K-Nearest-Rank Scores: A Tool for Local Structure Analysis in Embeddings

When using a low-dimensional projection, we should always be aware that it is merely a projection of a higher and more complex dimensional space. To truly trust these projections, we need to assess how well they preserve the original sample distribution.

Photo by Saint Rambo on Unsplash

Dimensionality reduction techniques such as PCA, t-SNE, and UMAP are widely used for both feature reduction and visualizing data in lower-dimensional spaces. Being able to visually explore how samples are distributed can reveal key insights that might otherwise remain hidden. However, before relying on these projections, it’s important to ask a few critical questions: 1. How well does the reduced-dimensional space represent the original high-dimensional structure? 2. How consistent are the embeddings generated by PCA, t-SNE, and UMAP with each other? In this blog, I’ll demonstrate how to quantify the similarity between different projections using the K-Nearest-Rank Similarity score (KNR-score).

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