Constructing a Neural-Net Model of Network Traffic Using the Topologic Analysis of Its Time Series Complexity

Abstract

The dynamics of data traffic intensity is examined using traffic measurements at the interface switch input. The wish to prevent failures of trunk line equipment and take the full advantage of network resources makes it necessary to be able to predict the network usage. The research tackles the problem of building a predicting neural-net model of the time sequence of network traffic.

Topological data analysis methods are used for data preprocessing. Nonlinear dynamics algorithms are used to choose the neural net architecture. Topological data analysis methods allow the computation of time sequence invariants. The probability function for random field maxima cannot be described analytically. However, computational topology algorithms make it possible to approximate this function using the expected value of Euler’s characteristic defined over a set of peaks. The expected values of Euler’s characteristic are found by constructing persistence diagrams and computing barcode lengths. A solution of the problem with the help of R-based libraries is given. The computation of Euler’s characteristics allows us to divide the whole data set into several uniform subsets. Predicting neural-net models are built for each of such subsets. Whitney and Takens theorems are used for determining the architecture of the sought-for neural net model. According to these theorems, the associative properties of a mathematical model depend on how accurate the dimensionality of the dynamic system is defined. The sub-problem is solved using nonlinear dynamics algorithms and calculating the correlation integral. The goal of the research is to provide ways to secure the effective transmission of data packets.