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How does Euclidean-norm in K-means cause it to have linear decision boundaries? The Euclidean-norm is a non-linear measure between two points, then how does it make the boundaries till linear?

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K-means clustering works by creating a Voronoi diagram that has linear decision boundaries between clusters, as you know. This means that you can draw lines/planes/hyperplanes to classify your data.

In practice, you are actually using the squared euclidean distance because the sum of squares is being minimised by K-means. Because the square root is monotone, this means that the euclidean distance is minimised as well.

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  • $\begingroup$ does this have any mathematical explanation? thannk you $\endgroup$ Oct 8 '18 at 11:34

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