How is LDA used for supervised dimensionality reduction?

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Answer

$Beyond classification, LDA finds up to K-1 linear directions (K = number of classes) that maximize between-class variance while minimizing within-class variance.$
$Project the data onto these axes and you get a low-dimensional embedding that keeps class separation.$
$Unlike PCA (unsupervised, maximizes total variance), LDA uses the labels — so it's the go-to supervised dim-reduction for classification, e.g., visualizing a K-class problem in K-1 dimensions.$

Check yourself — multiple choice

LDA projects onto directions that maximize total variance
It finds up to K-1 axes maximizing between-class over within-class variance — supervised dim reduction
LDA is the same as t-SNE
LDA gives K directions for K classes

LDA = supervised dim reduction onto up to K-1 discriminant axes (labels-aware).

#lda-qda#discriminant-analysis#features

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