# Behavior of a sum of kernel functions

Suppose we have 2 kernel functions $K_1(x,y)$ and $K_2(x,y)$. We know, that the dataset ($(x_1,y_1),\ldots,(x_l,y_l),$ $y_i \in \{-1,1\}$ ) is separated with the first one (that is, there are $w,$ $w_0$: $$y_i(K_1(w,x_i)-w_0)>0$$ for all $i=1,\ldots,l$ ), and not separated with the second kernel function. What we can say about kernel function $K_1(x,y)+K_2(x,y)$ ? How I can show that the same dataset is separated with it?

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possible duplicate of Machine Learning: Linear classifier and possibility to separate – onestop Apr 14 '12 at 22:00
Max, your question was already migrated at the time you posted this one. You should better register your account here, and I will close the other one (that apparently is no longer yours). – chl Apr 15 '12 at 8:30
Migrating @D.W. comment from the duplicate: Why do you believe the same dataset will be separated with $K_1(x,y)+K_2(x,y)$? Is this homework? – mbq Apr 15 '12 at 9:23
I can't say that I believe, but I suspect it's true. Because I've tried some examples (but with linear kernel). Do you have any ideas? It's not a homework, I try to learn SVM by myself. – Max Apr 15 '12 at 10:23