Beta-Divergence as a Subclass of Bregman Divergence

被引：18

作者：

Hennequin, Romain ^{[1
]}

David, Bertrand ^{[1
]}

Badeau, Roland ^{[1
]}

机构：

[1] Telecom ParisTech, CNRS LTCI, Inst Telecom, F-75634 Paris 13, France

来源：

IEEE SIGNAL PROCESSING LETTERS | 2011年 / 18卷 / 02期

关键词：

Beta-divergence; Bregman divergence; non-negative matrix factorization; NONNEGATIVE MATRIX FACTORIZATION;

D O I：

10.1109/LSP.2010.2096211

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

In this paper, we present a complete proof that the beta-divergence is a particular case of Bregman divergence. This little-known result makes it possible to straightforwardly apply theorems about Bregman divergences to beta-divergences. This is of interest for numerous applications since these divergences are widely used, for instance in non-negative matrix factorization (NMF).

引用

页码：83 / 86

页数：4

共 50 条

[1] A Characterization of the Domain of Beta-Divergence and Its Connection to Bregman Variational Model
Woo, Hyenkyun
[J]. ENTROPY, 2017, 19 (09):
[2] TOWARDS COMPLEX NONNEGATIVE MATRIX FACTORIZATION WITH THE BETA-DIVERGENCE
Magron, Paul
Virtanen, Tuomas
[J]. 2018 16TH INTERNATIONAL WORKSHOP ON ACOUSTIC SIGNAL ENHANCEMENT (IWAENC), 2018, : 156 - 160
[3] MAJORIZATION-MINIMIZATION ALGORITHMS FOR CONVOLUTIVE NMF WITH THE BETA-DIVERGENCE
Fagot, Dylan
Wendt, Herwig
Fevotte, Cedric
Smaragdis, Paris
[J]. 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2019, : 8202 - 8206
[4] The Bregman Chord Divergence
Nielsen, Frank
Nock, Richard
[J]. GEOMETRIC SCIENCE OF INFORMATION, 2019, 11712 : 299 - 308
[5] Functional Bregman Divergence
Frigyik, Bela A.
Srivastava, Santosh
Gupta, Maya R.
[J]. 2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6, 2008, : 1681 - +
[6] Multi-resolution beta-divergence NMF for blind spectral unmixing
Leplat, Valentin
Gillis, Nicolas
Fevotte, Cedric
[J]. SIGNAL PROCESSING, 2022, 193
[7] Rank-one Tensor Approximation with Beta-divergence Cost Functions
Vandecappelle, Michiel
Vervliet, Nico
De Lathauwer, Lieven
[J]. 2019 27TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2019,
[8] α-Divergence Is Unique, Belonging to Both f-Divergence and Bregman Divergence Classes
Amari, Shun-Ichi
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (11) : 4925 - 4931
[9] Blind Audio Source Separation With Minimum-Volume Beta-Divergence NMF
Leplat, Valentin
Gillis, Nicolas
Ang, Andersen M. S.
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, 68 : 3400 - 3410
[10] MAXIMIZING THE BREGMAN DIVERGENCE FROM A BREGMAN FAMILY
Rauh, Johannes
Matus, Frantisek
[J]. KYBERNETIKA, 2020, 56 (05) : 875 - 885

← 1 2 3 4 5 →