Editing Central tendency (section)

===Information geometry===
The notion of a "center" as minimizing variation can be generalized in [[information geometry]] as a distribution that minimizes [[divergence (statistics)|divergence]] (a generalized distance) from a data set. The most common case is [[maximum likelihood estimation]], where the maximum likelihood estimate (MLE) maximizes likelihood (minimizes expected [[surprisal]]), which can be interpreted geometrically by using [[Entropy (statistics)|entropy]] to measure variation: the MLE minimizes [[cross-entropy]] (equivalently, [[relative entropy]], Kullback–Leibler divergence).

A simple example of this is for the center of nominal data: instead of using the mode (the only single-valued "center"), one often uses the [[empirical measure]] (the [[frequency distribution]] divided by the [[sample size]]) as a "center". For example, given [[binary data]], say heads or tails, if a data set consists of 2 heads and 1 tails, then the mode is "heads", but the empirical measure is 2/3 heads, 1/3 tails, which minimizes the cross-entropy (total surprisal) from the data set. This perspective is also used in [[regression analysis]], where [[least squares]] finds the solution that minimizes the distances from it, and analogously in [[logistic regression]], a maximum likelihood estimate minimizes the surprisal (information distance).