We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Betaand Gam...

We discuss two families of two-parameter entropies and divergences, derived from the standard Rényi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as a...

We propose a simple method of construction of new families of φ-divergences. This method called convex standardization is applicable to convex and concave functions ψ(t) twice continuously differentiable in a neighborhood of t = 1 with nonzero second derivative at the point t = 1. Using this method we introduce several extensions of the LeCam, power, χ and Matusita divergences. The extended fam...

We derive a generalized notion of f divergences, called (f, l)-divergences. We show that this generalization enjoys many of the nice properties of f -divergences, although it is a richer family. It also provides alternative definitions of standard divergences in terms of surrogate risks. As a first practical application of this theory, we derive a new estimator for the Kulback-Leibler divergenc...

The entire nucleotide sequences were determined for hepatitis B virus (HBV) genotype B (HBV/B) genomes extracted from five patients in the Philippines and designated GenBank AB219426, AB219427, AB219428, AB219429 and AB219430. The serotype of the first four isolates was ayw and that of GenBank AB219430 was adw. Divergences of entire sequences were 1.0-2.0 % between the first four isolates and 3...

We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with ‘tadpole’ divergences in the effective field u theory with a cosmological term, which also contains an effective potential for the dilaton. Also, corrections to p-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. T...

We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities, and present two novel classes of Hölder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy-Schwarz divergence. We repo...

We record Limnonectes fastigatus for the first time from Vietnam based on a new amphibian collection Chu Mom Ray National Park, Kon Tum province. Morphological characteristics of specimens Park resemble those type series Cambodia. The differ Cambodia by having slightly larger size in males and distinct colour pattern dorsum. Genetic divergences between sequences Vietnamese available GenBank are...

In this paper we propose the use of φ-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, θ)dt + σ(Xt, θ)dWt, from discrete observations {Xti , i = 0, . . . , n} with ti = i∆n, i = 0, 1, . . . , n, under the asymptotic scheme ∆n → 0, n∆n → ∞ and n∆n → 0. The class of φ-divergences is wide and includes several special member...