lda() — Linear Discriminant Analysis

Separates classes with a straight line from their means.

lda(X, y)

Key idea

• LDA assumes both categories are bell-shaped with the SAME spread (covariance), differing only in their centres.
• Under that assumption the best dividing line is a straight line. (e.g. midway between the two group centres)
• It needs no tuning and is fast — a strong, simple starting classifier.
• Allowing different spreads gives the curved boundary of QDA.

Definition

$$\delta (x)=[{\Sigma }^{-1}({\mu }_1-{\mu }_0){]}^{\top }x>c$$

${\mu }_0,{\mu }_1$

the two class means

$\Sigma$

the shared covariance of both classes

$c$

the threshold (midpoint)

$\delta (x)$

the discriminant score

In plain words

Find the centre of each group, then draw the straight line that best keeps them apart.

Where you'd use it

• Classic face and pattern recognition where classes form tidy clusters.
• Bankruptcy / credit-default prediction from a few financial ratios.
• Reducing dimensions while keeping classes as separable as possible.

Frequently asked questions

What does LDA assume?

Each class is normal with the same covariance; if spreads differ, consider QDA.