Nonparametric Test for Change-Point Detection of IoT Time-Series Data

Abstract

The Internet of Things is a concept of computer networks consisting of devices interacting with each other without human intervention. The complete or partial absence of human participation in the operation of such a network makes it necessary to solve the problem of automatic recognition of a significant deviation of the current state of the network from its normal state. The concept of “significance” is vague until it is formalized with the help of rigorous statistical concepts, in particular, the concept of confidence intervals with a given level of significance. In this chapter, we offer a new effective online algorithm for detection of change-points in data generated by IoT devices (tracking data, health rate data etc.). This allows detecting failures, cyber attacks and other deviations in the data. We describe a non-parametric test for evaluation of the statistical hypothesis that data in two adjacent time intervals of a time series have the same distribution. When this hypothesis is true, we detect a change-point. The significance level for the test is less than 0.05. The test is universal in two aspects: it permits ties in a sample and it save the sensitivity when the distributions are greatly overlapped. We demonstrate the prevalence of the proposed test over widely used the Kolmogorov–Smirnov test and the Wilcoxon signed-rank tests using both artificial samples with various distributions and properties (disjoint, slightly overlapped, and strongly overlapped) and real examples. We show that our approach provides robust, sensitive and accurate results.