Time Series Clustering Method Research Articles

Multivariate time series clustering based on fuzzy cognitive maps and community detection

Most time series clustering methods mainly focus on univariate time series (UTS). Compared with UTS, multivariate time series (MTS) consists of multiple components. Although interest in MTS clustering is increasing, its performance is far from satisfactory. Most traditional MTS clustering methods may have two limitations. First, they do not consider both the temporal features of each component and the relationship between the components. Second, they can only identify the local relationship between adjacent data, but cannot obtain long-distance global relationships and capture clusters of arbitrary shapes. In this paper, we develop a method for MTS clustering based on fuzzy cognitive maps (FCMs) and community detection, termed as MTSC-FCM-CD. To overcome the first limitation, we use FCM to represent MTS; FCM can extract temporal features while preserving the relationship between components in MTS. To overcome the second limitation, we use the community detection algorithm to cluster the global relations, which is different from the traditional nearest neighbor distance-based method. In the calculation process, the similarity between FCMs should be used to build a complex network. Existing methods calculate the similarity between FCMs, only considering the numerical characteristics but ignoring the topological structure. To solve this problem, we design a two-stage similarity measure to build a complex network. In comparison to the existing methods, the experimental results on twenty benchmark datasets demonstrate the effectiveness of MTSC-FCM-CD in MTS clustering.

TSCAPE: time series clustering with curve analysis and projection on an Euclidean space

The ever-growing use of digital systems has led to the accumulation of vast datasets, particularly time series, depicting the temporal evolution of variables and systems. Analysing these time series presents a tremendous challenge due to their inherent complexity and heterogeneity. Addressing an industrial need in the pharmaceutical wholesale sector, this paper introduces a new clustering method for time series: TSCAPE. The TSCAPE method uses a distance matrix calculated using dynamic time warping, followed by multidimensional scaling to project time series into a 2D Euclidean space, thus improving the last clustering stage by K-Means. Unlike conventional techniques, this approach, based on clustering of representation of distances in a Euclidean plane rather than on the curve shape, directly enhances the efficiency of the clustering process. The methodology exhibits significant potential for diverse applications, accommodating varied data types and irregular time series shapes. The research compares multiple variants and proposes metrics to assess their effectiveness on two open-access datasets. The results demonstrate the method's superiority over “only distance comparison clustering techniques”, like dynamic time warping and K-Means, with future prospects aimed at predictive applications and refining the clustering process by exploring alternative, more powerful clustering algorithms.

Bayesian Semiparametric Local Clustering of Multiple Time Series Data

In multiple time series data, clustering the component profiles can identify meaningful latent groups while also detecting interesting change points in their trajectories. Conventional time series clustering methods, however, suffer the drawback of requiring the co-clustered units to have the same cluster membership throughout the entire time domain. In contrast to these “global” clustering methods, we develop a Bayesian “local” clustering method that allows the functions to flexibly change their cluster memberships over time. We design a Markov chain Monte Carlo algorithm to implement our method. We illustrate the method in several real-world datasets, where time-varying cluster memberships provide meaningful inferences about the underlying processes. These include a public health dataset to showcase the more detailed inference our method can provide over global clustering alternatives, and a temperature dataset to demonstrate our method’s utility as a flexible change point detection method. Supplemental materials for this article, including R codes implementing the method, are available online.

Characterizing Pairwise U-Turn Behavior in Fish: A Data-Driven Analysis.

