Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 26, Issue 4, Pages 653-662Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2013.2286175
Keywords
Fractional calculus; fractional differential; fractional energy norm; fractional extreme point; fractional gradient
Categories
Funding
- Foundation Franco-Chinoise Pour La Science Et Ses Applications
- National Natural Science Foundation of China [60972131, 61201438]
- Returned Overseas Chinese Scholars Project of Education Ministry of China [20111139]
- Science and Technology Support Project of Sichuan Province of China [2011GZ0201, 2013SZ0071]
- Soft Science Project of Sichuan Province of China [2013ZR0010]
- Scientific and Technical Innovation Seedling Project of Sichuan Province of China [2012ZZ023]
- Science and Technology Achievements Transformation Project of Chengdu of China [12DXYB255JH-002]
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The application of fractional calculus to signal processing and adaptive learning is an emerging area of research. A novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper. In particular, a fractional steepest descent approach is proposed. A fractional quadratic energy norm is studied, and the stability and convergence of our proposed method are analyzed in detail. The fractional steepest descent approach is implemented numerically and its stability is analyzed experimentally.
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