Time Series Clustering Method Research Articles

Multivariate time series clustering based on complex network

Recent years have seen an increase in research on time series data mining (especially time-series clustering) owing to the widespread existence of time series in various fields. Techniques such as clustering can extract valuable information and potential patterns from time-series data. In this regard, the clustering analysis of multivariate time series is challenging because of the high dimensionality. Our study led us to develop a novel method based on complex networks for multivariate time series clustering (BCNC). BCNC includes a new method for mapping multivariate time series into complex networks and a new method to visualize multivariate time series. The solution is innovatively based on a relationship network and relies on the use of community detection technology to achieve complete multivariate time series clustering. The detailed algorithm and the simulation experiments of the proposed BCNC method are reported. The experimental results on various datasets show that BCNC is superior to traditional multivariate time series clustering methods.

Disparate patterns of movements and visits to points of interest located in urban hotspots across US metropolitan cities during COVID-19.

We examined the effect of social distancing on changes in visits to urban hotspot points of interest. In a pandemic situation, urban hotspots could be potential superspreader areas as visits to urban hotspots can increase the risk of contact and transmission of a disease among a population. We mapped census-block-group to point-of-interest (POI) movement networks in 16 cities in the United States. We adopted a modified coarse-grain approach to examine patterns of visits to POIs among hotspots and non-hotspots from January to May 2020. Also, we conducted chi-square tests to identify POIs with significant flux-in changes during the analysis period. The results showed disparate patterns across cities in terms of reduction in hotspot POI visitors. Sixteen cities were divided into two categories using a time series clustering method. In one category, which includes the cities of San Francisco, Seattle and Chicago, we observed a considerable decrease in hotspot POI visitors, while in another category, including the cities of Austin, Houston and San Diego, the visitors to hotspots did not greatly decrease. While all the cities exhibited overall decreased visitors to POIs, one category maintained the proportion of visitors to hotspot POIs. The proportion of visitors to some POIs (e.g. restaurants) remained stable during the social distancing period, while some POIs had an increased proportion of visitors (e.g. grocery stores). We also identified POIs with significant flux-in changes, indicating that related businesses were greatly affected by social distancing. The study was limited to 16 metropolitan cities in the United States. The proposed methodology could be applied to digital trace data in other cities and countries to study the patterns of movements to POIs during the COVID-19 pandemic.

Research on Traffic Situation Analysis for Urban Road Network Through Spatiotemporal Data Mining: A Case Study of Xi’an, China

Severe traffic congestion has promoted the development of the Intelligent Transportation System (ITS). Accurately analyzing and predicting the traffic states of the urban road networks has important theoretical significance and practical value for improving traffic efficiency and formulating ITS scheme according to local conditions. This study aims to identify and predict the traffic operation status in the road network within the Third Ring Road in Xi’an and explore spatiotemporal patterns of traffic congestion. In this paper, firstly, we discriminated the traffic status of the urban road network used the GPS data of floating vehicles (e.g., taxis and buses) in Xi’an by the Travel Time Index (TTI). Secondly, we used the emerging hot spot analysis method to locate different hot spot patterns. The time series clustering method was used to divide the whole road network’s locations into distinct clusters with similar spatiotemporal characteristics. Thirdly, we applied three different time series forecasting models, including Curve Fit Forecast (CFF), Exponential Smoothing Forecast (ESF), Forest-based Forecast (FBF), to predict the traffic operation status. Finally, we summarized the spatiotemporal characteristics of the whole-network congestion. The results of this study can contribute some helpful insights for alleviating traffic congestion. For instance, it is essential to speed up the construction of urban traffic microcirculation and increase the road network density. Moreover, it is crucial to adhere to the urban public transport priority development strategy and increase public transportation travel sharing.

