Building Outlier-Resistant Centroids in Any Dimension

In this article, we also discuss an interesting physics problem: finding the point of maximum or minimum light, sound, radioactivity, or heat intensity, in the presence of an energy field produced by n energy source points. However, the main focus here is on finding the point that minimizes the sum of the "distances" to n points in a d-dimensional space. Both problems are closely related and use the same algorithm to find solutions. The sum of "distances" between an arbitrary point (u, v) and a set S { (x(1), y(1)) ... (x(n), y(n)) } of n points is defined as follows: The function H has one parameter p called power, and when p 2, we are facing the traditional problem of finding the centroid of a cloud of points: in this case, the solution is the classic average of the n points. This solution is notoriously sensitive to outliers.