Maximum Correntropy Estimation Is a Smoothed MAP Estimation

Chen, Badong; Prı́ncipe, José C.

doi:10.1109/lsp.2012.2204435

Cited by 232 publications

(137 citation statements)

References 11 publications

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“…Given two random variables X and Y , the correntropy is defined by [19,28] V( , ) There is a well-known generalization of Gaussian density function called the generalized Gaussian density (GGD) function, which with zero-mean is given by [26,27]   ,, In this work, we use the GGD density function as the kernel function of correntropy, and define , , ,…”

Section: A Definitionmentioning

confidence: 99%

Generalized Correntropy for RobustAdaptive Filtering

Chen

Liu

Zhao

et al. 2016

IEEE Trans. Signal Process.

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584

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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Section: A Definitionmentioning

confidence: 99%

Generalized Correntropy for RobustAdaptive Filtering

Chen

Liu

Zhao

et al. 2016

IEEE Trans. Signal Process.

Self Cite

584

198

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“…Remark: As one can see, when using the Gaussian kernel function, correntropy contains all even-order sums of random variables X and Y [12,14]. By using the above index, the MCC contains the high-order moment between the real value and the predicted value, and it is mostly guided by the local similarity of the data.…”

Section: Maximum Correntropy Criterionmentioning

confidence: 99%

“…is optimal only if the probability distribution function of the prediction errors is Gaussian [11,12]. In order to deal with the non-Gaussian and nonlinear problems in engineering applications, a novel criterion, namely, the maximum correntropy criterion (MCC), was introduced in [12,13], and its properties are discussed in [14,15]. Because the prediction errors under the small-sample electricity data have non-Gaussian statistical characteristics, the LSSVM prediction mechanism using the MCC is developed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion

Duan

Qiu

et al. 2018

Entropy

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Abstract:In recent years, with the deepening of China's electricity sales side reform and electricity market opening up gradually, the forecasting of electricity consumption (FoEC) becomes an extremely important technique for the electricity market. At present, how to forecast the electricity accurately and make an evaluation of results scientifically are still key research topics. In this paper, we propose a novel prediction scheme based on the least-square support vector machine (LSSVM) model with a maximum correntropy criterion (MCC) to forecast the electricity consumption (EC). Firstly, the electricity characteristics of various industries are analyzed to determine the factors that mainly affect the changes in electricity, such as the gross domestic product (GDP), temperature, and so on. Secondly, according to the statistics of the status quo of the small sample data, the LSSVM model is employed as the prediction model. In order to optimize the parameters of the LSSVM model, we further use the local similarity function MCC as the evaluation criterion. Thirdly, we employ the K-fold cross-validation and grid searching methods to improve the learning ability. In the experiments, we have used the EC data of Shaanxi Province in China to evaluate the proposed prediction scheme, and the results show that the proposed prediction scheme outperforms the method based on the traditional LSSVM model.

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“…However, these algorithms still cannot give the expected convergence achieved from the PNLMS at the beginning iteration stage for high sparseness impulse response applications. Recently, an information theoretic quantity has been presented to build the required cost function for adaptive signal processing applications [32][33][34][35][36][37][38]. To calculate the quantities, the entropy estimator was reported in detail.…”

Section: Introductionmentioning

confidence: 99%

A General Zero Attraction Proportionate Normalized Maximum Correntropy Criterion Algorithm for Sparse System Identification

Wang

Albu

et al. 2017

Symmetry

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Abstract:A general zero attraction (GZA) proportionate normalized maximum correntropy criterion (GZA-PNMCC) algorithm is devised and presented on the basis of the proportionate-type adaptive filter techniques and zero attracting theory to highly improve the sparse system estimation behavior of the classical MCC algorithm within the framework of the sparse system identifications. The newly-developed GZA-PNMCC algorithm is carried out by introducing a parameter adjusting function into the cost function of the typical proportionate normalized maximum correntropy criterion (PNMCC) to create a zero attraction term. The developed optimization framework unifies the derivation of the zero attraction-based PNMCC algorithms. The developed GZA-PNMCC algorithm further exploits the impulsive response sparsity in comparison with the proportionate-type-based NMCC algorithm due to the GZA zero attraction. The superior performance of the GZA-PNMCC algorithm for estimating a sparse system in a non-Gaussian noise environment is proven by simulations.

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Maximum Correntropy Estimation Is a Smoothed MAP Estimation

Cited by 232 publications

References 11 publications

Generalized Correntropy for RobustAdaptive Filtering

Generalized Correntropy for RobustAdaptive Filtering

Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion

A General Zero Attraction Proportionate Normalized Maximum Correntropy Criterion Algorithm for Sparse System Identification

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