Quantized Kernel Least Mean Square Research Articles

Automatic epileptic seizure detection approach based on multi-stage Quantized Kernel Least Mean Square filters

Epilepsy is one of the most common neurological disorders of the brain all over the world. For its detection, Electroencephalogram (EEG) is an important noninvasive diagnostic approach. This paper proposes a new automated real-time approach for EEG epileptic seizure detection based on serial concatenation of Quantized Kernel Least Mean Square (QKLMS) adaptive filters. The QKLMS filter is employed in the proposed system to achieve accurate real-time diagnosis with low hardware complexity. In the proposed serial concatenation filter design, the energy of prediction signal is investigated to detect the seizure interval on the EEG records and to classify healthy, epileptic inter-ictal, and epileptic ictal cases. The Grey Wolf Optimizer (GWO) algorithm is employed to find the optimum values of the energy threshold and the parameters of the QKLMS algorithm. The performance of the proposed QKLMS technique is compared with other adaptive filters, and the results reveal the superior performance of the QKLMS algorithm. The proposed system is examined with real EEG records taken from the Bonn University database, and the experimental results show that the proposed epileptic seizure detection system outperforms other state-of-the-art systems with an accuracy of 97.88 %, sensitivity of 98.80 %, specificity of 97.65 %, and computational time of 0.58 sec. This demonstrates that the proposed approach can be used to assist neurologists in enhancing the accuracy of epileptic seizure detection and speeding-up the diagnosis process without the need for visual inspection or analysis of a large volume of EEG data.

Gaussian kernel adaptive filters with adaptive kernel bandwidth

Gaussian kernel adaptive filters (GKAFs) have been successfully applied in functional approximation. The kernel bandwidth for GKAFs not only impacts on the smoothness of function approximation and the locality of training samples, but also affects the convergence rate and testing accuracy. However, in practice, it is hard to predesign an optimal one. In this paper, for practical applications, we propose a novel framework for kernel bandwidth adaptation in sparsification case. In this framework, we consider the latest K kernel bandwidths as free parameters, and sequentially update them using a gradient decent method to minimize the instantaneous squared error. Furthermore, we apply the proposed method to the quantized kernel least mean square (QKLMS) algorithm, and conduct convergence analysis for the algorithm. Extensive simulation results are provided and validate the superiority of our method compared to some state-of-the-art algorithms.

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.

A quantized kernel least mean square scheme with entropy-guided learning for intelligent data analysis

Quantized kernel least mean square (QKLMS) algorithm is an effective nonlinear adaptive online learning algorithm with good performance in constraining the growth of network size through the use of quantization for input space. It can serve as a powerful tool to perform complex computing for network service and application. With the purpose of compressing the input to further improve learning performance, this article proposes a novel QKLMS with entropy-guided learning, called EQ-KLMS. Under the consecutive square entropy learning framework, the basic idea of entropy-guided learning technique is to measure the uncertainty of the input vectors used for QKLMS, and delete those data with larger uncertainty, which are insignificant or easy to cause learning errors. Then, the dataset is compressed. Consequently, by using square entropy, the learning performance of proposed EQ-KLMS is improved with high precision and low computational cost. The proposed EQ-KLMS is validated using a weather-related dataset, and the results demonstrate the desirable performance of our scheme.

Quantized kernel maximum correntropy and its mean square convergence analysis

Online vector quantization (VQ) method has been successfully applied to the kernel adaptive filters (KAFs) for curbing their linearly growing radial basis function (RBF) network, thereby generating a family of quantized KAFs (QKAFs). However, the most existing QKAFs are based on the mean square error (MSE) criterion, which is actually not a good choice for non-Gaussian signals. In this paper, a new quantized kernel adaptive filter called quantized kernel maximum correntropy (QKMC) is developed, which is robust to large outliers or impulsive noises. The mean square convergence analysis for QKMC is conducted, and a sufficient condition for guaranteeing convergence is therefore obtained. The filtering accuracy of QKMC is also proved to be higher than that of the representative quantized kernel least mean square (QKLMS). In addition, to make full use of the information hidden in the input and the output spaces, we further propose a modified QKMC based on bilateral gradient (QKMC-BG). To limit the final network size of QKMC-BG, the QKMC-BG with fixed budget (QKMC-BG-FB) is also developed. Simulation results under the cases of Gaussian and non-Gaussian noises are presented to validate the proposed QKMC, QKMC-BG and QKMC-BG-FB.

A modified quantized kernel least mean square algorithm for prediction of chaotic time series

A modified quantized kernel least mean square (M-QKLMS) algorithm is proposed in this paper, which is an improvement of quantized kernel least mean square (QKLMS) and the gradient descent method is used to update the coefficient of filter. Unlike the QKLMS method which only considers the prediction error, the M-QKLMS method uses both the new training data and the prediction error for coefficient adjustment of the closest center in the dictionary. Therefore, the proposed method completely utilizes the knowledge hidden in the new training data, and achieves a better accuracy. In addition, the energy conservation relation and a sufficient condition for mean-square convergence of the proposed method are obtained. Simulations on prediction of chaotic time series show that the M-QKLMS method outperforms the QKLMS method in terms of steady-state mean square errors.

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.