In clustering methods such as K-means, the euclidean distance is the metric to use. As a result, we only calculate the mean values within each cluster. And then adjustments are made on the elements based on their distance to each mean value.
I was wondering why the Gaussian function is not used as the metric? Instead of using
xi -mean(X), we can use
exp(- (xi - mean(X)).^2/std(X).^2). Thus not only the similarity among the clusters are measured (mean), but the similarity within the cluster is also considered (std). Is this also equivalent to the Gaussian mixture model?
It is beyond my question here but I think mean-shift may arise the same question above.