BIZNIQUE / LINEAR ALGEBRA / 32
Make a nonlinear pattern linear in new coordinates
Make a nonlinear pattern linear in new coordinates
A feature map can reveal a separation that the original coordinates hide.
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THE IDEA
Read the example.
Read the example.
Our one-dimensional example gives outer points one class and inner points another. Lifting x to the two coordinates (x, x²) makes a horizontal separation possible. The picture illustrates a feature map, not a trained SVM.
φ(x) = (x, x²)
Use it well
Use it well
A valid positive-semidefinite kernel provides inner products in a feature space. A nonlinear-looking similarity is not automatically a valid kernel. Hyperparameters still require independent evaluation.
TRY IT YOURSELF
A quick check.
A quick check.
Why can a single threshold on x fail to separate both outer ends from the centre?
Check your reasoning
Check your reasoning
One threshold divides a line into two sides. The desired outer-versus-inner partition needs a different representation or a more flexible boundary.
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