English
Awarding Institution	HBKU College of Science and Engineering