Answers.Body: <p>The usage of the word "kernel" in the context of support vector machines probably comes from its usage in the context of <a href="https://en.wikipedia.org/wiki/Integral_transform" rel="nofollow noreferrer">integral transforms</a>. </p>
  
  <p>See the article <a href="https://www.encyclopediaofmath.org/index.php/Kernel_of_an_integral_operator" rel="nofollow noreferrer">Kernel of an integral operator</a>, and the questions <a href="https://math.stackexchange.com/q/22133/168764">What is the difference between a kernel and a function?</a> and <a href="https://math.stackexchange.com/q/1919305/168764">Why is the kernel of an integral transform called kernel?</a>.</p>
  
  <p>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 <a href="https://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf" rel="nofollow noreferrer">SIFT</a>.</p>
  
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Answers.CreationDate: 2020-05-16T17:32:47.147Z
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Body: <p>I've heard the expression "Gaussian kernel" in several contexts (e.g. in the kernel trick used in SVM). A <a href="https://datascience.stackexchange.com/q/17352/10640">Gaussian kernel</a> usually refers to a <a href="https://en.wikipedia.org/wiki/Gaussian_function" rel="nofollow noreferrer">Gaussian function</a> (that is, a function similar to the probability density function of a <a href="https://en.wikipedia.org/wiki/Normal_distribution" rel="nofollow noreferrer">Gaussian distribution</a>) that is used to measure the similarity between two vectors (or numbers). </p>
  
  <p>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 <a href="https://en.wikipedia.org/wiki/Kernel_(algebra)" rel="nofollow noreferrer">kernel of a linear transformation</a>?</p>
  
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Comments.Text: I believe we use the word kernel because we are transforming the basis.
Comments.UserDisplayName: underdisplayname
Tags: <machine-learning><terminology><math><history><support-vector-machine>
Title: Why do we use the word "kernel" in the expression "Gaussian kernel"?
UserDisplayName: nbro
ThreadText: # Why do we use the word "kernel" in the expression "Gaussian kernel"?
  
  (Asked by: username_0 on 2019-05-04)
  
  I've heard the expression "Gaussian kernel" in several contexts (e.g. in the kernel trick used in SVM). A [Gaussian kernel](https://datascience.stackexchange.com/q/17352/10640) usually refers to a [Gaussian function](https://en.wikipedia.org/wiki/Gaussian_function) (that is, a function similar to the probability density function of a [Gaussian distribution](https://en.wikipedia.org/wiki/Normal_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](https://en.wikipedia.org/wiki/Kernel_(algebra))?
  
  **Tags:** machine-learning, terminology, math, history, support-vector-machine
  
  > **Comments:**
  > **username_1**: I believe we use the word kernel because we are transforming the basis.  
  
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  ## 1 answers
  
  ### Answer by username_0 on 2020-05-16. Score: 1
  
  The usage of the word "kernel" in the context of support vector machines probably comes from its usage in the context of [integral transforms](https://en.wikipedia.org/wiki/Integral_transform).
  
  See the article [Kernel of an integral operator](https://www.encyclopediaofmath.org/index.php/Kernel_of_an_integral_operator), and the questions [What is the difference between a kernel and a function?](https://math.stackexchange.com/q/22133/168764) and [Why is the kernel of an integral transform called kernel?](https://math.stackexchange.com/q/1919305/168764).
  
  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](https://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf).
  
  
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