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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?

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  • $\begingroup$ it would help if you provided an accurate description of what the instructor said (or just talk ot him/her :) ). possibly they were talking about the squaring of euclidean distance, meaning that belonging will depend on the component with the largest difference ( 1 component wih absolute difference 10 beats 10 components with absolute difference 1) $\endgroup$ – seanv507 Jan 14 '18 at 13:43
  • $\begingroup$ Unfortunately the description is accurate, he said that, no more than that, (that is a systematic problem with that course) and, as I wrote, he was speaking about values of coordinates, not about distances $\endgroup$ – user110848 Jan 14 '18 at 14:53
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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.

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