Multivariate Change Point Detection Research Articles

Multivariate change point detection for heterogeneous series

The multivariate change point detection problem has been encountered across various fields. Most approaches to this problem assume the series is homogeneous, i.e., all the coordinates change concurrently. Hence, the specific subset of the coordinates containing the change points cannot be determined. In this work, we propose S-MCPD, which is capable of detecting the position of multivariate change points for heterogeneous series by identifying specific coordinates of those changed. Specifically, the problem is discussed in the context of variable selection and transformed into the form of sparse group lasso. In simulation studies, we compared S-MCPD with four existing methods, inspect, sbs, dc, and cpm. The results showed that the performance of S-MCPD was comparable to that of inspect and was superior to other methods in terms of evaluation metrics. In addition, S-MCPD can determine not only the positions of change points, but also the subset of coordinates containing the change points, while other existing methods are unable to achieve this. Moreover, S-MCPD does not depend on the constant variance assumption and works quite well even when the covariance changes, which makes our method more practical. These are the two important contributions of our work. Finally, we applied S-MCPD to two real-world datasets to show its effectiveness.

Kernel change point detection based on convergent cross mapping

In this paper, a new method called kernel change point detection based on convergent cross mapping (KCP-CCM) is proposed to address the causality change detection problem. Specifically, KCP is used for running CCM statistics computed by sliding windows based on CCM. Thus, the main goal of this paper is to introduce KCP-CCM as a multivariate change point detection method to capture the evolution of complex systems. To this aim, we choose three types of data sets with different construction methods for simulation experiments to show that KCP-CCM offers a substantial gain in performance over KCP based on correlation and transfer entropy in chaotic system such as the deterministic model. In addition, KCP-CCM, as a causal measurement method, effectively captures the asymmetric dependence between subsystems and provides more accurate information for decision-makers. Finally, we apply it to the financial system under the influence of the 2008 financial crisis to supplement the research on the linkage of Chinese and American stock markets.

Multi-Stage Change Point Detection with Copula Conditional Distribution with PCA and Functional PCA

A global uncertainty environment, such as the COVID-19 pandemic, has affected the manufacturing industry severely in terms of supply and demand balancing. So, it is common that one stage statistical process control (SPC) chart affects the next-stage SPC chart. It is our research objective to consider a conditional case for the multi-stage multivariate change point detection (CPD) model for highly correlated multivariate data via copula conditional distributions with principal component analysis (PCA) and functional PCA (FPCA). First of all, we review the current available multivariate CPD models, which are the energy test-based control chart (ETCC) and the nonparametric multivariate change point model (NPMVCP). We extend the current available CPD models to the conditional multi-stage multivariate CPD model via copula conditional distributions with PCA for linear normal multivariate data and FPCA for nonlinear non-normal multivariate data.

Quantifying the Contributions of Climate Change and Human Activities to Drought Extremes, Using an Improved Evaluation Framework

An increasing amount of studies have emphasized that more frequent and extensive extreme events have occurred around the world. The effects of climate change and anthropogenic activities on the variation in runoff have been studied extensively. However, the effects of variation in hydrological extremes have rarely been studied. In this study, a modeling framework was developed to quantify the time-varying probability of extreme hydrological drought events under a changing environment, and the framework includes standardized runoff index construction, a change point test, generalized extreme value modeling, a return years analysis and an evaluation of the impact of climate change and human activities. Importantly, unlike the common change point test in the individual runoff series, the copula method was introduced to determine the change in the precipitation-runoff dependence structure. Generalized extreme value models were developed to make inferences about the return probability of the extreme standardized runoff index. The new method was applied to the Jinshajiang River Basin (JSJR). The results show that a change point in the relationship between precipitation and runoff occurred in 1995. Even though the climate became slightly drier, extreme drought was alleviated in the JSJR, and human activities were the main contributors to drought mitigation. The copula multivariate change point detection was accurate. Studying the impacts of climate change and human activities on general runoff and hydrological drought extremes is important to better understanding complex water resource variations.

Nonparametric Bayesian approach to the detection of change point in statistical process control

This paper gives an intensive overview of nonparametric Bayesian model relevant to the determination of change point in a process control. We first introduce statistical process control and develop on it describing Bayesian parametric methods followed by the nonparametric Bayesian modeling based on Dirichlet process. This research proposes a new nonparametric Bayesian change point detection approach which in contrast to the Markov approach of Chib [6] uses the Dirichlet process prior to allow an integrative transition of probability from the posterior distribution. Although the Bayesian nonparametric technique on the mixture does not serve as an automated tool for the selection of the number of components in the finite mixture. The Bayesian nonparametric mixture shows a misspecication model properly which has been explained further in the methodology. This research shows the principal step-bystep algorithm using nonparametric Bayesian technique with the Dirichlet process prior defined on the distribution to the detection of change point. This approach can be further extended in the multi-variate change point detection which will be studied in the near future.

