Amari's dual geometries are used to study measures of influence in exponential family regression. The dual geometries are presented as a natural extension of the Euclidean geometry used for the normal regression model. These geometries are then used to extend Cook's distance to generalized linear models and exponential family regression. Some of these extensions lead to measures already considered while other extensions lead to new measures of influence. The advantages of one of these new measures are discussed.
"A Geometric Approach to Detecting Influential Cases." Ann. Statist. 19 (3) 1570 - 1581, September, 1991. https://doi.org/10.1214/aos/1176348262