In this paper, we propose a novel family of on?line censoring (OC) based complex-valued least mean kurtosis (CLMK) algorithms by inspiring the advantages of the online censoring strategy and kurtosis based cost function. We first develop important members of this family of algorithms such as OC based CLMK (OC-CLMK) and augmented CLMK (OC-ACLMK). These algorithms censor less informative complex-valued data streams in an online manner and keep only the most informative ones for performing their weight vector updates. Thus, they reduce the costs of data processing without markedly affecting performance accuracy. However, they do not take into account the possible outliers that disturb their performances considerably. Therefore, we also develop robust members such as robust OC-CLMK (ROC-CLMK) and OC-ACLMK (ROC?CLMK) algorithms, which censor the possible outliers as well as less informative complex-valued data streams. The convergence analyses of the proposed algorithms in the sense of Lyapunov are also presented to derive the bounds of their step sizes in a compact form. The simulation results on large-scale system identification and regression scenarios affirm the mentioned attractive features of the proposed algorithms. This study also shows that the noteworthy properties of the proposed algorithms will provide important contributions to the processing of complex-valued big data streams.