We applied the time-series clustering method to analyze the trajectory data of rummy-nose tetra (Hemigrammus rhodostomus), with a particular focus on their spontaneous paired turning behavior. Firstly, an automated U-turn maneuver identification method was proposed to extract turning behaviors from the open trajectory data of two fish swimming in an annular tank. We revealed two distinct ways of pairwise U-turn swimming, named dominated turn and non-dominated turn. Upon comparison, the dominated turn is smoother and more efficient, with a fixed leader-follower relationship, i.e., the leader dominates the turning process. Because these two distinct ways corresponded to different patterns of turning feature parameters over time, we incorporated the Toeplitz inverse covariance-based clustering (TICC) method to gain deeper insights into this process. Pairwise turning behavior was decomposed into some elemental state compositions. Specifically, we found that the main influencing factor for a spontaneous U-turn is collision avoidance with the wall. In dominated turn, when inter-individual distances were appropriate, fish adjusted their positions and movement directions to achieve turning. Conversely, in closely spaced non-dominated turn, various factors such as changes in distance, velocity, and movement direction resulted in more complex behaviors. The purpose of our study is to integrate common location-based analysis methods with time-series clustering methods to analyze biological behavioral data. The study provides valuable insights into the U-turn behavior, motion characteristics, and decision factors of rummy-nose tetra during pairwise swimming. Additionally, the study extends the analysis of fish interaction features through the application of time-series clustering methods, offering a fresh perspective for the analysis of biological collective data.

Refined Urban Grid Simulation Planning Based on Low Carbon Goal Achievement

Abstract In this paper, a new grid planning combined with low-carbon operation simulation is proposed, a new grid planning and low-carbon operation simulation model is proposed, and the new grid planning model is investigated and illustrated from the four dimensions of constraints. For the new grid simulation planning model, the solution efficiency of the new grid planning model combined with low-carbon operation simulation is improved by the time series clustering method and the extreme scenario identification method based on the amount of lost load. Starting from the low-carbon benefit dynamics of the generation side and the consumption side, a refined urban new grid low-carbon benefit dynamic evaluation model is constructed, while the model parameters and table functions are set, and the low-carbon urban grid simulation planning based on low-carbon simulation is empirically analyzed by means of simulation analysis. The results show that in grid planning, when the carbon emission intensity is 1000gCO2/kWh, the S4 scenario only needs to add an extreme scenario in the iterative process to achieve a relative error accuracy of 0.1%, and the method of using the new grid planning and the low-carbon operation simulation model is sufficient to achieve the target of the loss of load rate and carbon emission intensity. In the evaluation of the low-carbon effect, with the increase in investment amount, the installed capacity of clean energy and the total CO2 emission reduction of the refined urban grid will show two relatively obvious upward trends.

SE-shapelets: Semi-supervised Clustering of Time Series Using Representative Shapelets

Shapelets that discriminate time series using local features (subsequences) are promising for time series clustering. Existing time series clustering methods may fail to capture representative shapelets because they discover shapelets from a large pool of uninformative subsequences, and thus result in low clustering accuracy. This paper proposes a Semi-supervised Clustering of Time Series Using Representative Shapelets (SE-Shapelets) method, which utilizes a small number of labeled and propagated pseudo-labeled time series to help discover representative shapelets, thereby improving the clustering accuracy. In SE-Shapelets, we propose two techniques to discover representative shapelets for the effective clustering of time series. (1) A salient subsequence chain (SSC) that can extract salient subsequences (as candidate shapelets) of a labeled/pseudo-labeled time series, which helps remove massive uninformative subsequences from the pool. (2) A linear discriminant selection (LDS) algorithm to identify shapelets that can capture representative local features of time series in different classes, for convenient clustering. Experiments on UCR time series datasets demonstrate that SE-shapelets discovers representative shapelets and achieves higher clustering accuracy than counterpart semi-supervised time series clustering methods.

Strategies for improving the industrial carbon emission efficiency in China: an approach based on trend prediction and regional learning mechanism.

