How is the "correlation distance" obtained after k-means with correlation is applied?

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Jaime Almonacid-Caballer 2021-6-23

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https://ww2.mathworks.cn/matlabcentral/answers/863155-how-is-the-correlation-distance-obtained-after-k-means-with-correlation-is-applied

编辑： Jaime Almonacid-Caballer 2021-6-23

Hi,

I have performed k-means calculation to a set of curves. The traditional k-means calculation minimises euclidean distance but matlab makes possible to minimise the "correlation distance".

Once the centroids are obtained the error (distance) between a curve and its centroid, in the case con euclidean distance this error is equal to the root of the sum of squared difference between all the coordinates (values of the curves):

(sum( (xi - ci)^2 ))^0.5; being xi the values of the curve and ci the values of the centroid.

I have done it manually and it matches with the matlab's result, as expected.

Problem. I have tried to obtain the correlation distance between a curve and its correlation centroid (in order to understand the internal process) without success.

vector = [0.183, 0.212, 0.237, 0.266, 0.286, 0.293, 0.296, 0.285, 0.292, 0.285, 0.278, 0.249, 0.225, 0.184, 0.173, 0.153, 0.182, 0.207, 0.237, 0.232, 0.221, 0.203, 0.177, 0.168, 0.16]

centroid = [ -0.21855, -0.12294, -0.00591, 0.096538, 0.188009, 0.229715, 0.254094, 0.22736, 0.204908, 0.175345539, 0.133732, 0.046236, 0.03547, -0.00712, -0.02923, -0.03936, -0.0303, -0.02336, -0.06685, -0.10802, -0.13891, -0.17165, -0.20264, -0.20557, -0.221 ]

The correlation distance is defined as [ 1 - pearson(vector,centroid) ] but, where matlab gives 0.37917 I obtain 0.1437.

What am I doing bad?

Thank you all in advance,

Jaime