A note on the quasiconvex Jensen divergences and the quasiconvex Bregman divergences derived thereof

19 Sep 2019Frank NielsenGaëtan Hadjeres

We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are oriented (asymmetric) distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as the limit case of scaled and skewed quasiconvex Jensen divergences, and report a simple closed-form formula which shows that these divergences are only pseudo-divergences at countably many inflection points of the generators... (read more)

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