It is an important way for mining the characteristics of regional carbon emission efficiency and exploring regional similarity to learn from intergovernmental learning mechanisms and regional industrial low-carbon development experiences. This study proposes a regional learning mechanism of industrial carbon emission efficiency (ICEE) prediction and regional similarity analysis to explore strategies for carbon emission reduction. We first calculated the industrial carbon emission efficiency of 30 provinces in China from 2000 to 2021 using the super-SBM model. Secondly, the spatiotemporal characteristics of industrial carbon emission efficiency were explored through the space-time cube model, time series clustering method, and local outlier analysis. Finally, the screening of regions with low efficiency levels and the search for learning objects were realized by forest regression prediction and regional similarity calculation. The results of the study were as follows: (1) There were significant differences in industrial carbon emission efficiency among different provinces. (2) Based on the time series clustering results, we found that there were similar change characteristics of industrial carbon emission efficiency in different provinces. (3) The industrial carbon emission efficiency of most provinces had significant correlation in space and time, mainly in high-high clustering. (4) The industrial carbon emission efficiency of most regions will maintain a high efficiency level in the next 10 years, but the six provinces of Xinjiang, Qinghai, Gansu, Ningxia, Liaoning, and Heilongjiang will always be at a low efficiency level. It is possible to set appropriate learning targets for each region and to find lessons to be learned from the regions with high similarity by calculating the similarity between each province and the six provinces.

Mining the English application learning patterns of college students based on time series clustering

As a convenient learning tool in the We Media era, mobile apps have been paid more and more attention by college students because of their accompanying timeliness and practicality. With the increasing number of English learning apps, many such apps provide college students with new ways to obtain learning resources and diversified learning modes. The related research in the field of mobile-assisted language learning at home and abroad has developed over nearly 20 years, basically following the route from theory to application in practice, but there have been few process studies on learners’ individual language skill learning behaviors based on mobile platform data. In this study, the time series clustering method was adopted, and the learning behavior of college students in an English vocabulary learning app in China was selected for data mining. Firstly, taking the “single-day memorization amount” as the measurement index, the memorization records of college students in the whole use cycle were extracted and processed into trajectory data, and the KmL algorithm was used to cluster the trajectory of the memorization amount in the time series. According to the intra-class average trajectory, the characteristics of learning behavior changes among the different college students are summarized, and two learning modes are depicted. Secondly, through the experimental analysis, it was found that adopting the English learning model three weeks before an exam can effectively stimulate college students and improve their willingness to learn and continue using the app.

Time series clustering based on normal cloud model and complex network

When data mining research is conducted, it is difficult to obtain precise domain knowledge to set a similarity threshold. Furthermore, noise and missing values are inevitable. Missing values and noise without pre-processing are challenges for many algorithms. A time-series clustering method is proposed based on the normal cloud model and complex networks. Matrix profile similarity measurement, normal cloud model generation and filtering, cloud model expectation curve weighting, degree centrality reweighting, and community discovery in complex networks are the five stages of the proposed clustering algorithm. Local features are considered, and the effects of missing values are reduced when performing similarity measurements. The normal cloud model can be used to set thresholds adaptively. The Louvain algorithm accomplishes the clustering task in complex networks without specifying the clusters. Experiments are conducted on 94 datasets and are compared with 8 clustering methods in the UCR time-series clustering benchmark study. Experimental results indicate that the proposed method can perform well on many datasets.

A ternary-frequency cryptocurrency price prediction scheme by ensemble of clustering and reconstructing intrinsic mode functions based on CEEMDAN

Cryptocurrency, particularly Bitcoin, is a significant financial asset for investors, but predicting its price is challenging due to its volatile and erratic nature. In this study, we suggest a novel ternary-frequency (TF) prediction scheme for Bitcoin prices, which combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), a time series clustering method, and the reconstruction of intrinsic mode functions (IMFs). In the proposed scheme, CEEMDAN was utilized to decompose Bitcoin’s daily price into IMFs, then prototypes of time series clustering were used to construct robust ensemble clusters. The IMFs in the ensemble clusters were reconstructed into ensemble time series and then identified as three different frequencies, which were respectively used in a prediction model to generate different predicted values, and then aggregated to produce the final prediction results. To generate three different TF Bitcoin price prediction schemes, this study employed three prominent prediction algorithms: autoregressive integrated moving average with exogenous variables (ARIMAX), multivariate adaptive regression splines (MARS), and extreme gradient boosting (XGB); these resulted in three distinct models, named TF-ARIMAX, TF-MARS, and TF-XGB. Empirical results from the two daily Bitcoin and one daily Ethereum closing price datasets showed that the proposed TF prediction scheme outperformed other benchmark approaches. Moreover, among the three TF models, TF-MARS produced superior prediction accuracy compared to both TF-ARIMAX and TF-XGB models, and proved to be an effective alternative for cryptocurrency price prediction.

