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In SVM using kernels we map the original features to the higher, transformer space (feature mapping) and then perform linear SVM in this higher space. But when kernels are not useful? I could not find any limitations of it. Any help would be appreciated. Thanks in advance.

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The key idea behind using kernels is to map the data into a higher dimensions such that it becomes more linearly separable. If the data is already linearly separable, most real world data isn't but, at least close to it, you don't need to resort to transformations. So, it's a matter of necessity. This is similar with using polynomial features in linear regression when necessary or not using when it's not necessary.

I'd also like to point out that evaluating your data's separability is easy in two or three dimensional data because we can easily plot it, however it's not a straightforward task in general. You should obtain statistically significant improvements to conclude that your applied kernel is better than the linear kernel.

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  • $\begingroup$ Suppose for a given dataset, data points have dimension >= 4. So it's not possible to check linear separability. So how to know whether to apply kernels or not? $\endgroup$ – Satish May 7 at 11:01
  • $\begingroup$ I wouldn't say that it's not possible just because we can't visualize. Because if it's possible, you can fit your data with linear SVM and see if it's separable or not. If you get no errors, it's separable. But many datasets are not perfectly separable even if you apply kernels. They just become more separable, and evaluating the degree of separability is not straightforward as I've tried to point out in my second paragraph. If you're getting statistically significantly better results with let's say RBF kernel vs linear kernel, then it means you've succeeded to separate your data better. $\endgroup$ – gunes May 7 at 11:05
  • $\begingroup$ Thanks for your help. $\endgroup$ – Satish May 16 at 20:58
  • $\begingroup$ @Satish if you think it answers your question, can you please accept and/or upvote it? $\endgroup$ – gunes May 17 at 4:32

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