Short-term Prediction Of Chaotic Time Series Research Articles

Quantized kernel Lleast lncosh algorithm

This paper introduces the kernel least lncosh (KLL) algorithm, in which the lncosh (logarithm of hyperbolic cosine) cost function is successfully applied in the reproducing-kernel-Hilbert space. The online vector quantization (VQ) is then used to quantize the input space to construct the algorithm which can curb the growth of network size. As a result, the quantized kernel least lncosh (QKLL) algorithm is developed, which is robust in non-Gaussian environments. The sufficient condition for mean-square convergence of the QKLL algorithm has been conducted. The performance of the KLL and QKLL algorithms is demonstrated by the short-term chaotic time-series prediction and non-linear channel-equalization (NCE).

The Online Random Fourier Features Conjugate Gradient Algorithm

Kernel conjugate gradient (KCG) algorithms have been proposed to improve the convergence rate and filtering accuracy of kernel adaptive filters (KAFs). However, sparsification is still required in the KCG algorithms to curb the growth of network structure for online applications. To address this issue, a novel online random Fourier features conjugate gradient (RFFCG) algorithm based on the minimum mean-square error criterion is proposed by approximating the kernel with the random Fourier features. With no requirement of sparsification, the proposed RFFCG significantly reduces the computational and storage complexities in KAFs. Meanwhile, the RFFCG efficiently uses only one error in the loss function to approach the filtering accuracy of the KAF with sparsification based on all the errors in the loss function. Monte Carlo simulations on short-term chaotic time-series prediction validate the superiorities of the proposed RFFCG algorithm.

A Quantized Kernel Learning Algorithm Using a Minimum Kernel Risk-Sensitive Loss Criterion and Bilateral Gradient Technique

Recently, inspired by correntropy, kernel risk-sensitive loss (KRSL) has emerged as a novel nonlinear similarity measure defined in kernel space, which achieves a better computing performance. After applying the KRSL to adaptive filtering, the corresponding minimum kernel risk-sensitive loss (MKRSL) algorithm has been developed accordingly. However, MKRSL as a traditional kernel adaptive filter (KAF) method, generates a growing radial basis functional (RBF) network. In response to that limitation, through the use of online vector quantization (VQ) technique, this article proposes a novel KAF algorithm, named quantized MKRSL (QMKRSL) to curb the growth of the RBF network structure. Compared with other quantized methods, e.g., quantized kernel least mean square (QKLMS) and quantized kernel maximum correntropy (QKMC), the efficient performance surface makes QMKRSL converge faster and filter more accurately, while maintaining the robustness to outliers. Moreover, considering that QMKRSL using traditional gradient descent method may fail to make full use of the hidden information between the input and output spaces, we also propose an intensified QMKRSL using a bilateral gradient technique named QMKRSL_BG, in an effort to further improve filtering accuracy. Short-term chaotic time-series prediction experiments are conducted to demonstrate the satisfactory performance of our algorithms.

Kernel recursive maximum correntropy

In this letter, a robust kernel adaptive algorithm, called the kernel recursive maximum correntropy (KRMC), is derived in kernel space and under the maximum correntropy criterion (MCC). The proposed algorithm is particularly useful for nonlinear and non-Gaussian signal processing, especially when data contain large outliers or disturbed by impulsive noises. The superior performance of KRMC is confirmed by simulation results about short-term chaotic time series prediction in alpha-stable noise environments.

Kernel minimum error entropy algorithm

As an alternative adaptation criterion, the minimum error entropy (MEE) criterion has been receiving increasing attention due to its successful use in, especially, nonlinear and non-Gaussian signal processing. In this paper, we study the application of error entropy minimization to kernel adaptive filtering, a new and promising technique that implements the conventional linear adaptive filters in reproducing kernel Hilbert space (RKHS) and obtains the nonlinear adaptive filters in original input space. The kernel minimum error entropy (KMEE) algorithm is derived, which is essentially a generalized stochastic information gradient (SIG) algorithm in RKHS. The computational complexity of KMEE is just similar to the kernel affine projection algorithm (KAPA). We also utilize the quantization approach to constrain the network size growth, and develop the quantized KMEE (QKMEE) algorithm. Further, we analyze the mean square convergence of KMEE. The energy conservation relation is derived and a sufficient condition that ensures the mean square convergence is obtained. The performance of the new algorithm is demonstrated in nonlinear system identification and short-term chaotic time series prediction.

Quantized kernel least mean square algorithm.

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

An Information Theoretic Approach of Designing Sparse Kernel Adaptive Filters

This paper discusses an information theoretic approach of designing sparse kernel adaptive filters. To determine useful data to be learned and remove redundant ones, a subjective information measure called surprise is introduced. Surprise captures the amount of information a datum contains which is transferable to a learning system. Based on this concept, we propose a systematic sparsification scheme, which can drastically reduce the time and space complexity without harming the performance of kernel adaptive filters. Nonlinear regression, short term chaotic time-series prediction, and long term time-series forecasting examples are presented.