Time Series Clustering Method Research Articles

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.

Financial Market Correlation Analysis and Stock Selection Application Based on TCN-Deep Clustering

It is meaningful to analyze the market correlations for stock selection in the field of financial investment. Since it is difficult for existing deep clustering methods to mine the complex and nonlinear features contained in financial time series, in order to deeply mine the features of financial time series and achieve clustering, a new end-to-end deep clustering method for financial time series is proposed. It contains two modules: an autoencoder feature extraction network based on TCN (temporal convolutional neural) networks and a temporal clustering optimization algorithm with a KL (Kullback–Leibler) divergence. The features of financial time series are represented by the causal convolution and the dilated convolution of TCN networks. Then, the pre-training results based on the KL divergence are fine-tuned to make the clustering results discriminative. The experimental results show that the proposed method outperforms existing deep clustering and general clustering algorithms in the CSI 300 and S&P 500 index markets. In addition, the clustering results combined with an inference strategy can be used to select stocks that perform well or poorly, thus guiding actual stock market trades.

Time series clustering method with cluster validation to identify unknown local cell conditions in the aluminum reduction cell

It is important to identify local cell conditions in the aluminum reduction cell for cell control. However, in the actual aluminum electrolysis process, local cell conditions are unknown based on traditional measurements. Fortunately, the appearance of anode current signals as a new process variable makes it possible to identify local cell conditions. In this paper, without any prior knowledge on local cell conditions, a new time series clustering method with cluster validation is proposed to identify unknown local cell conditions. First, the nature of anode current signals is analyzed and a new process variable named the pseudo-resistance of an anode–cathode path (Rpseudo) is transformed from the anode current signals, which can provide more insights to the aluminum electrolysis process. Then, a time series clustering algorithm that combines fuzzy c-means with the dynamic time warping distance is used to cluster the anode current signals and Rpseudo. Finally, a new clustering validity index is designed and a cluster validation process is proposed to determine the optimal number of clusters. Moreover, different anode current signals for different local cell conditions such as normal working, anode deformation, anode effect and anode slippage are deliberately selected to verify the proposed method. The experimental results show that the proposed method can effectively identify local cell conditions.

Time series clustering via matrix profile and community detection

Time series clustering has been used in diverse scientific areas to extract valuable information from complex and massive time series datasets. To improve the quality and efficiency of the clustering method applied to the field of time series data mining, a method for time series clustering via matrix profile and social network techniques (TCMS) is proposed. Firstly, a matrix profile is utilised to quickly find one pair of the most similar subsequences derived from two time series. The degree of correlation between the two time series is measured as the number of the most similar subsequences. Then, a network is constructed which treats each time series as a vertex and regards the correlations between the time series as edges. The edge weights are assigned according to the degree of correlation. Finally, the network can be divided by a community detection method to achieve time series clustering. The experiments on 45 UCR datasets demonstrate that the proposed method is efficient. The comparison experiments with Multilevel-ɛNN, k-medoids, k-shape, RWS and fastKARs demonstrate that the proposed method is a better approach to clustering time series than state-of-the-art methods.

Decision making towards large-scale alternatives from multiple online platforms by a multivariate time-series-based method

With the increasing popularity of Internet-related techniques, decision-making problems with large-scale alternatives from multiple online platforms, such as consumer choice decisions and movie selections, have been emerging hot topics. How to make a selection from a set of alternatives in multiple online platforms is challenge for consumers. In this study, we introduce a multivariate time-series-based decision-making method to solve the problem with large-scale alternatives. Firstly, we set up a multivariate time series from multiple-platforms regarding each alternative. The weights of these platforms are determined based on the information entropy of time series and the number of received evaluations given by platform users. To calculate the information entropy regarding a large number of alternatives, we adopt a time series clustering method to classify alternatives into different clusters, and then calculate the information entropy of clusters and take it as the information entropy of all alternatives. Afterwards, the scores of alternatives are calculated based on the weighted averaging aggregation operator and the alternatives are ranked according to their scores. We demonstrate the effectiveness of the proposed method in guaranteeing the consistency between ranking results and users' consumption behaviors based on real ratings collected from three film-review websites. It is hoped that the proposed method would be helpful for users to intelligently make a selection from large-scale candidate products or services in multiple platforms.

