The generalized complex-valued kernel least mean square (gCKLMS) has shown superior performance in modeling circular and noncircular complex-valued nonlinear signals by leveraging both kernel and pseudo-kernel functions. However, its applicability to large-scale or real-time scenarios is hindered by the exponential increase in computational complexity caused by the growing number of kernel coefficients over iterations. To overcome this challenge, we first propose the online censoring (OC)-based gCKLMS (OC-gCKLMS), which integrates the OC strategy into the gCKLMS framework. The OC selectively retains informative input data and its corresponding kernel and pseudo-kernel coefficients by exploiting data redundancy and then incorporates them into the update process. This significantly reduces computational burden without compromising performance. Then, we theoretically analyze the mean square convergence of the OC-gCKLMS. Finally, the elegant properties of the OC-gCKLMS are validated through simulations on three benchmark problems.

To mitigate the bias caused by the strong correlation between the loudspeaker and source signals in the acoustic feedback (AF) canceller (AFC), the prediction error method (PEM) based AFC (PEMAFC) is the most popular solution but comes with two inherent drawbacks. Firstly, to improve the tracking performance of the PEM filter in the processing of nonstationary signals such as speech and music, the recursive least square (RLS) algorithm is a strong candidate, but this leads to unmanageable computational complexity in the PEMAFC system. Secondly, though the decorrelated least mean square (DLMS) algorithm is often preferred as an update algorithm for estimating the AF path due to its simple structure, it still suffers from inferior steady-state performance. By drawing inspiration from the online censoring (OC) strategy that has significantly contributed to the adaptive processing of Big Data streams, we develop two PEMAFC systems in this paper, called OC-PEMAFC-1 and OC-PEMAFC-2. The OC-PEMAFC-1 employs the OC based RLS (OC-RLS) algorithm to update the weight vector of the PEM filter and shows a comparable performance by considerably reducing the overall computational complexity of the PEMAFC arising from the classical RLS. On the contrary, the OC-PEMAFC-2 incorporates the OC based DLMS (OC-DLMS) algorithm using only informative data streams, thus substantially enhancing the steady-state performance and partially reducing the overall computational complexity of the PEMAFC. This study also provides the stability analyses of the OC-RLS and OC-DLMS used in the proposed PEMAFC systems. The mentioned superiorities of the proposed systems are confirmed through simulation results on real-world AF paths.

Streaming Big Data applications require the means to efficiently utilize large-scale data in an online manner. This issue becomes even more pressing when data are also multidimensional, as is the case with quaternion data streams. To this end, we first introduce the online censoring (OC) based quaternion least mean square (OC-QLMS) and OC-augmented QLMS (OC-AQLMS) algorithms, which censor less informative data in order to reduce computational complexity without severely affecting performance. Next, to censor both the outlier and noninformative data, we also propose the robust OC-QLMS (ROC-QLMS) and ROC-AQLMS. Fixed and adaptive threshold rules are introduced into the proposed OC algorithms to efficiently implement the desired censoring probability in the quaternion domain. The fundamental convergence analysis on the step size for all the proposed algorithms is also presented and the superior properties of the proposed algorithms are demonstrated in system identification scenarios.

An online censoring (OC) based weighted-frequency Fourier linear combiner (OC-WFLC) adaptive filtering structure is proposed to reduce data processing costs in the estimation of pathological hand tremor (PHT) measurements. The proposed OC-WFLC is combined with the Fourier linear combiner (FLC) to effectively separate the PHT and voluntary movement from the hand tremor signal. The OC-WFLC is shown to adaptively extract the most informative frequency information, that is readily employed within the FLC to adaptively decompose the measurement signal into its PHT and voluntary movement components. The utilization of the OC strategy in the proposed framework is shown to significantly reduce data processing costs without adverse effects on the performance. Simulation results on real-world PHT data demonstrate the ability of the proposed OC-WFLC to yield a dramatic reduction of the processing time, a prerequisite for real-time rehabilitative, wearable, and assistive technology designed for PHT patients.

A novel quaternion‐valued least‐mean kurtosis (QLMK) adaptive filtering algorithm is proposed for three‐ and four‐dimensional processes by using the recent generalised Hamilton‐real (GHR) calculus. The proposed QLMK algorithm based GHR calculus minimises the negated kurtosis of the error signal as a cost function in the quaternion domain, thus provides an elegant way to solve a trade‐off problem between the convergence rate and steady‐state error. Moreover, the proposed QLMK algorithm has naturally a robust behaviour for a wide range of noise signals due to its kurtosis‐based cost function. Furthermore, the steady‐state performance of the proposed QLMK algorithm is analysed to obtain convergence and misadjustment conditions. The comprehensive simulation results on benchmark and real‐world problems show that the use of this cost function defined by the quaternion statistics in the proposed QLMK algorithm allows us to process quaternion‐valued signals and thus, significantly enhances the performance of the adaptive filter in terms of both the steady‐state error and the convergence rate, as compared with the quaternion‐valued least‐mean‐square algorithm based on the recent GHR calculus.

In this paper, kurtosis-based complex-valued real-time recurrent learning (KCRTRL) and kurtosis-based augmented CRTRL (KACRTRL) algorithms are proposed for training fully connected recurrent neural networks (FCRNNs) in the complex domain. These algorithms are designed by minimizing the cost functions based on the kurtosis of a complex-valued error signal. The KCRTRL algorithm exploits the circularity properties of the complex-valued signals, and this algorithm not only provides a faster convergence rate but also results in a lower steady-state error. However, the KCRTRL algorithm is suboptimal in the processing of noncircular (NC) complex-valued signals. On the other hand, the KACRTRL algorithm contains a complete second-order information due to the augmented statistics, thus considerably improves the performance of the FCRNN in the processing of NC complex-valued signals. Simulation results on the one-step-ahead prediction problems show that the proposed KCRTRL algorithm significantly enhances the performance for only circular complex-valued signals, whereas the proposed KACRTRL algorithm provides more superior performance than existing algorithms for NC complex-valued signals in terms of the convergence rate and the steady-state error.

This paper presents a new approach for enhancing Auditory Evoked Potentials (AEP). In this study, we first generated synthetic single trial AEP data at some specified noise levels by using gamma-tone function technique and then applied the proposed Lyapunov theory based filter to the noisy AEP synthetic data. Simulation results have been demonstrated that enhanced AEP with LST based adaptive filter can effectively be used to cancel out background EEG noise for a better measurement.