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Danica
Danica
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I am attempting to use SVMs for my class project. For this project, I have selected the gaussian kernel as, well, the kernel. That is,

$$ k(\mathbf{x}_1, \mathbf{x}_n) = e^{-\gamma ||\mathbf{x}_1 - \mathbf{x}_n ||^2} $$

What I do not understand, is how this kernel is then 'written as a dot-product'. How do we get around doing that? This is because my professor says that when we finalize the training, we will be performing a dot-product between a new vector and the SVs. But given this kernel, how is this dot-product being done?

I am attempting to use SVMs for my class project. For this project, I have selected the gaussian kernel as, well, the kernel. That is,

$$ k(\mathbf{x}_1, \mathbf{x}_n) = e^{-\gamma ||\mathbf{x}_1 - \mathbf{x}_n ||^2} $$

What I do not understand, is how this kernel is then 'written as a dot-product'. How do we get around doing that? This is because my professor says that when we finalize the training, we will be performing a dot-product between a new vector and the SVs. But given this kernel, how is this dot-product being done?

I am attempting to use SVMs for my class project. For this project, I have selected the gaussian kernel as, well, the kernel. That is,

$$ k(\mathbf{x}_1, \mathbf{x}_n) = e^{-\gamma ||\mathbf{x}_1 - \mathbf{x}_n ||^2} $$

What I do not understand, is how this kernel is then 'written as a dot-product'. How do we get around doing that? This is because my professor says that when we finalize the training, we will be performing a dot-product between a new vector and the SVs. But given this kernel, how is this dot-product being done?

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Spacey
Spacey
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Using a gaussian kernel in SVM. How exactly is this then written as a dot product?

I am attempting to use SVMs for my class project. For this project, I have selected the gaussian kernel as, well, the kernel. That is,

$$ k(\mathbf{x}_1, \mathbf{x}_n) = e^{-\gamma ||\mathbf{x}_1 - \mathbf{x}_n ||^2} $$

What I do not understand, is how this kernel is then 'written as a dot-product'. How do we get around doing that? This is because my professor says that when we finalize the training, we will be performing a dot-product between a new vector and the SVs. But given this kernel, how is this dot-product being done?