In an example about kmeans for exploratory analysis the instructor examines the centroids and affirms that the centroid coordinates with the highest values are those that "drive" “belonging” to that cluster.
I am unable to understand that.
As an example let’s take a centroid that has, among its N coordinates, coordinates with values 100, 90, -90, -100. I am unable to understand why the coordinates with value 100 and 90 should “drive” the “belonging" to that cluster more than coordinates with value -90 or -100. Euclidean distance seems a relative measure to me, so absolute values should not matter, in general. It seems to me that what the instructor says might be true only if we assume non-negative domains for all the coordinates (not the case in the example he makes).
Can someone help me to understand, correct, confirm, integrate?