Projection Axis Angle θ
35.0°
Projected Variance Var(u)
82.4%
4.25
Reconstruction Error (MSE)
17.6%
0.91
Total Sample Variance
Constant
5.16
Var(u) + MSE = Constant (Pythagoras!)
Variance Profile vs Angle θ
Key Intuition: Drag the angle slider. As the projection axis rotates, notice how maximising
projected variance strictly minimises the sum of squared orthogonal error lines!