Time series clustering based on complex network with synchronous matching states

Due to the extensive existence of time series in various fields, more and more research on time series data mining, especially time series clustering, has been done in recent years. Clustering technology can extract valuable information and potential patterns from time series data. This paper proposes a time series Clustering method based on Synchronous matching of Complex networks (CSC). This method uses density peak clustering algorithm to identify the state of each time point and obtains the state sequence according to the timeline of the original time series. State sequences is a new method to represent time series. By comparing two state sequences synchronously, the length of state sequence with step is calculated and the similarity is presented, which forms a new method to calculate the similarity of time series. Based on the obtained time series similarity, the relationship network of time series is constructed. Simultaneously, the community discovery technology is applied to cluster the relationship network and further achieve the complete time series clustering. The detailed process and simulation experiments of CSC method are given. Experimental results on different datasets show that CSC method is superior to other traditional time series clustering methods.

Identifying Major Hydrologic Change Drivers in a Highly Managed Transboundary Endorheic Basin: Integrating Hydro‐Ecological Models and Time Series Data Mining Techniques

AbstractThe fragile balance of endorheic lakes in highly managed semiarid basins with transboundary water issues has been altered by the intertwined effects of global warming and long‐term water mismanagement to support agricultural and industrial demand. The alarming rate of global endorheic lakes' depletion in recent decades necessitates formulating mitigation strategies for ecosystem restoration. However, detecting and quantifying the relative contribution of causal factors (climate variability and anthropogenic stressors) is challenging. This study developed a diagnostic multivariate framework to identify major hydrologic drivers of lake depletion in a highly managed endorheic basin with a complex water distribution system. The framework integrates the Soil and Water Assessment Tool (SWAT) simulations with time series decomposition and clustering methods to identify the major drivers of change. This diagnostic framework was applied to the Salton Sea Transboundary Basin (SSTB), the host of the world's most impaired inland lake. The results showed signs of depletion across the SSTB since late 1998 with no significant changes in climate conditions. The time series data mining of the SSTB water balance components indicated that decreases in lake tributary inflows (−16.4 Mm3 yr−2) in response to decline in Colorado River inflows, associated with state water transfer agreements, are causing the Salton Sea to shrink, not changes in the irrigation operation as commonly believed. The developed multivariate detection and attribution framework is useful for identifying major drivers of change in coupled natural human systems.

Spatial–temporal short-term load forecasting framework via K-shape time series clustering method and graph convolutional networks

Load forecasting, especially short-term load forecasting, is of great significance to the safe operation of power grids and power system optimization. Historical data is commonly applied in the most of existing methods of load forecasting to predict the future data in one time step, which is considered to have a positive effect on the forecasting performance. However, a serious problem is ignored, which is the assumption that the interactions between end-users are often not considered. Such interaction could be considered as a paired non-Euclidean relationship, which could enhance the accuracy of forecasting effects. In this paper, we propose a graph convolutional network prediction framework based on K-shape time series clustering method for short-term load forecasting. User clusters with similar electricity consumption habits could be separated from a large number of users by the proposed framework. Simultaneously, the paired non-Euclidean relationship between users can also be captured by this framework. The proposed framework is evaluated by the dataset of business users in the southeastern United States. The results show that compared with baselines, the framework significantly improves the prediction accuracy in any scale of user groups, as well as future data in one time step and multi-time steps.

Revealing spatiotemporal matching patterns between traffic flux and road resources using big geodata - A case study of Beijing

Mismatch between road system and spatiotemporal heterogeneity of traffic flow is a key reason for traffic congestion. Existing studies mainly focus on local regions or specific times (morning and evening peak), while the spatiotemporal heterogeneity of match and its causes, especially at larger scales, are still insufficiently studied. Herein, we proposed a framework for analyzing the match between traffic flux, i.e. the number of individuals driving into or out of a region per unit time, and road resources, using mobile phone data covering approximately 17 million users over one week in Beijing. Matches were measured through comparisons between the share of traffic flux and that of road resources both globally and locally. First, a global analysis with Gini coefficient revealed the match in Beijing is at a long-lasting low level. Then, the spatiotemporal disparity of match was examined via our proposed regional match index. Specifically, overallocated areas (traffic flux exceeds its corresponding shares of road resources) were mainly along arterial roads, while underallocated ones were in suburbs and gated residential communities. To explore the mechanism, four spatiotemporal matching modes were identified through a time series clustering method, and their distributions were explained by urban function based on ‘point-of-interest’ data.