Estimation of Particulate Matter Contributions from Desert Outbreaks in Mediterranean Countries (2015–2018) Using the Time Series Clustering Method

North African dust intrusions can contribute to exceedances of the European PM10 and PM2.5 limit values and World Health Organisation standards, diminishing air quality, and increased mortality and morbidity at higher concentrations. In this study, the contribution of North African dust in Mediterranean countries was estimated using the time series clustering method. This method combines the non-parametric approach of Hidden Markov Models for studying time series, and the definition of different air pollution profiles (regimes of concentration). Using this approach, PM10 and PM2.5 time series obtained at background monitoring stations from seven countries were analysed from 2015 to 2018. The average characteristic contributions to PM10 were estimated as 11.6 ± 10.3 µg·m−3 (Bosnia and Herzegovina), 8.8 ± 7.5 µg·m−3 (Spain), 7.0 ± 6.2 µg·m−3 (France), 8.1 ± 5.9 µg·m−3 (Croatia), 7.5 ± 5.5 µg·m−3 (Italy), 8.1 ± 7.0 µg·m−3 (Portugal), and 17.0 ± 9.8 µg·m−3 (Turkey). For PM2.5, estimated contributions were 4.1 ± 3.5 µg·m−3 (Spain), 6.0 ± 4.8 µg·m−3 (France), 9.1 ± 6.4 µg·m−3 (Croatia), 5.2 ± 3.8 µg·m−3 (Italy), 6.0 ± 4.4 µg·m−3 (Portugal), and 9.0 ± 5.6 µg·m−3 (Turkey). The observed PM2.5/PM10 ratios were between 0.36 and 0.69, and their seasonal variation was characterised, presenting higher values in colder months. Principal component analysis enabled the association of background sites based on their estimated PM10 and PM2.5 pollution profiles.

Volatility Similarity and Spillover Effects in G20 Stock Market Comovements: An ICA-Based ARMA-APARCH-M Approach

Financial internationalization leads to similar fluctuations and spillover effects in financial markets around the world, resulting in cross-border financial risks. This study examines comovements across G20 international stock markets while considering the volatility similarity and spillover effects. We provide a new approach using an ICA- (independent component analysis-) based ARMA-APARCH-M model to shed light on whether there are spillover effects among G20 stock markets with similar dynamics. Specifically, we first identify which G20 stock markets have similar volatility features using a fuzzy C-means time series clustering method and then investigate the dominant source of volatility spillovers using the ICA-based ARMA-APARCH-M model. The evidence has shown that the ICA method can more accurately capture market comovements with nonnormal distributions of the financial time series data by transforming the multivariate time series into statistically independent components (ICs). Our findings indicate that the G20 stock markets are clustered into three categories according to volatility similarity. There are spillover effects in stock market comovements of each group and the dominant source can be identified. This study has important implications for investors in international financial markets and for policymakers in G20 countries.

A lane-changing risk profile analysis method based on time-series clustering

Lane-changing (LC) is an essential driving maneuver on roadways, and risky LC maneuvers account for a large number of crash accidents. This study investigates the LC risk profile during an LC process. A risk indicator based on driving safety field theory is employed to measure the instantaneous LC risk at each timestamp during an LC process and generate the LC risk profile. Then, Dynamic Time Warping (DTW) k-means clustering, as a time-series clustering method, is applied to partition the LC risk profiles into several categories. The Next Generation Simulation (NGSIM) US-101 dataset, which contains detailed records of vehicles’ trajectories, is used for case study. In the case study, the LC risk profiles are categorized into “uphill” shape, “bell” shape, and “downhill” shape. The LC risk profiles with “uphill” shape account for the majority of the LC risk profiles. Besides, we find that the LC process with “uphill” shaped risk profile generally has higher LC risk, and the crash risk between LC car and its preceding cars are more relevant to the LC risk. Those findings are likely due to the LC maneuver with the purpose to overtake the preceding car in the original lane. The risk indicator based on driving safety field theory can measure LC risk more comprehensively, compared to the conventional surrogate measures. The DTW k-means clustering method offers a promising approach to investigate the causation of risky LC maneuver based on the risk profile during an LC process.

