Interactive Change Point Detection Approaches in Time-Series

Abstract

Change point detection becomes more and more important as datasets increase in size, where unsupervised detection algorithms can help users process data. This is of importance for datasets where multiple phases are present and need to be separated in order to be compared. To detect change points, a number of unsupervised algorithms have been developed which are based on different principles. One approach is to define an optimisation problem and minimise a cost function along with a penalty function. Another approach uses Bayesian statistics to predict the probability of a specific point being a change point. This study examines how the algorithms are affected by features in the data, and the possibility to incorporate user feedback and a priori knowledge about the data. The optimisation and Bayesian approaches for offline change point detection are studied and applied to simulated datasets as well as a real world multi-phase dataset. In the optimisation approach, the choice of the cost function affects the predictions made by the algorithm. In extension to the existing studies, a new type of cost function using Tikhonov regularisation is introduced. The Bayesian approach calculates the posterior distribution for the probability of time steps being a change point. It uses a priori knowledge on the distance between consecutive change points and a likelihood function with information about the segments. Performance comparison in terms of accuracy of the two approaches form the foundation of this work. The study has found that the performance of the change point detection algorithms are affected by the features in the data. The approaches have previously been studied separately and a novelty lies in comparing the predictions made by the two approaches in a specific setting, consisting of simulated datasets and a real world example. Based on the comparison of various change point detection algorithms, several directions for future research are discussed. A potential extension is to apply the studied concept for offline algorithms, to the corresponding online algorithms. The study of other cost functions can be explored further, with emphasis on modified versions of the regularised cost functions presented in this work. Key