Click or drag to place points. The singular value spectrum and effective dimensionality react instantly as you draw.
feature space
NOISE LEVEL medium
PRESETS
0
Points
—
σ₁
—
σ₂
SINGULAR VALUE SPECTRUM
draw some points
VARIANCE EXPLAINED
—
Draw points to see the spectrum.
EFFECTIVE DIMENSIONALITY
—
out of max 2
(Σ λᵢ)²Σ λᵢ²
= —
Draw at least 4 points.
Step 02
3D intuition: same features, different dimensionality
Six clouds in ℝ³ — same number of features, very different effective dimensionalities. Drag to rotate, scroll to zoom.
Key insight: all six clouds live in ℝ³ — same number of features, same number of columns in the data matrix. Effective dimensionality ranges from 1 to 3 depending entirely on how variance is distributed. A flat eigenspectrum → high ED. A spiky one → low ED.