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.
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.