Change point detection in time series using martingales

Abstract

Data streaming is becoming a more critical area of research as hardware and software become more sophisticated over time. Therefore, observation and identification of anomalies in many time-series datasets have become imperative to improve the development of a variety of applications. However, current algorithms must deal with issues related to data extraction, inadequate data analytic models, and uncertainty in detecting changes in time varying data streams. Moreover, although conventional approaches can discover changes in time series datasets, they cannot completely isolate the issue of noise interference which can lead to false positives. This research critically focuses on the question: is there a robust method that can detect changes effectively across time series (univariate or multivariate)without supervision regardless of the time series characteristics and patterns? In that case, several new unsupervised methods are proposed to discover change points in univariate and multivariate time series using Martingales. Firstly, the proposed procedures apply weight to the Martingale points to isolate false positives in the sequence. Secondly, a threshold is determined to estimate changes in the data streams. Lastly, optimisation techniques are applied to improve the performance of the approaches by identifying the optimal tuning parameter values for the suggested algorithms. For univariate analysis, the suggested algorithms are the Moving median of the Martingale Sequence (MMS) and Gaussian Moving Average of the Martingale Sequence (GAS). These methods are adapted for multivariate analysis. The proposed methods show promising results (over 2% improvement) in accuracy, precision, recall, F1-score and G-mean over traditional methods such as randomised power martingale. These results show that the proposed methods can identify change points and gait bout(s) in electromagnetic and human activity recognition time series.

Date of Award	May 2023
Original language	English
Supervisor	Sally McClean (Supervisor) & Jorge Martinez Carracedo (Supervisor)