Comparison of time series clustering methods and application to power consumption pattern clustering

Comparison of time series clustering methods and application to power consumption pattern clustering

An Accelerated U-Shapelet Time Series Clustering Method with LSH

The clustering method of time series is based on the measurement of the whole time series, and the traditional clustering method is used for direct clustering. It was only recently that Keough came up with the concept of Shapelet. He later applied this concept to unsupervised time series clustering. This is a time series clustering method based on the feature of sub-series. This method has good clustering accuracy and stability. However, due to the fact that traversal sequences are all sub-sequences, the original violent search algorithm is very complex and difficult to be applied to a large number of time series data sets. In this paper, on the basis of the original method, you introduce the idea of data retrieval in the data preprocessing stage to quickly screen candidate subsequences. Then we introduce a position-aware hashing algorithm -LSH. The method is used to match the sub-sequences of the pre-processed time series data, and the wide representativeness of the high-quality u-Shapelet is used for selection. Therefore, LSH-us is proposed in this paper to speed up the extraction process of feature sub-sequences. Experimental results show that this algorithm can improve the speed of u-Shapelet time series clustering algorithm and ensure the accuracy of clustering.

Self-Supervised Time Series Clustering With Model-Based Dynamics.

Time series clustering is usually an essential unsupervised task in cases when category information is not available and has a wide range of applications. However, existing time series clustering methods usually either ignore temporal dynamics of time series or isolate the feature extraction from clustering tasks without considering the interaction between them. In this article, a time series clustering framework named self-supervised time series clustering network (STCN) is proposed to optimize the feature extraction and clustering simultaneously. In the feature extraction module, a recurrent neural network (RNN) conducts a one-step time series prediction that acts as the reconstruction of the input data, capturing the temporal dynamics and maintaining the local structures of the time series. The parameters of the output layer of the RNN are regarded as model-based dynamic features and then fed into a self-supervised clustering module to obtain the predicted labels. To bridge the gap between these two modules, we employ spectral analysis to constrain the similar features to have the same pseudoclass labels and align the predicted labels with pseudolabels as well. STCN is trained by iteratively updating the model parameters and the pseudoclass labels. Experiments conducted on extensive time series data sets show that STCN has state-of-the-art performance, and the visualization analysis also demonstrates the effectiveness of the proposed model.

Clustering and classification of time series using topological data analysis with applications to finance

In this paper, we propose new methods for time series classification and clustering. These methods are based on techniques of Topological Data Analysis (TDA) such as persistent homology and time delay embedding for analysing time-series data. We present a new clustering method SOM-TDA and a new classification method RF-TDA based on TDA. Using SOM-TDA we examine the topological similarities and dissimilarities of some well-known time-series models used in finance. We also use the RF-TDA to examine if the topological features can be used to distinguish between time series models using simulated data. The performance of RF-TDA on the classification task is compared against three other classification methods. We also consider an application of RF-TDA to financial time series classification using real-life price data of stocks belonging to different sectors. RF-TDA is seen to perform quite well in the two experiments based on real-life stock-price data. This implies that the topological features of the time series of stock prices in the different sectors are not identical and have distinctive features that can be discerned through the use of TDA. We also briefly consider multi-class classification using RF-TDA.

Exploring the Spatial-Temporal Characteristics of Traditional Public Bicycle Use in Yancheng, China: A Perspective of Time Series Cluster of Stations

Traditional dock-based public bicycle systems continue to dominate cycling in most cities, even though bicycle-sharing services are an increasingly popular means of transportation in many of China’s large cities. A few studies investigated the traditional public bicycle systems in small and mid-sized cities in China. The time series clustering method’s advantages for analyzing sequential data used in many transportation-related studies are restricted to time series data, thereby limiting applications to transportation planning. This study explores the characteristics of a typical third-tier city’s public bicycle system (where there is no bicycle-sharing service) using station classification via the time series cluster algorithm and bicycle use data. A dynamic time warping distance-based k-medoids method classifies public bicycle stations by using one-month bicycle use data. The method is further extended to non-time series data after format conversion. The paper identified three clusters of stations and analyzed the relationships between clusters’ features and the stations’ urban environments. Based on points-of-interest data, the classification results were validated using the enrichment factor and the proportional factor. The method developed in this paper can apply to other transportation analysis and the results also yielded relevant strategies for transportation development and planning.

