Dear Mahesh,

Before trying to understand how cluster centers relate to spatial coordinates, please understand what the K-means 'cluster center' represents in general.

The K-means algorithm aims to divide all observations (individual image pixels) into K clusters. It starts by assigning each cluster a representative observation which is known as the 'cluster centroid/center' also. Now the algorithm divides all remaining observations by comparing each non-centroid observation with the centroid observations and picking the centroid observation with smallest distance with non-centroid observation in question (distance may be Euclidean, Manhattan etc.)

Now, considering your question, We can delve into how it selects the cluster centers. The answer is, randomly. Thus, the efficiency of the algorithm is, to some extent, affected by randomness. The cluster center pixels for images are chosen randomly and then all other pixels are divided based on those chosen pixels. There are more advanced variants of K-Means such as K-Means++, K-Medoid, H-K-Means etc that tackle this problem to provide better results.

Dear Nahian Ahmed,

Thanks for your reply...

Excluding standard methods for determining spatial coordinates of K-means cluster you can try with other method to determine pixel or sub-pixel coordinates. Some of these methods are sub-pixel ratio methods and swapping pixel. If you are interested for non-standard numerical methods you can check more precise raiding those manuscripts :

Sub‐pixel mapping of rural land cover objects from fine spatial resolution satellite sensor imagery using super‐resolution pixel‐swapping

A linearised pixel-swapping method for mapping rural linear land cover features from fine spatial resolution remotely sensed imagery

GIS numerical and remote sensing analyses of forest changes in the Toplica region for the period of 1953–2013