Mean square convergence analysis for kernel least mean square algorithm

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Prı́ncipe, José C.

doi:10.1016/j.sigpro.2012.04.007

Cited by 43 publications

(13 citation statements)

References 14 publications

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“…And the number of input vectors in training set is n. Hence, the computational complexity of entropy calculation is O(kn). Similarly, the learning complexity of KLMS is also O(kn) [34,35]. Consequently, it could be concluded that the complexity of E-KLMS is also O(kn).…”

Section: Analysis Of Complexitymentioning

confidence: 94%

An Entropy-Based Kernel Learning Scheme toward Efficient Data Prediction in Cloud-Assisted Network Environments

Luo

Zhang

et al. 2016

Entropy

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Abstract:With the recent emergence of wireless sensor networks (WSNs) in the cloud computing environment, it is now possible to monitor and gather physical information via lots of sensor nodes to meet the requirements of cloud services. Generally, those sensor nodes collect data and send data to sink node where end-users can query all the information and achieve cloud applications. Currently, one of the main disadvantages in the sensor nodes is that they are with limited physical performance relating to less memory for storage and less source of power. Therefore, in order to avoid such limitation, it is necessary to develop an efficient data prediction method in WSN. To serve this purpose, by reducing the redundant data transmission between sensor nodes and sink node while maintaining the required acceptable errors, this article proposes an entropy-based learning scheme for data prediction through the use of kernel least mean square (KLMS) algorithm. The proposed scheme called E-KLMS develops a mechanism to maintain the predicted data synchronous at both sides. Specifically, the kernel-based method is able to adjust the coefficients adaptively in accordance with every input, which will achieve a better performance with smaller prediction errors, while employing information entropy to remove these data which may cause relatively large errors. E-KLMS can effectively solve the tradeoff problem between prediction accuracy and computational efforts while greatly simplifying the training structure compared with some other data prediction approaches. What's more, the kernel-based method and entropy technique could ensure the prediction effect by both improving the accuracy and reducing errors. Experiments with some real data sets have been carried out to validate the efficiency and effectiveness of E-KLMS learning scheme, and the experiment results show advantages of the our method in prediction accuracy and computational time.

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Section: Analysis Of Complexitymentioning

confidence: 94%

An Entropy-Based Kernel Learning Scheme toward Efficient Data Prediction in Cloud-Assisted Network Environments

Luo

Zhang

et al. 2016

Entropy

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“…Note that Gaussian kernel is usually a default choice in ANF due to its universal approximating capability and numerical stability [20].…”

Section: B Kernel Methods For Adaptive Filteringmentioning

confidence: 99%

Kernel normalized mixed-norm algorithm for system identification

You

Zhao

et al. 2015

2015 International Joint Conference on Neural Networks (IJCNN)

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Kernel methods provide an efficient nonparamet ric model to produce adaptive nonlinear filtering (ANF) algo rithms. However, in practical applications, standard squared error based kernel methods suffer from two main issues: (1) Algorithm System I System II KNLMS M -0.1 M -0.1 KAPA-2 M -0.09, E -0.01 M -O.l,E -0.01 KRMN M -O.l,A -0.25 M -O.l,A -0.3 KNMN M -O.l,A -0.25 M -O.l,A -0.25 KNMN-AMP M = 0.1, Al = 0.25, A2 = 0.75 M = 0.1, Al = 0.25, A2 = 0.55

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“…In this direction, we mention here the works by Al-Naffouri and Sayed [11,13], whose approach is based on the fundamental energy conservation relation (ECR). Recently, this relation has been extended into RKHS for analyzing the mean-square convergence performance of the kernel adaptive filters [12,14]. In this section, we study the mean-square convergence performance of the proposed KRMN algorithm, based on the ECR given in Lemma 1.…”

Section: Mean Square Convergence Analysismentioning

confidence: 99%

Kernel robust mixed-norm adaptive filtering

Liu

Chen

et al. 2014

2014 International Joint Conference on Neural Networks (IJCNN)

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Kernel methods are powerful for developing a nonlinear learning algorithm in a high-dimensional linear space. The least mean square (LMS) and the least absolute deviation (LAD) are two well-known linear adaptive filtering algorithms. The former performs very well when the noise is Gaussian, while the later possesses desirable performance when the noise has a long-tailed distribution (e.g. alpha-stable distribution). The combination of the LMS and LAD yields a robust mixed-norm (RMN) algorithm. In this paper, we combine the popular kernel methods and the RMN algorithm to develop a new kernel adaptive filtering algorithm, namely the kernel RMN (KRMN) algorithm, which is a robust adaptive algorithm in reproducing kernel Hilbert space (RKHS). The mean square convergence is analyzed, and the excellent and robust performance of the new algorithm is demonstrated by the simulation results of nonlinear time series prediction.

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Mean square convergence analysis for kernel least mean square algorithm

Cited by 43 publications

References 14 publications

An Entropy-Based Kernel Learning Scheme toward Efficient Data Prediction in Cloud-Assisted Network Environments

An Entropy-Based Kernel Learning Scheme toward Efficient Data Prediction in Cloud-Assisted Network Environments

Kernel normalized mixed-norm algorithm for system identification

Kernel robust mixed-norm adaptive filtering

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