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The RBF kernel is local in the feature space, so it can only work well if a nearest neighbour predictor also works fairly well. It is often worth trying Nearest Neighbour first - if its results are dreadful then I question whether I have the right feature set. But if you are going to use an SVM, it does not feel right to me to start with feature engineering ...

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The idea of using properties of a dataset to decide on classifier characteristics is called metalearning I do not know much about metalearning itself, nor any specific aspects of metalearning for SVMs and classification hardness A search on Google Scholar points to https://link.springer.com/article/10.1007/s10462-013-9406-y (open access) as a recent and well ...

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The second method is valid. It will converge because like you said, the problem is convex in terms of $\alpha$. However the two methods will not follow the same trajectory. The two methods are related via preconditioning. Section 4 of the Pegasos paper has some commentary on this. I give an explicit description of this preconditioning below. Since $G$ is ...

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$k(\cdot, \cdot)$, depending on the first term, may be any positive number, and is independent on the second term, hence kernel matrix $K$ can be any matrix having equal positive values whitin rows. Take a matrix $K$ all equal to 0 except for the first row, and make it equal to 1. Also take a vector $c$ equal to 1 in all its value except for $c_1=-1$: $c^T K ... 0 You can use the so-called ANOVA kernel construction, using tensor products and direct sums of kernels. If$k_c$is a kernel over a space$\cal X_c$and$k_d$a kernel over$\cal X_d$, then$k_{cd}\$ defined by $$k_{cd}((x_c,x_d),(x_c',x_d')) := k_{c}(x_c,x_c')k_{d}(x_d,x_d') \quad x_c,x_c'\in{\cal X}_c,x_d,x_d'\in{\cal X}_d$$ is a kernel over the product ...

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