# How to set weight in Weighted Kernel K-Means?

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

• 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] – Dawny33 Jan 11 '16 at 10:41

## 1 Answer

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.