# Unsupervised Offline Changepoint Detection Ensembles
## 1 Introduction
None of these papers focus on the analysis of various scaling functions and just two of them ([4; 19]) have compared more than one aggregation function. Moreover, just two of the works ([19; 20]) relate to the offline CPD problem, but they select only one base detector for the ensembles--the Lepage nonparametric test is able to assess changes in the mean or the variance. Among the papers, just one [21] uses a technical-related benchmark--KDD Cup 1999 network intrusion detection dataset--while others either use synthetic data or ecology-related data. Finally, all of the works in the CPDE field of knowledge lack generalizing ideas. They do not aim to formulate a framework for various detectors (models), search methods, aggregation, and combination functions for use and analysis. This paper proposes a novel model-centered, independent, scaled (normalized) ensemble approach for the offline changepoint detection problem. Moreover, we select and study various common aggregation functions from outlier, cluster, and classification ensembles and their applicability in CPD ensembles. The pseudocode of the particular suggested ensemble algorithms is presented in Appendix A. Our ensemble approach is based on and extends the famous changepoint detection procedure formulated in [22]. Additionally, we compare the proposed ensemble and original non-ensemble approachesand the various scaling and aggregation functions. For the comparison, we conducted numerical experiments on the two technical benchmarks that contain industrial faults and failures--Tennessee Eastman Process (TEP) benchmark and Skoltech Anomaly Benchmark (SKAB). The algorithms are applied in an unsupervised way without any fitting stage but for a known number of changepoints to look for. We also provide links to the Python source code with the implemented ensemble algorithms and experiment results. The proposed source code is based on the _ruptures_ Python scientific library, presented and described in [22] as well. Our work differs from previous in three key aspects. Firstly, most works focus on the single CPD algorithm and a few situational aggregation functions, not paying attention to the scaling functions. At the same time, we tried to embrace the most common CPD algorithms, scaling and aggregation functions, comparing them during the numerical experiment. Secondly, we work with several cost functions (models), aggregating their results. Just one of the works deals with various base detectors, while the closest to our work [19] not only uses a single model as the base detector but also highlights the aggregation of different test statistics (base detectors) in the ensemble as the possible future research direction. Third, none of the works focus on detecting changepoints in the industrial data. Still, one of the works [20] considers complex embedded systems modeled by an autoregressive moving-average (ARMA) process. One more [21] shows the results on the intrusion detection dataset. Therefore, our work is the first to apply CPDE on the benchmarks with industrial faults and failures, showing the possible applicability in technical diagnostics. Additionally, ensemble analysis for the CPD problem lacks research works, especially when compared with outlier detection, clustering, or classification problems. One of the possible applications of our research is the estimation of the failure time [20] for fault diagnosis, and isolation phases of the technical diagnostics or process monitoring loop [23]. It can help to determine which fault occurred. Accurate models and solutions for fault detection and diagnosis (FDD) make process monitoring systems more efficient and retrospective analysis more correct. Improving the FDD process can help to move to condition-based maintenance, which can be less expensive than other maintenance strategies [24]. Moreover, improving process monitoring develops smart manufacturing and industrial big data environment technologies helping managers to fit industry into the concept of Industry 4.0 [25].