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I am trying to implement k-means clustering on a 6x6 data set that looks like this:

2 3 6 0 1 7
4 9 9 6 2 2
0 1 7 9 5 0
2 3 2 7 8 3
8 2 9 2 3 1
8 0 0 1 7 9

Using rows 2 and 4 as the centroids:

4 9 9 6 2 2
2 3 2 7 8 3

Taking the firsts row of the dataset and the first centroid, I can calculate the Euclidean distance like so:

$ \sqrt ((4-2)^2 + (9-3)^2 + (9-6)^2 + (6-0)^2 + (2-1)^2 + (2-7)^2)$

I want to now run the algorithm using Modified Correlation instead of Euclidean Distance, defined as

$mc = 1 - r$, where $r$ is the Pearson Correlation Coefficient.

So how does this work? I have never really worked with covariance / standard deviation in more than 2-d space. Can somebody give me a quick runthrough on the first row like I did above (or point me in the right direction)? I can't seem to find documentation on how I can calculate this for a 6-d data set.

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