Kernel Composition Rules $2$

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Sana IIT Madras $|$ M$...$

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$\frac{0}{1}$ point $($graded$)$

Let $x$ and $x^{\text{'}}$ be two vectors of the same dimension. Use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. $($Note that you can use feature vectors $(x)$ that are not polynomial.$)$

$($Choose all those apply. $)$

$1$

$x*x^{\text{'}}$

$1+x*x^{\text{'}}$

$(1+x*x^{\text{'}}{)}^{2}q,$ exp$(x+x^{\text{'}}),$ for $x,x^{\text{'}}$inR

$q,$