Calculating Median in univariate is quite straight forward by just sorting the data. But , in multivariate case, where different features do not follow the same ranking order, how can someone calculate?
Dear Ashutosh,
As you have already figured out, the median of a multivariate distribution is not.a simple concept, and there is no single algorithm to depend on. However, there are several concepts well enough developed that you will find literature on them - e.g. vectors of marginal medians, the spatial median, and the Oja median. For a version with known computational simplicity try Hettmansperger, T. P., & Randles, R. (2002). A practical affine equivariant multivariate median. Biometrika, 89, 851–860.
Hope this helps.
There are different methods to rank order in higher dimensions, as suggested above.
No need to see it as complex.
Think of the geometry first.
Median lines in triangles.
Etc...
Median hyperplanes, separating clouds of data points in a balanced manner (to be defined by criterion...) into two regions.
Does it help you?
Renaud Di Francesco Could you please explain a bit more about the concept of median hyperplane?
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