منابع مشابه
Metrics Defined by Bregman Divergences †
Bregman divergences are generalizations of the well known Kullback Leibler divergence. They are based on convex functions and have recently received great attention. We present a class of “squared root metrics” based on Bregman divergences. They can be regarded as natural generalization of Euclidean distance. We provide necessary and sufficient conditions for a convex function so that the squar...
متن کاملSymmetrized Bregman Divergences and Metrics
While Bregman divergences [3] have been used for several machine learning problems in recent years, the facts that they are asymmetric and does not satisfy triangle inequality have been a major limitation. In this paper, we investigate the relationship between two families of symmetrized Bregman divergences and metrics, which satisfy the triangle inequality. Further, we investigate kmeans-type ...
متن کاملClustering with Bregman Divergences
A wide variety of distortion functions, such as squared Euclidean distance, Mahalanobis distance, Itakura-Saito distance and relative entropy, have been used for clustering. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences. The proposed algorithms unify centroid-based parametric clust...
متن کاملBregman Divergences and Triangle Inequality
While Bregman divergences have been used for clustering and embedding problems in recent years, the facts that they are asymmetric and do not satisfy triangle inequality have been a major concern. In this paper, we investigate the relationship between two families of symmetrized Bregman divergences and metrics, which satisfy the triangle inequality. The first family can be derived from any well...
متن کاملSubmodular-Bregman and the Lovász-Bregman Divergences with Applications
We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize...
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ژورنال
عنوان ژورنال: Communications in Mathematical Sciences
سال: 2008
ISSN: 1539-6746,1945-0796
DOI: 10.4310/cms.2008.v6.n4.a6