A novel time series clustering method with fine-tuned support vector regression for customer behavior analysis

Exploring and forecasting customers’ behavior via time series analysis techniques has gained much attention in recent years. In this context, distance-based time series clustering methods are widely utilized to divide customers into segments. However, the performance of distance-based clustering is highly influenced by the distance metrics chosen. Determining a suitable distance metric for raw time series is a challenging task that must consider several factors. Therefore, in this study, we focus on feature-based time series clustering and propose a new featurization technique exploiting the Laplacian feature ranking method to obtain meaningful customer segments. We evaluate the proposed featurization approach with four state-of-the-art clustering methods using the point-of-sale (POS) transaction data. The clustering results indicate that the proposed method outperforms the baseline method in terms of the Silhouette measure. Besides, we present an hybrid support vector regression with the grasshopper optimization (SVRGOA) to forecast customers’ behavior. This method is compared against three benchmarks, and the results reveal that SVRGOA outperforms other models in the majority of cases in terms of the symmetric mean absolute percentage error (SMAPE).

Dynamic characteristics of the COVID-19 epidemic in China’s major cities

ABSTRACT The novel coronavirus disease of 2019 (COVID-19) first appeared in Wuhan and subsequently spread rapidly in cities and provinces across the country and all over the world. In order to effectively control the spread of the epidemic in different areas, zonal management and endemic prevention and control policies should be implemented according to local epidemic situations. This study proposes a time-series clustering method to discover dynamic characteristics of the COVID-19 epidemic by categorizing the epidemic situations in China’s major cities into groups based on daily reported confirmed cases and analysing the driving factors of the city background conditions for each category. Our results show that according to the dynamic patterns of the COVID-19 epidemic there are eight types of epidemic situations, including extreme outbreak areas, large spread areas, potential resurged areas, middle spread areas, controlled outbreak areas, limited growth areas, delayed outbreak areas, and lag report areas. These dynamic patterns are mainly related to the city background conditions, such as population flow, local resident number, government emergency response capability, and medical resource conditions. Based on our results, different endemic prevention and control measures are recommended for containing the COVID-19 epidemic in cities with different types of epidemic situations.

Improved time series clustering based on new geometric frameworks

Most existing methods for time series clustering rely on distances calculated from the entire raw data using the Euclidean distance or Dynamic Time Warping distance. In this work, we propose to embed the time series onto higher-dimensional spaces to obtain geometric representations of the time series themselves. Particularly, the embedding on Rn×p, on the Stiefel manifold and on the unit Sphere are analyzed for their performances with respect to several yet well-known clustering algorithms. The gain brought by the geometrical representation for the time series clustering is illustrated through a large benchmark of databases. We particularly exhibit that, firstly, the embedding of the time series on higher dimensional spaces gives better results than classical approaches and, secondly, that the embedding on the Stiefel manifold - in conjunction with UMAP and HDBSCAN clustering algorithms - is the recommended framework for time series clustering.

Evaluation of multivariate time series clustering for imputation of air pollution data

Abstract. Air pollution is one of the world's leading risk factors for death, with 6.5 million deaths per year worldwide attributed to air-pollution-related diseases. Understanding the behaviour of certain pollutants through air quality assessment can produce improvements in air quality management that will translate to health and economic benefits. However, problems with missing data and uncertainty hinder that assessment. We are motivated by the need to enhance the air pollution data available. We focus on the problem of missing air pollutant concentration data either because a limited set of pollutants is measured at a monitoring site or because an instrument is not operating, so a particular pollutant is not measured for a period of time. In our previous work, we have proposed models which can impute a whole missing time series to enhance air quality monitoring. Some of these models are based on a multivariate time series (MVTS) clustering method. Here, we apply our method to real data and show how different graphical and statistical model evaluation functions enable us to select the imputation model that produces the most plausible imputations. We then compare the Daily Air Quality Index (DAQI) values obtained after imputation with observed values incorporating missing data. Our results show that using an ensemble model that aggregates the spatial similarity obtained by the geographical correlation between monitoring stations and the fused temporal similarity between pollutant concentrations produces very good imputation results. Furthermore, the analysis enhances understanding of the different pollutant behaviours and of the characteristics of different stations according to their environmental type.

