knn-null-baseline-k-over-n-minus-1

IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-2.md

Created 2026-08-24T17:10:50+00:00

Under H₀ (independence), the expected mKNN similarity is E[mKNN(X,Y)] = k/(n−1), derived from the hypergeometric distribution of two uniform random k-subsets of an (n−1)-set with expected intersection k²/(n−1)

Summary

If two data points are truly unrelated, the overlap you'd expect between their k nearest-neighbor sets is just the chance level: k squared divided by the total pool size. This baseline tells the system how much neighborhood similarity is noise, so any observed overlap above it signals genuine structure rather than coincidence.