I have a set of N samples belong to K classes. I am using k-means clustering with Euclidean distance in order to cluster these samples into K clusters. To help the k-means algorithm to group samples of a specific class into one cluster, I initialized the k-means algorithm so that the mean value of each cluster is the mean value of the samples of a specific class.
My question is not about the usefulness of what I mentioned above or the purpose of it, however, my question is: In machine learning, is this called "supervised clustering", "semi-supervised clustering" or just "normal clustering initialized by means of samples of the real class"? I want to know the correct terminology when we use k-means initialized by real-class mean values.