431 citations · 1.2k across the 62 of their papers we have counts for
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Generalizing Jensen and Bregman divergences with comparative convexity and the statistical Bhattacharyya distances with comparable means
Frank Nielsen, Richard Nock
Comparative convexity is a generalization of convexity relying on abstract notions of means. We define the Jensen divergence and the Jensen diversity from the viewpoint of comparat…
A series of maximum entropy upper bounds of the differential entropy
Frank Nielsen, Richard Nock
We present a series of closed-form maximum entropy upper bounds for the differential entropy of a continuous univariate random variable and study the properties of that series. We…
Optimal interval clustering: Application to Bregman clustering and statistical mixture learning
Frank Nielsen, Richard Nock
We present a generic dynamic programming method to compute the optimal clustering of scalar elements into pairwise disjoint intervals. This case includes 1D Euclidean -m…
On conformal divergences and their population minimizers
Richard Nock, Frank Nielsen, Shun-ichi Amari
Total Bregman divergences are a recent tweak of ordinary Bregman divergences originally motivated by applications that required invariance by rotations. They have displayed superio…
Total Jensen divergences: Definition, Properties and k-Means++ Clustering
Frank Nielsen, Richard Nock
We present a novel class of divergences induced by a smooth convex function called total Jensen divergences. Those total Jensen divergences are invariant by construction to rotatio…
On the Chi square and higher-order Chi distances for approximating f-divergences
Frank Nielsen, Richard Nock
We report closed-form formula for calculating the Chi square and higher-order Chi distances between statistical distributions belonging to the same exponential family with affine n…