f -divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an f -dive...

Montane species distributions interrupted by valleys can lead to range fragmentation, differentiation and ultimately speciation. Paleoclimatic fluctuations may accentuate or reduce such diversification by temporally altering the extent of montane habitat and may affect species differentially. We examined how an entire montane bird community of the Western Ghats--a linear, coastal tropical mount...

The scope of the well-known k-means algorithm has been broadly extended with some recent results: first, the kmeans++ initialization method gives some approximation guarantees; second, the Bregman k-means algorithm generalizes the classical algorithm to the large family of Bregman divergences. The Bregman seeding framework combines approximation guarantees with Bregman divergences. We present h...

A Jensen-Bregman divergence is a distortion measure defined by a Jensen convexity gap induced by a strictly convex functional generator. Jensen-Bregman divergences unify the squared Euclidean and Mahalanobis distances with the celebrated information-theoretic JensenShannon divergence, and can further be skewed to include Bregman divergences in limit cases. We study the geometric properties and ...

We present a novel class of divergences induced by a smooth convex function called total Jensendivergences. Those total Jensen divergences are invariant by construction to rotations, a feature yieldingregularization of ordinary Jensen divergences by a conformal factor. We analyze the relationships be-tween this novel class of total Jensen divergences and the recently introduced tota...

We study Bregman divergences in probability density space embedded with the $$L^2$$ –Wasserstein metric. Several properties and dualities of transport are provided. In particular, we derive Kullback–Leibler (KL) divergence by a negative Boltzmann–Shannon entropy space. also analytical formulas generalizations KL for one-dimensional densities Gaussian families.