Overcoming the Limits of Dimensionality Reduction. Making t-SNE Smarter: Adjusting Affinity Matrix for Better Insights
Abstract
t-SNE is one of the most widely used methods for visualizing high-dimensional data, yet its limited two-dimensional capacity forces trade-offs between local and global structure. As a result, embeddings often contain artefacts such as misleading clusters or gaps. We ask whether t-SNE can be improved by adjusting its affinity matrix — the probability distribution that encodes neighborhood relations to be preserved. Our approach decomposes the affinity matrix into two parts: Acaptured, neighbors that remain close in the initial embedding, and Adismissed, neighbors that were mapped to different clusters. By down-weighting the latter, we relax some of the demands placed on t-SNE, allowing the algorithm to focus on relationships that can realistically be preserved. Preliminary experiments show that this adjustment produces locally sharper clusters, with rank analysis confirming improvements for already close neighbors while losses are confined to distant ones. Although global neighborhood preservation is not improved, our results demonstrate that the affinity matrix can be modified to steer t-SNE's focus. This opens new directions for exploring alternative formulations of the affinity matrix and for developing metrics that better capture what dimensionality reduction methods actually preserve and sacrifice.