BIZNIQUE / LINEAR ALGEBRA / 33
Use kernel similarity beyond SVMs
Use kernel similarity beyond SVMs
Watch the width of a radial similarity change which neighbours matter.
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THE IDEA
Read the example.
Read the example.
The radial basis function kernel gives a similarity that falls with squared distance. A larger length scale ℓ makes the similarity decay more slowly. Related kernel ideas appear in regression, smoothing and Gaussian-process models.
k(x,z) = exp(−‖x−z‖² / (2ℓ²))
Use it well
Use it well
A kernel value is a similarity, not automatically a probability or a causal relationship. Scaling and the choice of length scale shape the comparison.
TRY IT YOURSELF
A quick check.
A quick check.
What is k(x,x) for any positive length scale?
Check your reasoning
Check your reasoning
The distance is zero, so k(x,x) = exp(0) = 1.
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