Principal Component Analysis

step 01 — draw your dataset, components update in real time

Click or drag to place points. PC1 (red) points in the direction of greatest spread; PC2 (green) is perpendicular.

feature space

noise level medium

presets

0

Points

—

Corr. r

variance explained

add points to compute

PC1

PC2

Data

Add at least 10 points, or use a preset above.

step 02 — project onto fewer dimensions

Reduce from 2 components to 1. Red lines show reconstruction error — the information lost in compression.

projection

components kept 2

information

100%

Kept

0%

Lost

Original

Projected

Error

Use 2 components to keep all information.

step 03 — why standardscaler matters

Two correlated variables with different units. Drag the slider to change the scale ratio — watch PCA get misled, then fix it with standardisation.

scale ratio (X : Y) 1× (equal)

1× (equal scale) ← drag to increase ratio → 64× (huge difference)

✕ Without scaling

✓ With StandardScaler

variance — raw

variance — scaled

At equal scales, raw and scaled PCA are identical — PC1 captures the real correlation. Drag the slider right to see what happens as the scales diverge.