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Leockl
Leockl

Reputation: 2156

Will SVMs always succeed in finding a linear decision boundary?

SVMs works by mapping points to a higher and higher dimension until it can find a boundary which is linear.

Does SVM always succeed in finding a decision boundary which is linear?

Upvotes: 0

Views: 106

Answers (1)

hychou
hychou

Reputation: 632

First, SVM do not map points to a higher and higher dimension. If linear kernel is used, points are not mapped; for some other kernel, e.g. RBF kernel, they are mapped to an infinite dimensional space.

To your question, I suppose you mean whether SVM with RBF kernel can find a separating hyperplane in the mapped space. It is proven here that with a small enough σ^2 and large enough C, it can always find a separating hyperplane, i.e., the training accuracy is 100%.

Upvotes: 2

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