Talk:Positive-definite kernel

Explanation

If I am correct, this one of the most basic "kernels" there exist. However, to explain the term quite complex concepts are used. I would appreciate a link to a more detailed explanation of the "positive definite kernel" concept, with illustrations instead of only those theoretical "examples". Some practical applications. And if not possible, some links that explains this concept in this way. —Preceding unsigned comment added by Saviourmachine (talk • contribs) 14:22, 13 March 2008 (UTC)[reply]

If anyone would like to generalize the definition given in this article, a great explanation can be found here: http://math.stackexchange.com/questions/58575/understanding-positive-definite-kernel Jess (talk) 00:09, 2 April 2015 (UTC)[reply]

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Yours truly AlexNewArtBot 13:43, 26 March 2007 (UTC)[reply]

Heading

The idea of an encyclopedia article is to give some explanation as well, it's not a math book. It would be nice if someone could write a good heading for this article, with some explanation for someone like me, who doesn't know what a positive definite kernel is. A definition does not really help me. Piet | Talk 07:37, 2 April 2008 (UTC)[reply]

Error in formula ?

In the first part we have :

A(i,j)\in {\mathcal {L}}(H_{i},H_{j})

is called a positive definite kernel if for all m > 0 and

h_{i}\in H_{i}

, the following positivity condition holds:

\sum _{-m\leq i\quad \, \atop j\leq m}\langle A(i,j)h_{j},h_{i}\rangle \geq 0.

I think it's $\sum _{-m\leq i\quad \, \atop j\leq m}\langle A(i,j)h_{i},h_{j}\rangle \geq 0.$

because $A(i,j)$ is in ${\mathcal {L}}(H_{i},H_{j})$ and not in ${\mathcal {L}}(H_{j},H_{i})$

Am I right ? —Preceding unsigned comment added by 84.14.112.202 (talk) 09:43, 20 October 2010 (UTC)[reply]

Context: make this clearer for, e.g., non-mathematicians interested in machine-learning

Here is a bit more context for the "context" template I added to the main article :) This article is referenced from various articles intended for non-mathematicians doing machine learning and allied fields. But as others have noted, it dives deeply into the math right away. An introduction, e.g. including text from Kernel trick, would be helpful. ★NealMcB★ (talk) 03:00, 3 November 2011 (UTC)[reply]

A good explanation of a specific kernel trick that helps a lot is in a youtube video of the Stanford AI Class http://www.youtube.com/watch?v=xRf9wAeU1kI