Identifying Pacing Profiles in 2000 Metre World Championship Rowing

The pacing strategy adopted by athletes is a major determinants of success during timed competition. Various pacing profiles are reported in the literature and its importance depends on the mode of sport. However, in 2000 metre rowing, the definition of these pacing profiles has been limited by the minimal availability of data. Purpose: Our aim is to objectively identify pacing profiles used in World Championship 2000 metre rowing races using reproducible methods. Methods: We use the average speed for each 50 metre split for each available boat in every race of the Rowing World Championships from 2010-2017. This data was scraped from www.worldrowing.com. This data set is publicly available (https://github.com/danichusfu/rowing_pacing_profiles) to help the field of rowing research. Pacing profiles are determined by using k-shape clustering, a time series clustering method. A multinomial logistic regression is then fit to test whether variables such as boat size, gender, round, or rank are associated with pacing profiles. Results: Four pacing strategies (Even, Positive, Reverse J-Shaped, and U-Shaped) are identified from the clustering process. Boat size, round (Heat vs Finals), rank, gender, and weight class are all found to affect pacing profiles. Conclusion: We use an objective methodology with more granular data to identify four pacing strategies. We identify important associations between these pacing profiles and race factors. Finally, we make the full data set public to further rowing research and to replicate our results.

A two-stage deep graph clustering method for identifying the evolutionary patterns of the time series of animation view counts

Time-series clustering of view counts with changes in online time can identify animated series with similar evolutionary count patterns over time, which may help companies reduce their investment risk. For time-series data of animation view counts, most existing time-series clustering methods ignore both the local relationships within data and global relationships between data, making it challenging to identify animated series with similar evolutionary patterns. Therefore, we propose a two-stage deep graph clustering method that involves graph data construction and deep graph clustering. Specifically, graph data construction converts time-series data into graph data, while deep graph clustering uses a temporal convolutional network and graph convolutional network to learn features from the time-series data and graph data, respectively. The entire model is then trained end-to-end to complete the clustering task, utilizing a dual self-supervised module. This study utilizes two datasets to evaluate the clustering performance of our proposed model in comparison to baseline methods. The datasets consist of view count data from 185 animated series on Tencent Video from 2018 to 2022, as well as a public time-series BME dataset. The experimental results demonstrate that our model outperforms the baseline methods on both datasets. Additionally, through visualizing the identified three classes of evolutionary patterns, we propose new product development strategies for animation enterprises.

Comparison of time series clustering methods for identifying novel subphenotypes of patients with infection.

Severe infection can lead to organ dysfunction and sepsis. Identifying subphenotypes of infected patients is essential for personalized management. It is unknown how different time series clustering algorithms compare in identifying these subphenotypes. Patients with suspected infection admitted between 2014 and 2019 to 4 hospitals in Emory healthcare were included, split into separate training and validation cohorts. Dynamic time warping (DTW) was applied to vital signs from the first 8h of hospitalization, and hierarchical clustering (DTW-HC) and partition around medoids (DTW-PAM) were used to cluster patients into subphenotypes. DTW-HC, DTW-PAM, and a previously published group-based trajectory model (GBTM) were evaluated for agreement in subphenotype clusters, trajectory patterns, and subphenotype associations with clinical outcomes and treatment responses. There were 12 473 patients in training and 8256 patients in validation cohorts. DTW-HC, DTW-PAM, and GBTM models resulted in 4 consistent vitals trajectory patterns with significant agreement in clustering (71-80% agreement, P < .001): group A was hyperthermic, tachycardic, tachypneic, and hypotensive. Group B was hyperthermic, tachycardic, tachypneic, and hypertensive. Groups C and D had lower temperatures, heart rates, and respiratory rates, with group C normotensive and group D hypotensive. Group A had higher odds ratio of 30-day inpatient mortality (P < .01) and group D had significant mortality benefit from balanced crystalloids compared to saline (P < .01) in all 3 models. DTW- and GBTM-based clustering algorithms applied to vital signs in infected patients identified consistent subphenotypes with distinct clinical outcomes and treatment responses. Time series clustering with distinct computational approaches demonstrate similar performance and significant agreement in the resulting subphenotypes.