Space–time series clustering: Algorithms, taxonomy, and case study on urban smart cities

This paper provides a short overview of space–time series clustering, which can be generally grouped into three main categories such as: hierarchical, partitioning-based, and overlapping clustering. The first hierarchical category is to identify hierarchies in space–time series data. The second partitioning-based category focuses on determining disjoint partitions among the space–time series data, whereas the third overlapping category explores fuzzy logic to determine the different correlations between the space–time series clusters. We also further describe solutions for each category in this paper. Furthermore, we show the applications of these solutions in an urban traffic data captured on two urban smart cities (e.g., Odense in Denmark and Beijing in China). The perspectives on open questions and research challenges are also mentioned and discussed that allow to obtain a better understanding of the intuition, limitations, and benefits for the various space–time series clustering methods. This work can thus provide the guidances to practitioners for selecting the most suitable methods for their used cases, domains, and applications.

Simulator Pre-Screening of Underprepared Drivers Prior to Licensing On-Road Examination: Clustering of Virtual Driving Test Time Series Data.

BackgroundA large Midwestern state commissioned a virtual driving test (VDT) to assess driving skills preparedness before the on-road examination (ORE). Since July 2017, a pilot deployment of the VDT in state licensing centers (VDT pilot) has collected both VDT and ORE data from new license applicants with the aim of creating a scoring algorithm that could predict those who were underprepared.ObjectiveLeveraging data collected from the VDT pilot, this study aimed to develop and conduct an initial evaluation of a novel machine learning (ML)–based classifier using limited domain knowledge and minimal feature engineering to reliably predict applicant pass/fail on the ORE. Such methods, if proven useful, could be applicable to the classification of other time series data collected within medical and other settings.MethodsWe analyzed an initial dataset that comprised 4308 drivers who completed both the VDT and the ORE, in which 1096 (25.4%) drivers went on to fail the ORE. We studied 2 different approaches to constructing feature sets to use as input to ML algorithms: the standard method of reducing the time series data to a set of manually defined variables that summarize driving behavior and a novel approach using time series clustering. We then fed these representations into different ML algorithms to compare their ability to predict a driver’s ORE outcome (pass/fail).ResultsThe new method using time series clustering performed similarly compared with the standard method in terms of overall accuracy for predicting pass or fail outcome (76.1% vs 76.2%) and area under the curve (0.656 vs 0.682). However, the time series clustering slightly outperformed the standard method in differentially predicting failure on the ORE. The novel clustering method yielded a risk ratio for failure of 3.07 (95% CI 2.75-3.43), whereas the standard variables method yielded a risk ratio for failure of 2.68 (95% CI 2.41-2.99). In addition, the time series clustering method with logistic regression produced the lowest ratio of false alarms (those who were predicted to fail but went on to pass the ORE; 27.2%).ConclusionsOur results provide initial evidence that the clustering method is useful for feature construction in classification tasks involving time series data when resources are limited to create multiple, domain-relevant variables.

