I said:
o Rotating, translating or scaling the points should do the same to the result. o Embedding in a higher-dimensional space shouldn't matter.
"Afine equivariant."
More generally, you want a function that finds the middle of the pack, tending to pay less attention to stragglers.
"Outliers". In statistics, trying to be insensitive to outliers or noise is called "robustness," and convex peeling (as well as later non-convex peeling) is one way to do this for "multivariate" data. Gastwirth, J.L. (1966), On Robust Procedures. Journal of the American Statistical Association, 61, 929-948 My first method (the second was nonsense but could be patched but doesn't matter) starts out seeming simple and well-motivated, but when it has to iterate it gets complicated in a way that's ill-motivated anyway. Peelings seem more arbitrary at first, but second-through-nth peels are at least arbitrary in the same way. You could get more plausible by building a model that's a mapping of a normal distribution. Or, you could get simpler by taking my method one step and then taking an average. The nice thing about the 1D median is its grand indifference to details. --Steve