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Linear Discriminant Analysis (LDA) vs PCA — the difference.

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Answer

  • PCA is unsupervised — max variance.
  • LDA is supervised — projects to maximize class separability: max Tr(SB)  /  Tr(SW)\mathrm{Tr}(S_{B})\; / \;\mathrm{Tr}(S_{W}), where SB  =  betweenclassS_{B}\; = \;\mathrm{between} - \mathrm{class} scatter, SW  =  withinclassS_{W}\; = \;\mathrm{within} - \mathrm{class} scatter.
  • Yields at most (k-1) components for k classes.
  • Uses: dimensionality reduction as preprocessing for classifiers, face recognition (Fisherfaces).
  • Assumes normally distributed classes with equal covariance.
Check yourself — multiple choice
  • Same as PCA
  • PCA unsupervised max variance; LDA supervised max Tr(SB)/Tr(SW)\mathrm{Tr}(S_{B}) / \mathrm{Tr}(S_{W}) with ≤ k-1 components; assumes equal-cov Gaussians
  • Random
  • Only for regression

LDA: supervised max between/within scatter; ≤ k-1 components; equal-cov Gaussian.

#dimensionality-reduction

Practise Unsupervised Learning

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