I've heard the expression "Gaussian kernel" in several contexts (e.g. in the kernel trick used in SVM). A Gaussian kernel usually refers to a Gaussian function (that is, a function similar to the probability density function of a Gaussian distribution) that is used to measure the similarity between two vectors (or numbers).

Why is this Gaussian function called a "kernel"? Why not just calling it a Gaussian (similarity) function? Does it have something to do with the kernel of a linear transformation?

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    $\begingroup$ I believe we use the word kernel because we are transforming the basis. $\endgroup$ – soobster Mar 17 '20 at 16:43

The usage of the word "kernel" in the context of support vector machines probably comes from its usage in the context of integral transforms.

See the article Kernel of an integral operator, and the questions What is the difference between a kernel and a function? and Why is the kernel of an integral transform called kernel?.

The word "kernel" has been used in many other contexts, such as in computer vision, to refer to a certain function with a special purpose. See e.g. the paper that introduced SIFT.


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