A new robust fixed-point algorithm and its convergence analysis

In recent years, research on information theoretic learning (ITL) criteria has become very popular and ITL concepts are widely exploited in several applications because of their robust properties in the presence of heavy-tailed noise distributions. Minimum error entropy with fiducial points (MEEF),...

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Veröffentlicht in:Fixed point theory and algorithms for sciences and engineering Jg. 19; H. 4; S. 3191 - 3215
Hauptverfasser: Heravi, Ahmad Reza, Hodtani, Ghosheh Abed
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2017
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Bandwidths
Convergence
Criteria
Entropy
Information theory
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Methods
Random variables
Robustness (mathematics)
Theorems
information theoretic learning
Fixed-point algorithm
order of convergence
convergence
contraction mapping theorem
58C30: Fixed point theorems on manifolds
ISSN:1661-7738, 1661-7746, 2730-5422
Online-Zugang:Volltext
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Zusammenfassung:In recent years, research on information theoretic learning (ITL) criteria has become very popular and ITL concepts are widely exploited in several applications because of their robust properties in the presence of heavy-tailed noise distributions. Minimum error entropy with fiducial points (MEEF), as one of the ITL criteria, has not yet been well investigated in the literature. In this study, we suggest a new fixed-point MEEF (FP-MEEF) algorithm, and analyze its convergence based on Banach’s theorem (contraction mapping theorem). Also, we discuss in detail the convergence rate of the proposed method, which is able to converge to the optimal solution quadratically with the appropriate selection of the kernel size. Numerical results confirm our theoretical analysis and also show the outperformance of FP-MEEF in comparison with FP-MSE in some non-Gaussian environments. In addition, the convergence rate of FP-MEEF and gradient descent-based MEEF is evaluated in some numerical examples.
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ISSN:1661-7738
1661-7746
2730-5422
DOI:10.1007/s11784-017-0474-5