Maximum correntropy Kalman filter

Chen, Baodong; Liu, Xi; Zhao, Haiquan; Prı́ncipe, José C.

doi:10.1016/j.automatica.2016.10.004

Cited by 613 publications

(329 citation statements)

References 31 publications

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“…While there are some measures with which to approximate its value, there is no perfect one [27, 28]. Here, we use disagreement to measure diversity and also Q -Statistic which is recommended in [29].…”

Section: Simulation and Discussionmentioning

confidence: 99%

Improving Classification Performance through an Advanced Ensemble Based Heterogeneous Extreme Learning Machines

Abuassba

Zhang

Luo

et al. 2017

Computational Intelligence and Neuroscience

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Extreme Learning Machine (ELM) is a fast-learning algorithm for a single-hidden layer feedforward neural network (SLFN). It often has good generalization performance. However, there are chances that it might overfit the training data due to having more hidden nodes than needed. To address the generalization performance, we use a heterogeneous ensemble approach. We propose an Advanced ELM Ensemble (AELME) for classification, which includes Regularized-ELM, L2-norm-optimized ELM (ELML2), and Kernel-ELM. The ensemble is constructed by training a randomly chosen ELM classifier on a subset of training data selected through random resampling. The proposed AELM-Ensemble is evolved by employing an objective function of increasing diversity and accuracy among the final ensemble. Finally, the class label of unseen data is predicted using majority vote approach. Splitting the training data into subsets and incorporation of heterogeneous ELM classifiers result in higher prediction accuracy, better generalization, and a lower number of base classifiers, as compared to other models (Adaboost, Bagging, Dynamic ELM ensemble, data splitting ELM ensemble, and ELM ensemble). The validity of AELME is confirmed through classification on several real-world benchmark datasets.

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Section: Simulation and Discussionmentioning

confidence: 99%

Improving Classification Performance through an Advanced Ensemble Based Heterogeneous Extreme Learning Machines

Abuassba

Zhang

Luo

et al. 2017

Computational Intelligence and Neuroscience

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“…e n H n = a n + ηJ cn e n H n (24) where e n = y n − H n a n is the estimation error, and η is the step size. (24) is called the MCC algorithm [34].…”

Section: Parameter Updatingmentioning

confidence: 99%

“…(24) is called the MCC algorithm [34]. When (24), the MCC algorithm reduces to the least mean square (LMS) adaption algorithm which uses MSE criterion as its cost function, a n+1 = a n + ηe n H n (25) However, comparing (24) and (25), it can be observed that the MCC algorithm obtains an extra scaling factor that is also the correntropy criterion function J cn . The extra scaling factor J cn = exp(− e 2 n 2σ 2 ) is an exponential function of the error e n and depicts the outlier rejection property of the correntropy similarity measure.…”

Section: Parameter Updatingmentioning

confidence: 99%

“…To tackle the nonGaussian nature of the modeling errors, an effective way is to adopt the information content of the error distribution as a quality criterion [24]- [26]. By capturing the higher moments of the error distribution, the information contained in the higher moments are passed to the EFNSs instead of remaining in the error distribution.…”

Section: Introductionmentioning

confidence: 99%

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Correntropy-Based Evolving Fuzzy Neural System

Bao

Rong

Angelov

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-In this paper, a correntropy-based evolving fuzzy neural system (correntropy-EFNS) is proposed for approximation of nonlinear systems. Different from the commonly used meansquare error criterion, correntropy has a strong outliers rejection ability through capturing the higher moments of the error distribution. Considering the merits of correntropy, this paper brings contributions to build EFNS based on the correntropy concept to achieve a more stable evolution of the rule base and update of the rule parameters instead of the commonly used meansquare error criterion. The correntropy-EFNS (CEFNS) begins with an empty rule base and all rules are evolved online based on the correntropy criterion. The consequent part parameters are tuned based on the maximum correntropy criterion where the correntropy is used as the cost function so as to improve the nonGaussian noise rejection ability. The steady-state convergence performance of the CEFNS is studied through the calculation of the steady-state excess mean square error (EMSE) in two cases: i) Gaussian noise; and ii) non-Gaussian noise. Finally, the CEFNS is validated through a benchmark system identification problem, a Mackey-Glass time series prediction problem as well as five other real-world benchmark regression problems under both noise-free and noisy conditions. Compared with other evolving fuzzy neural systems, the simulation results show that the proposed CEFNS produces better approximation accuracy using the least number of rules and training time and also owns superior non-Gaussian noise handling capability.

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“…The MCC as a measure of the information content in information theoretic learning was developed by principe with his team to deal with error distributions with non-Gaussian characteristics, and it has been widely used in pattern classification, feature selection, dimension reduction and adaptive filtering [21][22][23][24][25]. The MCC indicates the similarity between the predicted output and the real sample in the correntropy sense; it shows good robustness for nonlinear and non-Gaussian data processing, such as determining whether electricity is suitable for the prediction of time series non-stationary and time-varying predictions [26].…”

Section: Maximum Correntropy Criterionmentioning

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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Maximum correntropy Kalman filter

Cited by 613 publications

References 31 publications

Improving Classification Performance through an Advanced Ensemble Based Heterogeneous Extreme Learning Machines

Improving Classification Performance through an Advanced Ensemble Based Heterogeneous Extreme Learning Machines

Correntropy-Based Evolving Fuzzy Neural System

Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion

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