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What is VC dimension in SVM?
h is the Vapnik Chervonenkis (VC) dimension and is a measure of the capacity or complexity of the machine. Note the bound is independent of P(x,y)!!! For example, the VC dimension of a set of oriented lines in R2 is three. In general, the VC dimension of a set of oriented hyperplanes in Rn is n+1.
What is the VC dimension for an n dimensional linear classifier?
For a configuration of N points, there are 2^N possible assignments of positive or negative, so the classifier must be able to properly separate the points in each of these. In the below example, we show that the VC dimension for a linear classifier is at least 3, since it can shatter this configuration of 3 points.
What is the exact definition of VC dimension?
If of all arrangements of 3 points you can find at least one such arrangement that can be shattered by the classifier, and cannot find 4 points that can be shattered, then VC dimension is 3. The points should fulfil points in general condition before consider for VC dimension.
Why is the VC dimension of H 3?
And that’s why the VC dimension of H is 3. Because for any 4 points in 2D plane, a linear classifier can not shatter all the combinations of the points. For example, For this set of points, there is no separating hyper plane can be drawn to classify this set. So the VC dimension is 3.
Thus, the sample-complexity is a linear function of the VC dimension of the hypothesis space. The VC dimension is one of the critical parameters in the size of ε-nets, which determines the complexity of approximation algorithms based on them; range sets without finite VC dimension may not have finite ε-nets at all. 0.
How to calculate the VC dimension in machine learning?
VC-Dimension 2: It can classify all four situations correctly. class (0) = True, class (42) = True => a = − 1, b = 1337 classifies this correctly. VC-Dimension 3: No, that doesn’t work.