Family Historian User Group

I am at present trying to deal with the Cemetery route.

I am fooling around with k-means clustering. it lacks several things I need for it to work correctly. one of the major issues is that it does not select centroids (major nodes) other than randomly and it can give a very different outcome depending on what it selects as centroids and it does not have a method to optimize centroids.

has anyone done a pure lua:
Expectation-maximization algorithm (EM)
Gaussian Mixture Models (GMM)
?
I had sort of wanted to end up with something like this picture in idea, logically. where starting from the root, where I live, it finds routes to large datapoints (lati.long of cemeteries) and a center. by example, lets say I fly into london, and there is a great number of places, tenterden, bethersden, romney, small hythe, high halden, stone in oxney, etc that have graveyards in my files. so where should I stay in the center of that, what is my route to london from there, and what are my routes to graveyards from that point.

I'm playing devil's advocate.
I wonder if you are trying to solve with mathematics something that is not a maths problem, but a logistics problem?
If you are coming to the congested south-east of England, the best way to travel between a number of places depends on the type of transport you intend to use and the available transport links between those places.
The maths solution assumes direct line of sight routes between places and travel time equal to distance, neither of which are valid.

the point is even in direct line that given say a center of tenterden; folkstone is never beyond dover, and: tonbridge, sevenoaks, and swanley are beyond each in order, and each in order 'on the way' to greenwich. by near every form of transport on a cartesian coordinate system where 0, 0 is tenterden, and each is plotted latitude as x, and longitude as y, from that, routes would be in a direct and other than cases of water crossings and the like, I should think within 2 * their crow flies distance.

centroids are fundamentally those points centeralized in an arbitrary radius. Kmeans is round, GMM can be elliptical.

however, I am open to how I would build in lua a logistics solution, and for the present case, assume driving as the mode.