Divergence measure is a tool used to quantify the discrimination of two subsets of universal set. In this paper, we proposed some relations between the divergence measure based on cardinalities of a fuzzy set and uncertainty due to nonspecificity of fuzzy set. Due to that relation, a new class of divergence measures are also obtained. The application of above measure in the field of image segme...

In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum skew divergence, including its relation to other state distinguishability measures. Finally, we present a number of important applications: new continuity i...

Entropy-based divergence measures have shown promising results in many areas of engineering and image processing. In this paper, we define a new generalized divergence measure, namely, the Jensen–Rényi divergence. Some properties such as convexity and its upper bound are derived. Based on the Jensen–Rényi divergence, we propose a new approach to the problem of image registration. Some appealing...

This paper discusses a local parametric modeling by the use of U-divergence in a statistical pattern recognition. The class of U-divergence measures commonly has an empirical loss function in a simple form including Kullback-Leibler divergence, the power divergence and mean squared error. We propose a minimization algorithm for parametric models of sequentially increasing dimension by incorpora...

Many applications require the use of divergence measures between probability distributions. Several of these, such as the Kullback Leibler (KL) divergence and the Bhattacharyya divergence, are tractable for single Gaussians, but intractable for complex distributions such as Gaussian mixture models (GMMs) used in speech recognizers. For tasks related to classification error, the Bhattacharyya di...

An axiomatic definition of divergence measure for intuitionistic fuzzy sets (IFSs, for short) is presented in this work, as a particular case of dissimilarity between IFSs. As the concept of divergence measure is more restrictive, it has particular properties which are studied. Furthermore, the relationships among IF-divergences, dissimilarities and distances are studied. We also provide some m...

Entropy-based divergence measures have shown promising results in many areas of engineering and image processing. In this paper, a generalized information-theoretic measure called Jensen-Rényi divergence is proposed. Some properties such as convexity and its upper bound are derived. Using the Jensen-Rényi divergence, we propose a new approach to the problem of ISAR (Inverse Synthetic Aperture R...

This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without requirement of absolute continuity. We establish properties the divergence, in particular derive exploit representation as an infimum convolution optimal transport cost entropy. Also included are examples computation approximation demonstration useful when one quantifie...

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TOTAL BREGMAN DIVERGENCE, A ROBUST DIVERGENCE MEASURE, AND ITS APPLICATIONS By Meizhu Liu December 2011 Chair: Baba C. Vemuri Major: Computer Engineering Divergence measures provide a means to measure the pairwise dissimilarity between “...

of dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TOTAL BREGMAN DIVERGENCE, A ROBUST DIVERGENCE MEASURE, AND ITS APPLICATIONS By Meizhu Liu December 2011 Chair: Baba C. Vemuri Major: Computer Engineering Divergence measures provide a means to measure the pairwise dissimilarity between “...