Journal ArticleDOI
A new robust fixed-point algorithm and its convergence analysis
TLDR
This study suggests a new fixed-point MEEF (FP-MEEF) algorithm, and analyzes its convergence based on Banach’s theorem (contraction mapping theorem), which is able to converge to the optimal solution quadratically with the appropriate selection of the kernel size.Abstract:
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.read more
Citations
More filters
Journal ArticleDOI
Broad Learning System Based on Maximum Correntropy Criterion
TL;DR: In this paper, the authors adopt the maximum correntropy criterion (MCC) to train the output weights, obtaining a Correntropy-based BLS (C-BLS), which is expected to achieve excellent robustness to outliers while maintaining the original performance of the standard BLS in the Gaussian or noise-free environment.
Information Theoretic Learning.
TL;DR: This work states that there is information in the error signal that is not captured during the training of nonlinear adaptive systems under non-Gaussian distribution conditions when one insists on secondorder statistical criteria.
Journal ArticleDOI
Convergence Analysis of a Fixed Point Algorithm Under Maximum Complex Correntropy Criterion
TL;DR: This letter provides the convergence analysis of fixed point based MCCC algorithm in complex-domain filtering by using the matrix inversion lemma and provides the stability analysis and the excess mean square error for MCCC.
Journal ArticleDOI
A New Information Theoretic Relation Between Minimum Error Entropy and Maximum Correntropy
TL;DR: This letter derives a new information theoretic relation between MEE and MCC, leading to better understanding of the theoretical differences, and illustrates the findings in a common example.
Journal ArticleDOI
Fixed-point generalized maximum correntropy: Convergence analysis and convex combination algorithms
Ji Zhao,Hongbin Zhang,Gang Wang +2 more
TL;DR: A novel robust filtering algorithm is proposed, which relies on the convex combination of two RGMC algorithms with different memories, and is called AC-RGMC-C algorithm, which is tested in plant identification scenarios with abrupt change under impulsive noise environment.
References
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Book
Adaptive Filter Theory
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
BookDOI
Finite mixture models: McLachlan/finite mixture models
Geoffrey J. McLachlan,David Peel +1 more
TL;DR: The important role of finite mixture models in statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the statistical and geospatial literature.
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Finite Mixture Models
Geoffrey J. McLachlan,David Peel +1 more
TL;DR: The important role of finite mixture models in the statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the mathematical and statistical literature.
Book
Numerical Analysis
TL;DR: This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.