I am attaching a book page screenshot from 'Hands on Machine Learning with Scikit Learn and TensorFlow' book where it is shown that if we reconstruct a 2D space into feature space, it will produce a infinite dimension feature space. My question is why? The original dataset is 3D. Please see the screenshot content for details.
Dear Kazi Mahmudul Hassan
When there are m different training points, the gaussian radial basis kernel causes the SVM to function in an m-dimensional space. We argue that the radial basis kernel translates to an infinite-dimensional space because you may make m as large as you like and the space it functions in grows indefinitely.
Kind Regards
Qamar Ul Islam
It is just a linear transformation or local imbedding or in other words you combine a heugh bundle of small patches that could be the components of nonlinear Hilbert space. In summary, you transform Hilbert space into Euclidean and VICE VERSA.
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