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I've read many interesting comments here, but let me add that Matlab's "personal" implementation of k-means supports 4 non-Euclidean distances [between data points and cluster centres]. The only comment from the documentation I can see about that is:

Distance measure, in p-dimensional space, used for minimization, specified as the comma-separated pair consisting of 'Distance' and a string.

kmeans computes centroid clusters differently for the different, supported distance measures. This table summarizes the available distance measures. In the formulae, x is an observation (that is, a row of X) and c is a centroid (a row vector).

Then a list of functions of c and x follows. Thus, considering that p is the dimensionality of the input data, it seems that no Euclidean embedding is performed beforehand.

BTW in the past I've been using Matlab's k-means with correlation distance and it (unsurprisingly) did what it was supposed to do.

I've read many interesting comments here, but let me add that Matlab's "personal" implementation of k-means supports 4 non-Euclidean distances. The only comment from the documentation I can see about that is:

Distance measure, in p-dimensional space, used for minimization, specified as the comma-separated pair consisting of 'Distance' and a string.

kmeans computes centroid clusters differently for the different, supported distance measures. This table summarizes the available distance measures. In the formulae, x is an observation (that is, a row of X) and c is a centroid (a row vector).

Then a list of functions of c and x follows. Thus, considering that p is the dimensionality of the input data, it seems that no Euclidean embedding is performed beforehand.

BTW in the past I've been using Matlab's k-means with correlation distance and it (unsurprisingly) did what it was supposed to do.

I've read many interesting comments here, but let me add that Matlab's "personal" implementation of k-means supports 4 non-Euclidean distances [between data points and cluster centres]. The only comment from the documentation I can see about that is:

Distance measure, in p-dimensional space, used for minimization, specified as the comma-separated pair consisting of 'Distance' and a string.

kmeans computes centroid clusters differently for the different, supported distance measures. This table summarizes the available distance measures. In the formulae, x is an observation (that is, a row of X) and c is a centroid (a row vector).

Then a list of functions of c and x follows. Thus, considering that p is the dimensionality of the input data, it seems that no Euclidean embedding is performed beforehand.

BTW in the past I've been using Matlab's k-means with correlation distance and it (unsurprisingly) did what it was supposed to do.

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source | link

I've read many interesting comments here, but let me add that Matlab's "personal" implementation of k-means supports 4 non-Euclidean distances. The only comment from the documentation I can see about that is:

Distance measure, in p-dimensional space, used for minimization, specified as the comma-separated pair consisting of 'Distance' and a string.

kmeans computes centroid clusters differently for the different, supported distance measures. This table summarizes the available distance measures. In the formulae, x is an observation (that is, a row of X) and c is a centroid (a row vector).

Then a list of functions of c and x follows. Thus, considering that p is the dimensionality of the input data, it seems that no Euclidean embedding is performed beforehand.

BTW in the past I've been using Matlab's k-means with correlation distance and it (unsurprisingly) did what it was supposed to do.