All visualisationsClassical machine learning
How can a feature map turn a circular boundary into a flat one?
- Difficulty
- Intermediate
- Estimated time
- 5 min
A rotatable three-dimensional feature space. An explicit radial feature raises the outer class above the inner class so a horizontal threshold can separate them.
Preparing the 3D visualisation…
Explicit map: φ(x,y) = (x,y,(r/R)²)
An inner group is surrounded by an outer ring, so no straight line separates the groups.
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This exhibit draws the explicit map phi(x, y) = (x, y, (r / R)^2), with the third axis enlarged 4.2 times for legibility. A kernel can evaluate dot products from the unscaled map without drawing its coordinates. The horizontal separator is the midpoint between the nearest lifted samples in this authored radial example; the scene does not solve a general SVM.