Equivalence partition based morphological similarity clustering for large-scale time series

Data clustering belongs to the category of unsupervised learning and plays an important role in the dynamic systems and big data. The clustering problem of sampled time-series data is undoubtedly much more challenging than that of repeatable sampling data. Most of the existing time-series clustering methods stay at the level of algorithm design, lacking rigorous theoretical foundation and being inefficient in dealing with large-scale time series. To address this issue, in this paper, we establish the mathematical theory for the large-scale time series clustering of dynamic system. The main contributions of this paper include proposing the concept of time series morphological isomorphism, proving that translation isomorphism and stretching isomorphism are equivalent relations, developing the calculation method of morphological similarity measure, and establishing a new time series clustering method based on equivalent partition and morphological similarity. These contributions provide a new theoretical foundation and practical method for the clustering of large-scale time series. Simulation results in typical applications verify the validity and practicability of the aforementioned clustering methods.

A Multivariate Time Series Anomaly Detection Method Based on Clustered Particle Swarm Optimization

Due to the advent of 5G and the integration of sensors, sensor nodes need to collect data from multiple sources simultaneously.Traditional anomaly detection methods for single attribute time series detect multivariate data, low detection accuracy, and significant node energy consumption. To avoid these problems, this paper provides an improved FCM multivariate time series clustering method based on the sliding window. Based on the CPSO optimal weight, the reconstruction error realizes anomaly detection. Experiments on different datasets demonstrate the effectiveness of the algorithm. Moreover, compared with the three classical methods, the results show that the proposed algorithm has higher detection accuracy and accuracy.

Time-series clustering and forecasting household electricity demand using smart meter data

This study forecasts electricity consumption in a smart grid environment. We present a bottom-up prediction method using a combination of forecasting values based on time-series clustering using advanced metering infrastructure (AMI) data, one of the core smart grid technologies. Remote data metering every 15 min to 1 h is possible with real-time communication on power generation information, consumption, and AMI development. Hence, its prediction is more challenging due to the large variation of each household’s electricity. These issues were solved by time-series clustering methods using Euclidean distances and Dynamic Time Warping distance. The auto-regressive integrated moving average (ARIMA), ARIMA exogenous (ARIMAX), double seasonal Holt–Winters (DSHW), trigonometric, Box–Cox transform, autoregressive moving average errors, trend and seasonal components (TBATS), neural network nonlinear autoregressive (NNAR), and nonlinear autoregressive exogenous (NARX) models were used for demand forecasting based on clustering. The result showed that the time-series clustering method performed better than that using the total amount of electricity demand regarding the mean absolute percentage error and root mean squared error.Hence, various exogenous variables were considered to improve model accuracy. The model considering exogenous variables—cooling degree day, humidity, insolation, indicator variables, and generation power consumption performed better than that without exogenous variables.

Time series clustering with an EM algorithm for mixtures of linear Gaussian state space models

In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the dynamics in various time series. To address this problem, we propose a novel model-based time series clustering method with mixtures of linear Gaussian state space models, which have high flexibility. The proposed method uses a new expectation-maximization algorithm for the mixture model to estimate the model parameters, and determines the number of clusters using the Bayesian information criterion. Experiments on a simulated dataset demonstrate the effectiveness of the method in clustering, parameter estimation, and model selection. The method is applied to real datasets commonly used to evaluate time series clustering methods. Results showed that the proposed method produces clustering results that are as accurate or more accurate than those obtained using previous methods.

Analysis of Worldwide Greenhouse and Carbon Monoxide Gas Emissions: Which Countries Exhibit a Special Pattern? A Closer Look via Twitter.

