Development of an Algorithm for Identifying Changes in System Dynamics from Time Series

TL;DR

This paper presents an algorithm that detects changes in system dynamics from time series data by analyzing the second largest eigenvalue of a Markov chain, with applications in medical monitoring.

Contribution

The paper introduces a novel method using the second largest eigenvalue of a Markov chain to identify system dynamic changes, supported by empirical and theoretical analysis.

Findings

Change in SLEM correlates with system dynamic shifts.

Method successfully detects hemorrhage in blood pressure data.

Theoretical justification links SLEM changes to transition probability alterations.

Abstract

The development of an algorithm with related mathematical concepts and supporting hypothesis for detecting changes in system dynamics from time series along with empirical analysis and theoretical justification is presented. For the method, changes in the second largest eigenvalue of Markov Chain (SLEM) or mixing rate, is observed as an indicator of the changes in system dynamics. The Markov chain is created from empirical transition probabilities of a time series. The method is developed for the application of detecting hemorrhage from arterial blood pressure in anesthetized swine. The rationale of the change in the SLEM is investigated empirically with an artificial blood pressure model and, by studying correlations with other measures such as smoothness of time series, and density of the transition probability matrix of the Markov chain. The mathematical analysis shows that the change in the SLEM is a consequence of the change in the transition probabilities between different states and reflects information about the system dynamics.