Time Series Clustering of Electricity Demand for Industrial Areas on Smart Grid

This study forecasts electricity demand in a smart grid environment. We present a prediction method that uses a combination of forecasting values based on time-series clustering. The clustering of normalized periodogram-based distances and autocorrelation-based distances are proposed as the time-series clustering methods. Trigonometrical transformation, Box–Cox transformation, autoregressive moving average (ARMA) errors, trend and seasonal components (TBATS), double seasonal Holt–Winters (DSHW), fractional autoregressive integrated moving average (FARIMA), ARIMA with regression (Reg-ARIMA), and neural network nonlinear autoregressive (NN-AR) are used for demand forecasting based on clustering. The results show that the time-series clustering method performs better than the method using the total amount of electricity demand in terms of the mean absolute percentage error (MAPE).

Using a distributed air sensor network to investigate the spatiotemporal patterns of PM2.5 concentrations

Spatiotemporal variations in PM2.5 are a key factor affecting personal pollution exposure levels in urban areas. However, fixed-site monitoring stations are so sparsely distributed that they hardly capture the dynamic and fine-scale variations in PM2.5 in urban areas with complex geographical features and urban forms. Recently, a distributed air sensor network (DASN) was deployed in Dezhou city, China, to monitor fine-scale air pollution information and obtain deep insight into variations in PM2.5. Based on the data collected by the DASN, this paper investigated the spatiotemporal patterns of PM2.5 using the time-series clustering method. The results demonstrated that there were four stages of PM2.5 daily variations, i.e., accumulation, continuous pollution, dispersion, and cleaning. Generally, the stage of dispersion occurred more rapidly than the stage of accumulation, and PM2.5 accumulated easily in warm and humid weather with low wind speeds. However, the stage of dispersion was affected mainly by high wind speeds and precipitation. Additionally, the results suggested that four variation stages did not strictly correspond to seasonal divisions. The spatial distributions of PM2.5 revealed that the main pollution source was located in a southeastern industrial park, which exhibited a significant impact throughout the four stages. Considering both the temporal and spatial characteristics of PM2.5, this study successfully identified pollution hotspots and confirmed the effect of industrial parks. The study demonstrates that the DASN has high prospective applicability for assessing the fine-scale spatial distribution of PM2.5, and the time-series clustering method can also assist environmental researchers in further exploring the spatiotemporal characteristics of urban air pollution.

Fuzzy clustering based on feature weights for multivariate time series

As an important set of techniques for data mining, time series clustering methods had been studied by many researchers. Although most existing solutions largely focus on univariate time series clustering, there has been a surge in interest in the clustering of multivariate time series data. In this paper, a feature-weighted clustering method is proposed based on two distance measurement methods called dynamic time warping (DTW) and shape-based distance (SDB). There are four stages in the proposed clustering algorithm. First, we pick cluster centers by the pop clustering method called clustering by fast search and find of density peaks (DPC). Next, by considering the overall matching of multivariate time series, a fuzzy membership matrix is generated by performing DTW on all variables. We then reconsider the contribution of each independent dimension by utilizing SBD to measure distances within each dimension and construct multiple fuzzy membership matrices. Finally, we utilize a traditional fuzzy clustering algorithm called fuzzy c-means to cluster the fuzzy membership matrices and generate clustering results. Simultaneously, a feature weight calculation method and novel equation for constructing fuzzy membership matrices are applied during the clustering process. We compare the proposed method to other clustering methods and the results indicate that the proposed method can improve clustering accuracy for multivariate time series datasets.

Temporal Pattern Analysis of Local Rainstorm Events in China During the Flood Season Based on Time Series Clustering

Similar to the rainfall depth, duration and intensity, the temporal pattern is also an important characteristic of rainstorm events. Studies have shown that temporal patterns will influence runoff modelling, flash flood warning thresholds as well as urban and infrastructure flood inundation simulations. In this study, a time series clustering method using dynamic time warping (DTW) as similarity measurement criteria is proposed to analyze rainfall temporal patterns. Compared with the existing approaches, it can better reflect the real rainfall processes. Based on this novel method, five representative temporal patterns were extracted from 13,299 rainstorm events during the flood season in China. Through the analysis of their statistical characteristics, the disaster-causing risks of each temporal pattern were compared. Furthermore, we found that for rainstorm events whose durations are less than 24 h, the rainfall is mainly concentrated in 3 to 6 h, which proposes higher requirements for the design of flood control and drainage projects compared with those using average intensities of 12 or 24 h as design standards. Finally, through regional analysis, we found that the rainfall depth, intensity and peak value are affected by the macroclimate. However, the temporal patterns are not strongly related to the macroclimate but are more likely to be affected by the local climate and topography, which needs further studies at smaller scales.

