Bregman divergence as relative operator entropy

被引：15
作者：
Petz, D. [1 ]
机构：
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1053 Budapest, Hungary
来源：
ACTA MATHEMATICA HUNGARICA | 2007年 / 116卷 / 1-2期
关键词：
Bregman divergence; f-divergence; quantum relative entropy;
D O I：
10.1007/s10474-007-6014-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Bregman operator divergence is introduced for density matrices by differentiation of the matrix-valued function x -> x log x. This quantity is compared with the relative operator entropy of Fujii and Kamei. It turns out that the trace is the usual Umegaki's relative entropy which is the only intersection of the classes of quasi-entropies and Bregman divergences.
引用
收藏
页码：127 / 131
页数：5
相关论文
共 50 条
  • [41] A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence
    Yonel, Bariscan
    Yazici, Birsen
    SIAM JOURNAL ON IMAGING SCIENCES, 2022, 15 (02): : 491 - 520
  • [42] A modified EM algorithm for mixture models based on Bregman divergence
    Fujimoto, Yu
    Murata, Noboru
    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2007, 59 (01) : 3 - 25
  • [43] TESTING FOR RANDOM EFFECTS IN COMPOUND RISK MODELS VIA BREGMAN DIVERGENCE
    Jeong, Himchan
    ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION, 2020, 50 (03) : 777 - 798
  • [44] Screening-based Bregman divergence estimation with NP-dimensionality
    Zhang, Chunming
    Guo, Xiao
    Chai, Yi
    ELECTRONIC JOURNAL OF STATISTICS, 2016, 10 (02): : 2039 - 2065
  • [45] A Characterization of the Domain of Beta-Divergence and Its Connection to Bregman Variational Model
    Woo, Hyenkyun
    ENTROPY, 2017, 19 (09):
  • [46] Quantum conditional relative entropy and quasi-factorization of the relative entropy
    Capel, Angela
    Lucia, Angelo
    Perez-Garcia, David
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2018, 51 (48)
  • [47] AN ADVANCED LEVEL SET METHOD BASED ON BREGMAN DIVERGENCE FOR INHOMOGENEOUS IMAGE SEGMENTATION
    Shi, Daming
    Zhu, Meilu
    Zhang, Yongqiang
    Tian, Feng
    PROCEEDINGS OF 2017 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS (ICMLC), VOL 2, 2017, : 334 - 339
  • [48] Convergence of Two-Stage Method with Bregman Divergence for Solving Variational Inequalities*
    D. A. Nomirovskii
    B. V. Rublyov
    V. V. Semenov
    Cybernetics and Systems Analysis, 2019, 55 : 359 - 368
  • [49] Convergence of Two-Stage Method with Bregman Divergence for Solving Variational Inequalities*
    Nomirovskii, D. A.
    Rublyov, B. V.
    Semenov, V. V.
    CYBERNETICS AND SYSTEMS ANALYSIS, 2019, 55 (03) : 359 - 368
  • [50] Wireless Sensor Network Localization via Matrix Completion Based on Bregman Divergence
    Liu, Chunsheng
    Shan, Hong
    Wang, Bin
    SENSORS, 2018, 18 (09)
12345