Component Analysis
Updated 2026-08-10
INTRODUCTION
English translation pending.
CORE DEFINITION
Component analysis is the family of methods that breaks a correlated set of variables into a smaller set of uncorrelated components and keeps the ones that explain most of the variance. Principal component analysis is the standard instance: an orthogonal transform turns correlated variables into uncorrelated principal components ordered by the variance each carries, so the first few usually preserve most of the information while the rest can be discarded as noise.
SCAFFOLDING EFFECT
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- Standardize: remove scale effects before comparing the variables. - Decompose: compute the covariance matrix and its eigen-decomposition. - Keep the top: retain enough components to preserve most of the variance.
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Correlated variables carry redundant information, so their joint variance concentrates along a few directions rather than spreading evenly. Projecting the data onto those directions preserves most of the information while discarding redundancy, which is why a high-dimensional object can be represented accurately by a handful of components.
MINIMUM ACTION
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Component_analysisverified
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