On the Surprising Behavior of Distance Metrics in High Dimensional Space.¶
Aggarwal, C. C., Hinneburg, A., & Keim, D. A. (2001). On the Surprising Behavior of Distance Metrics in High Dimensional Space. Proceedings of the 8th International Conference on Database Theory (ICDT '01).
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Primes¶
- Curse Of Dimensionality
- The qualitative-threshold property is visible: at \(d = 2\) or $3$ nearest-neighbour search works fluently, by \(d = 20\) it has degraded, and by \(d = 1000\) raw-distance retrieval is meaningless — a regime change, not a gradual decline.
This sourceDemonstrates the qualitative breakdown of distance discrimination as dimension rises across norms.
- The qualitative-threshold property is visible: at \(d = 2\) or $3$ nearest-neighbour search works fluently, by \(d = 20\) it has degraded, and by \(d = 1000\) raw-distance retrieval is meaningless — a regime change, not a gradual decline.
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