Recent changes (1973-2014 versus 1903-1972) in the flow regime of the Lower Paraná River and current fluvial pollution warnings in its Delta Biosphere Reserve.

Alterations in flow regimes of large rivers may originate or increase risks to ecosystems and humans. The Paraná River basin (South America) undergoes human pressures (e.g., heavy damming in the upper basin, deforestation, and mixed pollution) that may affect the water quantity and quality of its terminal Delta (Argentina). In this study, after applying univariate and multivariate change-point detection and trend analyses to the daily data series of flows incoming to the Delta (Paraná-Santa Fe section), flow characteristics were compared by Indicators of Hydrologic Alteration (IHA) and Environmental Flow Components (EFC). Some flood characteristics were also compared from hydrometric levels in the middle Delta (San Pedro station). Chemical and microbiological water variables in the main rivers of the "Paraná Delta" Biosphere Reserve were examined during two extreme hydrologic years (October 2008 to July 2010) to detect potential risk factors in association with hydrologic conditions. In the Lower Paraná River, a historical period (1903-1972) and two more altered periods (1973-1999wet period and 2000-2014dry period) were identified. Flow duration curves evidenced different changes in both altered periods, reflecting the joint effect of climatic variability and human influence. The most evident alterations in the flow regime were the lack of record of the extreme-low-flow component, the attenuation of monthly flow seasonality, and the increase in the number of reversals (dry period) and in the variability of maximum and minimum flow dates. These alterations are consistent with the monthly and daily flow regulation by upstream dams evidenced by available data from the current dry period. In the middle Delta, the marked monthly seasonality in flood days decreased only in the wet period. The proportion between the number of flood days exceeding the evacuation level and that of those exceeding the warning level doubled in the wet period but decreased only slightly in the dry period. In the Delta Reserve rivers, concentrations of Escherichia coli, cadmium, lead, iron, manganese, and ammonium exceeded guideline levels under a severe drought and a dispersal of cyanobacteria appeared under a high-flow pulse in La Niña year. The ammonium concentration exceeded the level for human drink with the overbanking flood stage in El Niño year. These occasional detections pose a potential risk to the aquatic life and, especially, to the inhabitants of the Reserve. Flow duration curves, IHA, and EFC are useful tools to evaluate trends or changes of ecological and social relevance in flow regime characteristics.

Expectation Maximization method for multivariate change point detection in presence of unknown and changing covariance

Data analysis plays an important role in system modeling, monitoring and optimization. Among those data analysis techniques, change point detection has been widely applied in various areas including chemical process, climate monitoring, examination of gene expressions and quality control in the manufacturing industry, etc. In this paper, an Expectation Maximization (EM) algorithm is proposed to detect the time instants at which data properties are subject to change. The problem is solved in the presence of unknown and changing mean and covariance in process data. Performance of the proposed algorithm is evaluated through simulated and experimental study. The results demonstrate satisfactory detection of single and multiple changes using EM approach.

Bayesian and Expectation Maximization methods for multivariate change point detection

Process data are the most important information in all aspects of plant monitoring and control applications. These data, stemming from instruments, carry the necessary information that assists plant operations. One of the common problems of process instrument readings is their deviation from true values due to instrument bias or systematic error. Detection of change points in process data is the first step for a more insightful analysis of hidden factors affecting the process. In this paper, both Bayesian and Expectation and Maximization (EM) methods are considered for change point detection problem of multivariate data with both single and multiple changes. The performance of EM is compared with the Bayesian approach. Simulation results show superiority of EM in the case of improper selection of priors while the Bayesian approach has less computation demand. The proposed algorithms are evaluated through several examples, two from simulated random data and one from a CSTR problem. It is also verified through an experimental study of a hybrid tank system.

A Multivariate Change Point Detection Procedure for Monitoring Mean and Covariance Simultaneously

The signal issued by a control chart triggers the process professionals to investigate the special cause. Change point methods simplify the efforts to search for and identify the special cause. In this study, using maximum likelihood estimation, a multivariate joint change point estimation procedure for monitoring both location and dispersion simultaneously is proposed. After a signal is generated by the simultaneously used Hotelling's T 2 and/or generalized variance control charts, the procedure starts detecting the time of the change. The performance of the proposed method for several structural changes for the mean vector and covariance matrix is discussed.