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Kernel Mixture Correntropy Conjugate Gradient Algorithm for Time Series Prediction

1,2,3, 1,2,3,*, 4, 1,2,3, 1,2,3, 1,2,3 and 5
1
School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China
2
Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China
3
Beijing Key Laboratory of Knowledge Engineering for Materials Science, Beijing 100083, China
4
China Information Technology Security Evaluation Center, Beijing 100085, China
5
Department of Electrical Engineering and Computer Science, Cleveland State University, Cleveland, OH 44115, USA
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(8), 785; https://doi.org/10.3390/e21080785
Received: 17 June 2019 / Revised: 9 August 2019 / Accepted: 9 August 2019 / Published: 11 August 2019
(This article belongs to the Special Issue Information Theoretic Learning and Kernel Methods)
PDF [3147 KB, uploaded 20 August 2019]

Abstract

Kernel adaptive filtering (KAF) is an effective nonlinear learning algorithm, which has been widely used in time series prediction. The traditional KAF is based on the stochastic gradient descent (SGD) method, which has slow convergence speed and low filtering accuracy. Hence, a kernel conjugate gradient (KCG) algorithm has been proposed with low computational complexity, while achieving comparable performance to some KAF algorithms, e.g., the kernel recursive least squares (KRLS). However, the robust learning performance is unsatisfactory, when using KCG. Meanwhile, correntropy as a local similarity measure defined in kernel space, can address large outliers in robust signal processing. On the basis of correntropy, the mixture correntropy is developed, which uses the mixture of two Gaussian functions as a kernel function to further improve the learning performance. Accordingly, this article proposes a novel KCG algorithm, named the kernel mixture correntropy conjugate gradient (KMCCG), with the help of the mixture correntropy criterion (MCC). The proposed algorithm has less computational complexity and can achieve better performance in non-Gaussian noise environments. To further control the growing radial basis function (RBF) network in this algorithm, we also use a simple sparsification criterion based on the angle between elements in the reproducing kernel Hilbert space (RKHS). The prediction simulation results on a synthetic chaotic time series and a real benchmark dataset show that the proposed algorithm can achieve better computational performance. In addition, the proposed algorithm is also successfully applied to the practical tasks of malware prediction in the field of malware analysis. The results demonstrate that our proposed algorithm not only has a short training time, but also can achieve high prediction accuracy.
Keywords: kernel adaptive filtering; conjugate gradient; correntropy; sparsification criterion; malware prediction kernel adaptive filtering; conjugate gradient; correntropy; sparsification criterion; malware prediction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Xue, N.; Luo, X.; Gao, Y.; Wang, W.; Wang, L.; Huang, C.; Zhao, W. Kernel Mixture Correntropy Conjugate Gradient Algorithm for Time Series Prediction. Entropy 2019, 21, 785.

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