256 citations · 2.3k across the 100 of their papers we have counts for
6 papers · 1 filter
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…
Logging safely in public spaces using color PINs
Frank Nielsen
Nowadays, we are increasingly logging on many different Internet sites to access private data like emails or photos remotely stored in the clouds. This makes us all the more concer…
On the symmetrical Kullback-Leibler Jeffreys centroids
Frank Nielsen
Due to the success of the bag-of-word modeling paradigm, clustering histograms has become an important ingredient of modern information processing. Clustering histograms can be per…
Cramer-Rao Lower Bound and Information Geometry
Frank Nielsen
This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbr…