I have written a custom clustering function which takes a vector of initial position estimates of k cluster centres (a 1 dimensional vector). Internally the function then "calibrates" the final clustering result using a minimum distance measure over weighted data, based on this input. Each cluster centre k has its own variance associated with the points it clusters. There is no random initialisation and between cluster distance/disimilarity is irrelevant although, conceptually, the function can be thought of as being similar to kmeans in 1 dimension. The initial position estimate is the model.
I would like to use AIC to select the best of several different possible initial position estimates (models) post calibration, but I am confused as to how I should count the parameters k for the model AIC score. Obviously each given cluster centre counts as 1 parameter, but what about the variance? If I have, e.g. 5 cluster centres, do I count parameters for AIC as 5 plus 1 for a total global variance, or 5 plus 5 for individual variances?