Rough-Fuzzy CPD: a gradual change point detection algorithm

• Published in: Journal of data, information and management (Online) Vol. 4; no. 3; pp. 243 - 266
• Main Authors: Bhaduri, Ritwik, Roy, Subhrajyoty, Pal, Sankar K.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2022; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Business and Management; Computational Intelligence; Engineering; Fuzzy set theory; Fuzzy sets; Hypotheses; Hypothesis testing; Language; Methods; Nonparametric statistics; Null hypothesis; Original; Original Article; Performance evaluation; Quality control; Robustness (mathematics); Set theory; Signal processing; Signal to noise ratio; Simulation; Statistical analysis; Time series; Gradual changepoint detection; Fuzzy set; Python package; Rough set
• ISSN: 2524-6356; 2524-6364; 2524-6364
• DOI: 10.1007/s42488-022-00077-3

Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint detection problem, although there is not much work devoted towards gradual changepoints as compared to abrupt ones. Here we present a new approach to solve the changepoint detection problem using the fuzzy rough set theory which is able to detect such gradual changepoints. An expression for the rough-fuzzy estimate of changepoints is derived along with its mathematical properties concerning fast computation. In a statistical hypothesis testing framework, the asymptotic distribution of the proposed statistic on both single and multiple changepoints is derived under the null hypothesis enabling multiple changepoint detection. Extensive simulation studies have been performed to investigate how simple crude statistical measures of disparity can be subjected to improve their efficiency in the estimation of gradual changepoints. Also, the said rough-fuzzy estimate is robust to signal-to-noise ratio, a high degree of fuzziness in true changepoints, and also to hyperparameter values. Simulation studies reveal that the proposed method beats other methods of gradual changepoint detection (including MJPD, HSMUCE, fuzzy methods like FCP, FCMLCP etc) and also popular crisp methods like Binary Segmentation, PELT, and BOCD in detecting gradual changepoints. The applicability of the estimate is demonstrated using multiple real-life datasets including Covid-19. We have developed the python package roufcp for broader dissemination of the methods.