I've been doing color image segmentation using kmeans and it does wonders. However, this question has been bugging me as long and I still yet to find an answer for it.
Example (I'll use one data point and 4 cluster centroids):
data point, A = [3,4]
cluster centroid = [0,8;6,8;0,0;6,0]
Note that the (Euclidean distance) mean of A to all 4 cluster centroids is same = 5
How does kmeans decide which centroid A belongs to? Does it depends on the parameter we set? (eg using different distance measure, number of replicates)
I'm using three components of RGB for my image segmentation, thus it makes me even more confused.
Regarding the observation, is it possible to use 1d data matrix for kmeans, eg only Red component of the image? I Googled and searched all over the place and did not find anything.