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Overcoming the Limits of Dimensionality Reduction. Making t-SNE Smarter: Adjusting Affinity Matrix for Better Insights

Shirin Mohebi

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.

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Overcoming the Limits of Dimensionality Reduction Making t-SNE Smarter: Adjusting Affinity Matrix for Better Insights Why This Matters • Dimensionality reduction is key for exploring high-dimensional data. • t-SNE is widely used for visualization. The Challenge • projections cannot preserve all local & global relationships. • t-SNE introduces artefacts: some clusters and gaps are not real. Key Idea • 2D embeddings cannot preserve all pairwise relationships from high-dimensional space. • Limited 2D capacity forces trade-offs between local and global structure. •Can we improve t-SNE by adjusting its Affinity Matrix? •Our Approach • Decompose Affinity Matrix: • 𝑨𝐝𝐢𝐬𝐦𝐢𝐬𝐬𝐞𝐝 : neighbors that cannot be accurately preserved. • 𝑨𝐜𝐚𝐩𝐭𝐮𝐫𝐞𝐝 : neighbors that preserved accurately. • Focus on maintaining the most important relationships (captured neighbors) Shirin Mohebi Supervisors: Jefrey Lijffijt, Tijl De Bie Introduction Intuition Approach Experiment Next Steps “Schematic Overview of the t-SNE Algorithm.” Laura Twomey, Biostatsquid. 𝑨 = 𝑨𝒄+𝑨𝒅 •Analyze how t-SNE decides what to preserve. •Explore and propose new Affinity Matrix formulations. •Develop metrics that capture what t-SNE actually preserves and sacrifices. •Test robustness across diverse datasets. •Aim for clearer and more reliable embeddings. Contact [email protected] Rank improvements are mainly seen for close neighbors, while losses mostly involve already distant ones. This shows the modification sharpens local structure rather than recovers far relationships.