Random projection — how does it work?

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Answer

$m\; = \;O(\operatorname{log}\;n\; / \;{\varepsilon}^{2})$
$Extremely cheap (no data-dependent fit).$
$Uses: dimensionality reduction for huge sparse data, approximate nearest neighbors (LSH), streaming.$
$Less informative than PCA but scales linearly.$

Check yourself — multiple choice

Random
Johnson-Lindenstrauss: random Gaussian R with $m\; = \;O(\operatorname{log}\;n\; / \;{\varepsilon}^{2})$ preserves pairwise distances (1±ε); cheap; foundation of LSH / streaming DR
Same as PCA
Not real

Random projection: JL lemma; $O(\operatorname{log}\;n\; / \;{\varepsilon}^{2})$ dims; cheap streaming DR.

#dimensionality-reduction

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