There is significant global concern about the harmful effects of greenhouse gas and carbon monoxide emissions (deforestation, air pollution, global warming, etc.). The 2015 Paris Agreement on climate change aspires to reduce global warming by achieving a climate-neutral world. Research has been carried out to calculate and diminish the aforementioned emissions in waste, power industry, transport, building, in addition to other areas. The aim of this paper is to analyse the carbon and greenhouse gas emissions across countries around the globe in order to find patterns and correlate them to socio-economic indicators [gross national income (GNI), industrial production (IPI) and human development indexes (HDI)] as well as Twitter interactions regarding climate change. For this purpose, time series and socio-economic data have been downloaded from different repositories including EDGAR (Emissions Database for Global Atmospheric Research), World Bank and UNDP (United Nations Development Programme). Although classical clustering algorithms have already been used in the examination of some environmental issues, we use a non-parametric time series clustering method, which has been suggested in certain scientific literature as a more flexible approach, since any ad hoc parametric assumptions are required. The chosen socio-economic indicators have also demonstrated their relevance in pieces of research related to various fields. With respect to Twitter, which is one of the most popular social networks nowadays, significant analysis has also been performed on the basis of capturing citizens' perceptions on a multitude of matters. We found that several countries such as Brazil, India, China, Nigeria, Russia, United States, Spain, Andorra, Greece, and Qatar show differences in carbon and greenhouse gas emissions patterns. Besides, there does not seem to be a correlation between GNI, IPI and HDI as well as the above mentioned emissions Regarding Twitter interactions, a dissimilarity in the distribution of hashtags was detected between the aforementioned countries and the rest of the world. This research can help to identify countries in which more governmental measures are needed to reduce the type of emissions analysed in certain industrial sectors. In addition, it points out the topics related to climate change that seem to generate the most debate on Twitter for countries with an unusual pattern. The online version contains supplementary material available at 10.1007/s41742-023-00510-4.

Deployment of Renewable Energy Sources: Empirical Evidence in Identifying Clusters with Dynamic Time Warping

Deployment of renewable energy sources has caused a seismic shift in the world energy arena. Individual and coordinated efforts across countries and regions are shaping the world for the future, including business models which are supported globally to achieve net zero goals by 2050. This has resulted in changing cost structures, prices, and investment in energy uses, and approaching towards most sustainable environments for most of the regions. Our aim in this paper is to identify clusters of countries, where within a particular cluster, the levels of deployment of renewable energy sources are similar while across clusters, they are different. We propose a time series clustering method capturing the time-varying features of the renewable energy time series of 130 countries to enable the assessment of how similar or how different the usage is in relation to the Organisation for Economic Co-operation and Development (OECD) status of countries, their regional location and their income grouping. We use Dynamic Time Warping (DTW) which is a method that calculates an optimal match between two given time series with certain restrictions. Using DTW, we the adopt the Partitioning Around Medoids technique in a fuzzy framework to obtain cluster solutions. Our analysis shows that both 4-cluster and 5-cluster solutions best capture country separation based on OECD status, regional location and income grouping.

CSMVC: A Multiview Method for Multivariate Time-Series Clustering.

Multivariate time-series (MTS) clustering is a fundamental technique in data mining with a wide range of real-world applications. To date, though some approaches have been developed, they suffer from various drawbacks, such as high computational cost or loss of information. Most existing approaches are single-view methods without considering the benefits of mutual-support multiple views. Moreover, due to its data structure, MTS data cannot be handled well by most multiview clustering methods. Toward this end, we propose a consistent and specific non-negative matrix factorization-based multiview clustering (CSMVC) method for MTS clustering. The proposed method constructs a multilayer graph to represent the original MTS data and generates multiple views with a subspace technique. The obtained multiview data are processed through a novel non-negative matrix factorization (NMF) method, which can explore the view-consistent and view-specific information simultaneously. Furthermore, an alternating optimization scheme is proposed to solve the corresponding optimization problem. We conduct extensive experiments on 13 benchmark datasets and the results demonstrate the superiority of our proposed method against other state-of-the-art algorithms under a wide range of evaluation metrics.