Two-Phase Multivariate Time Series Clustering to Classify Urban Rail Transit Stations

Consider the problem of clustering objects with temporally changing multivariate variables, for instance, in the classification of cities with several changing socioeconomic indices in geographical research. If the changing multivariate can be recorded simultaneously as a multivariate time series, in which the length of each subseries is equal and the subseries can be correlated, the problem is transformed into a multivariate time series clustering problem. The available methods consider the correlations between distinct time series but overlook the shape of each time series, which causes multivariate time series with similar correlations and opposite shapes to be clustered into the same class. To overcome this problem, this paper proposes a two-phase multivariate time series clustering algorithm that considers both correlation and shape. In Phase I, the discrete wavelet transform is applied to capture the wavelet variances and the correlation coefficients between each pair of variables to realize the initial clustering of multivariate time series, where time series with a similar correlation but opposite shape may be assigned to the same cluster. In Phase II, multivariate time series are clustered based on shape via the symbolic aggregate approximation (SAX) method. In this phase, time series with similar correlations but opposite morphologies are differentiated. The method is evaluated using multivariate time series of incoming and outgoing passenger volumes from Beijing IC card data; these volume data were collected between March 4, 2013 and March 17, 2013. Based on the silhouette coefficient, our approach outperforms two popular multivariate time series clustering methods: a wavelet-based method and the SAX method.

Interactions between Bus, Metro, and Taxi Use before and after the Chinese Spring Festival

Public transport plays an important role in developing sustainable cities. A better understanding of how different public transit modes (bus, metro, and taxi) interact with each other will provide better sustainable strategies to transport and urban planners. However, most existing studies are either limited to small-scale surveys or focused on the identification of general interaction patterns during times of regular traffic. Transient demographic changes in a city (i.e., many people moving out and in) can lead to significant changes in such interaction patterns and provide a useful context for better investigating the changes in these patterns. Despite that, little has been done to explore how such interaction patterns change and how they are linked to the built environment from the perspective of transient demographic changes using urban big data. In this paper, the tap-in-tap-out smart card data of bus/metro and taxi GPS trajectory data before and after the Chinese Spring Festival in Shenzhen, China, are used to explore such interaction patterns. A time-series clustering method and an elasticity change index (ECI) are adopted to detect the changing transit mode patterns and the underlying dynamics. The findings indicate that the interactions between different transit modes vary over space and time and are competitive or complementary in different parts of the city. Both ordinary least-squares (OLS) and geographically weighted regression (GWR) models with built environment variables are used to reveal the impact of changes in different transit modes on ECIs and their linkage with the built environment. The results of this study will contribute to the planning and design of multi-modal transport services.

Soybean Price Pattern Discovery Via Toeplitz Inverse Covariance-Based Clustering

The high volatility of world soybean prices has caused uncertainty and vulnerability particularly in the developing countries. The clustering of time series is a serviceable tool for discovering soybean price patterns in temporal data. However, traditional clustering method cannot represent the continuity of price data very well, nor keep a watchful eye on the correlation between factors. In this work, the authors use the Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data (TICC) to soybean price pattern discovery. This is a new method for multivariate time series clustering, which can simultaneously segment and cluster the time series data. Each pattern in the TICC method is defined by a Markov random field (MRF), characterizing the interdependencies between different factors of that pattern. Based on this representation, the characteristics of each pattern and the importance of each factor can be portrayed. The work provides a new way of thinking about market price prediction for agricultural products.