Equation 2 · Embeddings and the Geometry of Similarity
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subscript
subscript
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Beyer and colleagues proved the canonical result. Under broad conditions on the data and query distributions — much broader than independence and identical distribution across dimensions — as dimensionality rises the distance to the nearest data point approaches the distance to the farthest. Formally, writing for the distance function in m dimensions, for a data point and for a query point:
Sources cited in the article section
- [11] When Is "Nearest Neighbor" Meaningful? ↗
- [12] On the Surprising Behavior of Distance Metrics in High Dimensional Space ↗
- [13] Hubs in Space: Popular Nearest Neighbors in High-Dimensional Data ↗
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