# How to transform this dataset to make classes linearly separable?

I have this data set:

And I want to transform the data (with a RBF kernel?) in order to be able to do a simple linear ridge-classifier.

I know I can do more or less the same thing using a kernel SVM with a RBF kernel but I have to use the ridge classifier.

Does anyone know how it (if?) can be done? This is kinda homeworkish so I don't want a full solution I just want some input.

• Transforming the data with an RBF kernel would result in a dataset that is infinite-dimensional! That is why people invented kernel trick that allows to implement algorithms like SVM or PCA as if they work on the transformed dataset. But one never actually transforms the data. Is this maybe the kind of answer you were looking for? – amoeba Dec 3 '14 at 1:19

## 1 Answer

Have you tried putting the data into $r,\theta$? You could pick the origin as as the mean value of all of the data. You'd end up with two, slightly overlapping ellipsoidal blobs.

• That prooved to be an interesting idea but the interleaving zone is still quite problematic (in fact it gives worst results than just applying the ridge classifier directly on the dataset without any modification). – AdrienNK Oct 18 '13 at 18:17
• @AdrienNK: This is weird. Your dataset looks like it will become a lot more linearly separable after the transformation suggested by Dave (+1). If you are still interested in this question, you could make an update showing the scatter plot after Dave's transformation. – amoeba Dec 3 '14 at 1:15
• Maybe if the mean is not where we'd think it to be from the scatter plot, the $r,\theta$ decomposition doesn't work well. – Dave Dec 3 '14 at 2:44