Zero-Crossing Analysis and Information Divergence of Lévy Walks for Real-Time Feature Extraction

A method, based on the Smirnov transform, for generating synthetic data with the statistical properties of Lévy-walks is presented. This method can be utilized for generating arbitrary prescribed probability density functions (pdf). A cybersecurity engineering problem associated with Internet traffic is addressed. The synthetic Lévy-walks process is intertwined with sections of distinct characteristics creating a composite signal that is analyzed through zero-crossing rate (ZCR) within a varying-size window to identify sections. The advantages of the ZCR computation directly in the time-domain are appealing for real-time implementations. Moreover, the characterization of the degree of closeness, via the Kullback-Leibler divergence (KLD), among the pdfs of arbitrary processes (focusing on Lévy walks) and model pdfs is presented. The results obtained from the KLD experiments provide a categorical determination of the closeness degree. These results, a remarkable achievement in this research, are also promising to be used as features for classification of complex signals in real-time.