I was reading thispaper related to kernel SVM. It states
Support Vector Machine (SVM) (Cortes and Vap- nik, 1995) as the state-of-the-art classification algo- rithm has been widely applied in various scientific do- mains. The use of kernels allows the input samples to be mapped to a Reproducing Kernel Hilbert S- pace (RKHS), which is crucial to solving linearly non- separable problems. While kernel SVMs deliver the state-of-the-art results, the need to manipulate the k- ernel matrix imposes significant computational bottle- neck, making it difficult to scale up on large data.
I didn't get what they mean by manipulate the kernel matrix. I mean lets say I am using the RBF kernel. Then my kernel matrix will have elements of the form
which I can calculate once and then have it there. So what is meant by kernel manipulation