Transient analysis of adaptive filters with error nonlinearities

Al-Naffouri, Tareq Y.; Sayed, Ali H.

doi:10.1109/tsp.2002.808108

Cited by 116 publications

(65 citation statements)

References 35 publications

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“…Similarly, Fig. 8b shows the performances of the algorithms in the underfitting scenario, where the desired data is generated by the third order piecewise linear model in (28). From the figures, it is observed that the DAT algorithm outperforms its competitors by learning the optimal partitioning for the given depth, which illustrates the power of the introduced algorithm under possible mismatches in terms of d.…”

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confidence: 87%

“…Although nonlinear approaches can be more powerful than linear methods in modeling, they usually suffer from overfitting, stability and convergence issues [1], [26]- [28], which considerably limit their application to signal processing problems. These issues are especially exacerbated in adaptive filtering due to the presence of feedback, which is even hard to control for linear models [26], [27], [29].…”

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confidence: 99%

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A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees

Vanli

Kozat

2014

IEEE Trans. Signal Process.

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Abstract-In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regressors in a nested structure. The introduced algorithms adapt not only their regression functions but also the complete tree structure while achieving the performance of the "best" linear mixture of a doubly exponential number of partitions, with a computational complexity only polynomial in the number of nodes of the tree. While constructing these algorithms, we also avoid using any artificial "weighting" of models (with highly data dependent parameters) and, instead, directly minimize the final regression error, which is the ultimate performance goal. The introduced methods are generic such that they can readily incorporate different tree construction methods such as random trees in their framework and can use different regressor or partitioning functions as demonstrated in the paper.Index Terms-Nonlinear regression, nonlinear adaptive filtering, binary tree, universal, adaptive.

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confidence: 87%

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confidence: 99%

A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees

Vanli

Kozat

2014

IEEE Trans. Signal Process.

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“…With a similar derivation presented in [35], one can analyze the mean square transient behaviors of the algorithm (31). This is a trivial but quite tedious task since we have to evaluate the expectations only analyze the steady-state mean square performance by using the Taylor expansion method [23].…”

Section: B Steady-state Mean Square Performancementioning

confidence: 99%

Generalized Correntropy for RobustAdaptive Filtering

Chen

Liu

Zhao

et al. 2016

IEEE Trans. Signal Process.

613

198

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Abstract-As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this work, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel (not necessarily a Mercer kernel), and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC), and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the mean square convergence performance is studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm.

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“…To study the performance behaviour of the Leaky Least Mean Mixed Norm algorithm we make use of the basic fundamental energy conservation relation [4], [23]- [25], proves out to be a useful framework in the analysis of adaptive filters in this thesis. Because of its wide spread application it can used in different adaptive algorithms without resorting to any restrictive assumptions that are generally en-countered in the literature review of adaptive filtering algorithms.…”

Section: Fundamental Energy Conservation Relationmentioning

confidence: 99%