I have a given cluster of N points in 2-space. The goal is to find the geometric median of this cluster, and the x co-ordinate of the geometric median is known. What is the most computationally efficient way to find the y coordinate of the geometric median?
I have got a working solution iterating over the distance sum to find the minimum using Newton's method, but this is computationally intensive. It is also unpredictable in terms of convergence time.
To clarify, I am working with Euclidian distances, not Manhattan distances or distances squared.