Cognitive Scaffold

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MENTAL MODEL · M0304

Curse of Dimensionality

Curse of Dimensionality
TechnicalHigh supportMathematics
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

The higher the dimensionality of the data, the sparser the sample distribution in space, making distance metrics and estimates less reliable, and causing the performance of many algorithms to deteriorate sharply.

SCAFFOLDING EFFECT

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The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic optimization.

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This is the same phenomenon as the curse of dimensionality: increased dimensionality brings sparsity, distance failure, and an explosion in sample requirements.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Curse_of_dimensionalityZH · Explicit
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