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This is a purely hypothetical question and doesn't relate to any specific application.

Suppose you have two separate linear boundaries that can divide a bunch of data points into either categories A and B, or categories C and D. Is there a standard way of measuring their degree of "similarity" such as looking at the angle between them, computing the dot product etc.

I am wondering if such a metric exists for non-linear boundaries as well. Assuming of course that the classifiers are of the same type (e.g. both SVM).

Thank you!

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  • $\begingroup$ One way to compare them would be by their respective error rates on a reference test set. $\endgroup$ – Vladislavs Dovgalecs Jan 4 '18 at 21:57
  • $\begingroup$ Thanks for this. But I was hoping for something more direct. $\endgroup$ – user2855666 Jan 4 '18 at 23:13
  • $\begingroup$ It sounds like you're interested in similarity from a geometric perspective, but what would it mean to "also take accuracy into account"? Why not measure these two things separately? Could you say more about what you're actually trying to do here? $\endgroup$ – user20160 Jan 5 '18 at 0:35
  • $\begingroup$ On further thought there's no reason why I wouldn't compute accuracy separately. It's really just hypothetical: Let's suppose that machine 1 separates the data points into category A and B. And I'm assuming that machine 2 is using the categories A and B to classify the data points into C and D. I'm trying to infer whether that's the case by comparing the degree to which the linear boundaries of machine 1 and 2 overlap. $\endgroup$ – user2855666 Jan 5 '18 at 1:59
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    $\begingroup$ You can take the learned alphas and compute a cosine between the two vectors. Normalize the vectors before. I don't see how you will interpret/use the resulting similarity. $\endgroup$ – Vladislavs Dovgalecs Jan 5 '18 at 3:17

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