Health care visits during the COVID-19 pandemic: A spatial and temporal analysis of mobile device data.

Transportation disruptions caused by COVID-19 have exacerbated difficulties in health care delivery and access, which may lead to changes in health care use. This study uses mobile device data from SafeGraph to explore the temporal patterns of visits to health care points of interest (POIs) during 2020 and examines how these patterns are associated with socio-demographic and spatial characteristics at the Census Block Group level in North Carolina. Specifically, using the K-medoid time-series clustering method, we identify three distinct types of temporal patterns of visits to health care facilities. Furthermore, by estimating multinomial logit models, we find that Census Block Groups with higher percentages of elderly persons, minorities, low-income individuals, and people without vehicle access are areas most at-risk for decreased health care access during the pandemic and exhibit lower health care access prior to the pandemic. The results suggest that the ability to conduct in-person medical visits during the pandemic has been unequally distributed, which highlights the importance of tailoring policy strategies for specific socio-demographic groups to ensure equitable health care access and delivery.

COVID-19 pandemic spread against countries\u2019 non-pharmaceutical interventions responses: a data-mining driven comparative study

BackgroundThe first half of 2020 has been marked as the era of COVID-19 pandemic which affected the world globally in almost every aspect of the daily life from societal to economical. To prevent the spread of COVID-19, countries have implemented diverse policies regarding Non-Pharmaceutical Intervention (NPI) measures. This is because in the first stage countries had limited knowledge about the virus and its contagiousness. Also, there was no effective medication or vaccines. This paper studies the effectiveness of the implemented policies and measures against the deaths attributed to the virus between January and May 2020.MethodsData from the European Centre for Disease Prevention and Control regarding the identified cases and deaths of COVID-19 from 48 countries have been used. Additionally, data concerning the NPI measures related policies implemented by the 48 countries and the capacity of their health care systems was collected manually from their national gazettes and official institutes. Data mining, time series analysis, pattern detection, machine learning, clustering methods and visual analytics techniques have been applied to analyze the collected data and discover possible relationships between the implemented NPIs and COVID-19 spread and mortality. Further, we recorded and analyzed the responses of the countries against COVID-19 pandemic, mainly in urban areas which are over-populated and accordingly COVID-19 has the potential to spread easier among humans.ResultsThe data mining and clustering analysis of the collected data showed that the implementation of the NPI measures before the first death case seems to be very effective in controlling the spread of the disease. In other words, delaying the implementation of the NPI measures to after the first death case has practically little effect on limiting the spread of the disease. The success of implementing the NPI measures further depends on the way each government monitored their application. Countries with stricter policing of the measures seems to be more effective in controlling the transmission of the disease.ConclusionsThe conducted comparative data mining study provides insights regarding the correlation between the early implementation of the NPI measures and controlling COVID-19 contagiousness and mortality. We reported a number of useful observations that could be very helpful to the decision makers or epidemiologists regarding the rapid implementation and monitoring of the NPI measures in case of a future wave of COVID-19 or to deal with other unknown infectious pandemics. Regardless, after the first wave of COVID-19, most countries have decided to lift the restrictions and return to normal. This has resulted in a severe second wave in some countries, a situation which requires re-evaluating the whole process and inspiring lessons for the future.

Working from Home and Digital Divides: Resilience during the Pandemic

This article offers a new perspective on telecommuting from the viewpoint of the complex web of digital divides. Using the United Kingdom as a case study, this article studies how the quality and reliability of Internet services, as reflected in experienced Internet upload speeds during the spring 2020 lockdown, might reinforce or redress the spatial and social dimensions of digital divisions. Fast, reliable Internet connections are necessary for the population to be able to work from home. Although not every place hosts individuals in occupations that allow for telecommuting or with the necessary skills to effectively use the Internet to telecommute, good Internet connectivity is also essential to local economic resilience in a period like the current pandemic. Employing data on individual broadband speed tests and state-of-the-art time series clustering methods, we create clusters of UK local authorities with similar temporal signatures of experienced upload speeds. We then associate these clusters of local authorities with their socioeconomic and geographic characteristics to explore how they overlap with or diverge from the existing economic and digital geography of the United Kingdom. Our analysis enables us to better understand how the spatial and social distributions of both occupations and online accessibility intersect to enable or hinder the practice of telecommuting at a time of extreme demand.

