# Is there a way to determine the important features (weight) for an SVM that uses an RBF kernel?

Using sklearn, I did both a linear kernel SVM and a rbf one. While the rbf gave really great results, I can't determine the important features that the algorithm kept (or used more).

I know that "coef_" does only work for a linear kernel, since for rbf the data space is no longer finite (or at least, it changes [I think]).

Is there a way to actually determine the important features for an RBF kernel SVM ?

Thanks,

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In fact, SVMs with the RBF kernel behave more like soft nearest neighbours. To see this, denote by $\{x_i,y_i\}_{i=1}^N$ the training data, and $K(.,.)$ the kernel of choice: in this case $K(x,x')=\exp(-\gamma\|x-x'\|^2)$. Then the SVM prediction for an example $x$ takes the form $$\mathrm{sign}\left( \sum_{i=1}^N \alpha_i y_i K(x_i, x) + \rho \right),$$ where $\rho$ is the intercept_ and $\alpha_i$ are the dual_coef_ in sklearn (see here). As you can see, the decision function is just a linear combination of training labels $y_i$, where the influence of each training example $x_i$ is determined by its overall importance $\alpha_i$ and its distance from $x$, as given by $K$. Closer points have an exponentially larger effect on the prediction, hence the nearest neighbour analogy.