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The objective function of kernel K-means is

$$ \sum\limits_{c=1}^k \sum\nolimits_{a_i \in c} w_i \Vert \phi(a_i)- m_c \Vert^2 \ $$

where

$$ m_c = \frac{\sum\nolimits_{a_i \in c }w_i\phi(a_i)}{\sum\nolimits_{a_i \in c }w_i} $$ I need to know how to determine wi

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  • $\begingroup$ If possible, it would be better if you can rewrite the Obj. func. in Latex :) [I don't know Latex, so couldn't make the edit] $\endgroup$ – Dawny33 Jan 11 '16 at 10:41
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These weights should be introduced by a user. With a weight you tell the K-means algorithm, that one feature is more important than the other.

[0] These might represent a measure of importance, a frequency count, or some other information. The intent is that a point with a weight of 5.0 is twice as "important" as a point with a weight of 2.5, for instance. This gives rise to the "weighted" K-Means problem.

[0] http://people.sc.fsu.edu/~jburkardt/m_src/kmeans/kmeans.html

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