kmeans: Question about feature values

Question

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?

Answer 1

There is no reason to assume high values are more indicative, except (as you said) if the data was, e.g., normalized to the unit sphere, for example in spherical k-means.

You can, obviously, translate the result to move any center to 0.

Or assume your cluster centers are (1000,1) and (1000,-1). Clearly, only the second attribute is relevant in this data (and the overall mean is not 0).

If you want to identify discriminatory attributes, analyze with a separate algorithm. For example, with a decision tree or linear discriminant analysis.