Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning

This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence result...

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Bibliographic Details
Published in:	IEEE transactions on signal processing Vol. 65; no. 3; pp. 794 - 816
Main Authors:	Ying Sun, Babu, Prabhu, Palomar, Daniel P.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.02.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Basic converters Convergence Convexity Estimation Linear programming Machine learning Majorization-minimization Minimization non-convex optimization Optimization Signal processing Signal processing algorithms surrogate function Taylor series Upper bounds upperbounds
ISSN:	1053-587X, 1941-0476
Online Access:	Get full text
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Abstract	This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.
AbstractList	This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.
Author	Babu, Prabhu Ying Sun Palomar, Daniel P.
Author_xml	– sequence: 1 surname: Ying Sun fullname: Ying Sun email: ysunac@ust.hk organization: Dept. of Electron. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong, China – sequence: 2 givenname: Prabhu surname: Babu fullname: Babu, Prabhu email: prabhubabu@care.iitd.ac.in organization: CARE, IIT Delhi, Delhi, India – sequence: 3 givenname: Daniel P. surname: Palomar fullname: Palomar, Daniel P. email: palomar@ust.hk organization: Dept. of Electron. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong, China
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Snippet	This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with...
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SubjectTerms	Algorithms Basic converters Convergence Convexity Estimation Linear programming Machine learning Majorization-minimization Minimization non-convex optimization Optimization Signal processing Signal processing algorithms surrogate function Taylor series Upper bounds upperbounds
Title	Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning
URI	https://ieeexplore.ieee.org/document/7547360 https://www.proquest.com/docview/1844435170
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