A clustering method for inter-annual NDVI time series

ABSTRACT Inter-annual Normalized Difference Vegetation Index (NDVI) time series has been applied to change detection in many fields. Research on change detection in inter-annual NDVI time series always requires several related parameters or sample training, which may limit the transferability of the methods to some extent. In this letter, we try to develop a shape-based clustering to analyse the inter-annual NDVI time series by considering the shapes of time series. The method adopts shape-based distance based on cross-correlation analysis to measure the distance between time series and uses shape-based averaging method named Dynamic Time Warping Barycentre Averaging to get the cluster centroids. Through experimental analysis, the shape-based clustering can well gather the NDVI time series with similar trends into a cluster. Also, the shape-based clustering is proven to be reliable with 94.4% overall accuracy for detection of vegetation disturbance.

Time-Series Analysis of Continuous Glucose Monitoring Data to Predict Treatment Efficacy in Patients with T2DM.

There is a challenge to predict treatment effects in patients with type 2 diabetes mellitus (T2DM). To assess and predict treatment effects in patients with T2DM through time-series analysis of continuous glucose monitoring (CGM) measurements. We extracted and clustered the trend components of CGM measurements to generate representative time-series profiles, which were used as a predictor of treatment effects in groups of patients. We recruited 111 outpatients with T2DM at Ningbo City First Hospital, China. The patients underwent CGM measurement for 14 days at the beginning of glucose-lowering treatment. Hemoglobin A1c (HbA1c) and fasting plasma glucose (FPG) were obtained at the beginning and after 6 months of treatment. 111 patients each had 960 to 1344 CGM measurements for 14 days at 96 measurements per day. The patients were classified into 3 groups according to the profiles of trend components of CGM observed values by time-series clustering method, including decreasing (47 patients), increasing (26 patients), and unchanged (38 patients) profiles. After 6 months of glucose-lowering treatment, FPG declined from 10.2 to 6.8 mmol/L (a decline of 3.4 mmol/L) in the decreasing group, from 8.9 to 9.2 mmol/L (a rise of 0.3 mmol/L) in the increasing group, and from 8.4 to 7.5 mmol/L (a decline of 0.9 mmol/L) in the unchanged group. The changes of HbA1c were 2.3%, 0.2%, and 0.9% for the 3 groups (P < 0.01), respectively. Clustering of the trend components of CGM data generates representative CGM profiles that are predictive of 6-month therapeutic effects for T2DM.

Identifying the module structure of swarms using a new framework of network-based time series clustering

Swarm is a collective motion phenomenon whose dynamic mechanism and cooperation structure could be identified based on observations. Unmanned Aerial Vehicles (UAV) is a special artificial swarm with unique rules and structures. Therefore, corresponding identification methods need to be developed. One critical identification problem is distinguishing the swarm’s cooperation structure, which is usually clustered and grouped to achieve stability of behaviors and low communication cost. This paper proposes a framework of Overlay Network Integrated Time series clustering (ONIT) to identify the UAV swarm structures based on trajectories. The framework consists of Snapshot, Net Growth and Net Split. It can fuse with most distance functions in time series clustering, achieving high accuracy, update ability, and fault tolerance with various datasets. We create point-based and sliding window-based snapshots, allowing the framework compatible with more methods. In particular, the Dynamic Time Wrapping (DTW) correspondence in point-based snapshots shows the high scalability of the framework, and the Euclidean Distance (ED) correspondence shows that the framework can still significantly improve the accuracy while maintaining the simplicity of calculation. The test results show that the fused ONIT-clustering algorithms, especially the point-based ones, outperform original time series clustering methods separately in simulation datasets of UAV swarms and UCR repository by 28% and 27%. In summary, the proposed framework is a flexible and scalable time series clustering method that can solve various time series clustering problems especially the trajectory clustering of the UAV swarm and has great potential for general time series analysis.