Time Series Similarity Measures Research Articles

Using cross-recurrence quantification analysis to compute similarity measures for time series of unequal length with applications to sleep stage analysis

Comparing time series of unequal length requires data processing procedures that may introduce biases. This article describes, validates, and applies Cross-Recurrence Quantification Analysis (CRQA) to detect and quantify correlation and coupling among time series of unequal length without prior data processing. We illustrate and validate this application using continuous and discrete data from a model system (study 1). Then we use the method to re-analyze the Sleep Heart Health Study (SHHS), a rare large dataset comprising detailed physiological sleep measurements acquired by in-home polysomnography. We investigate whether recurrence patterns of ultradian NREM/REM sleep cycles (USC) predict mortality (study 2). CRQA exhibits better performance compared with traditional approaches that require trimming, stretching or compression to bring two time series to the same length. Application to the SHHS indicates that recurrence patterns linked to stability of USCs are associated with all-cause mortality even after controlling for other sleep parameters, health, and sociodemographics. We suggest that CRQA is a useful tool for analyzing categorical time series, where the underlying structure of the data is unlikely to result in matching data points—such as ultradian sleep cycles.

Evaluating rail transit assignment models in the temporal dimension: The problem and its solution

Passenger flow is the foundation for urban rail transit (URT) operations. However, its calculated results from assignment models may deviate from the actual situation in both spatial and temporal dimensions, which arouses more attention and needs to be evaluated in particular. On the other hand, onboard video data from URT trains provides a potential way for model evaluation. This study defines the evaluation problem and proposes a methodological solution for evaluating rail transit assignment models in the temporal dimension, including qualitative validation and difference quantification. A suitable time granularity is determined for the best effectiveness and onboard video data is used for actual passenger flow extraction. The gap between the actual and the calculated by the model is identified with nonparametric statistical techniques (NPSTs) and quantified with time series similarity measurement (TSSM) methods. A case study on the Shanghai metro demonstrates the performance of the proposed approach, and several practice implications for URT operation agencies are also discussed.

Improved collaborative filtering for cross-store demand forecasting

Accurate and reliable demand forecasting is crucial for decision-making in assortment planning, store location, and various operational aspects. This study proposes a hybrid TS-SimPMF framework for multi-store multi-product demand forecasting, employing probabilistic matrix factorization (PMF) with time-series similarity measures to capture product and store heterogeneity. The heterogeneity enables the framework to achieve multi-step demand forecasting under unknown item-store combinations through an adaptive integration strategy. We first employ a hybrid dynamic regularization approach to measure the similarity of product sales simultaneously, and then the PMF framework is applied to generate latent vectors of products and stores. The performance of the proposed framework is verified by the real-world retail data, in which the dataset includes all sales records with 50 SKUs in 10 locations, totaling over 180,000 sales records. These experimental results demonstrate the superior performance of the proposed hybrid model compared to state-of-the-art methods.

A Study on the Effectiveness of Time Series Similarity Measures for the Comparison of Degradation Curves of Similar Engineering Systems

A Study on the Effectiveness of Time Series Similarity Measures for the Comparison of Degradation Curves of Similar Engineering Systems

A new similarity measurement method for time series based on image fusion of recurrence plots and wavelet scalogram

The core of data series classification and clustering is how to evaluate the similarity between time series. However, for one-dimensional time series, the vast majority of similarity measurement methods currently relied on one-dimensional information. Although some classifications of time series were achieved by the images transformed from time series, they mostly relied on a single imaging mechanism (time domain or frequency domain). In order to give a new idea for time series similarity measurement, this paper proposed a similarity measurement method of time series based on the fused images. According to recurrence plots (RP) and wavelet scalogram (WS), the original time series was first transformed into images. Then, RP and WS were fused into an image. Next, the feature in the image was extracted by ResNet-18. Finally, the similarity of the time series can be obtained by the Euclidean distance between the features extracted by ResNet-18. The proposed method was verified by the time series from UCR Time Series Classification/Clustering Homepage. The results showed that the similarity measurement of time series can be effectively improved by fusing the images obtained by different imaging mechanisms in the time domain and frequency domain.

Fluorescent Photoelectric Detection of Peroxide Explosives Based on a Time Series Similarity Measurement Method.

Due to the characteristics of peroxide explosives, which are difficult to detect via conventional detection methods and have high explosive power, a fluorescent photoelectric detection system based on fluorescence detection technology was designed in this study to achieve the high-sensitivity detection of trace peroxide explosives in practical applications. Through actual measurement experiments and numerical simulation methods, the derivative dynamic time warping (DDTW) algorithm and the Spearman correlation coefficient were used to calculate the DDTW-Spearman distance to achieve time series correlation measurements. The detection sensitivity of triacetone triperoxide (TATP) and H2O2 was studied, and the detection of organic substances of acetone, acetylene, ethanol, ethyl acetate, and petroleum ether was carried out. The stability and specific detection ability of the fluorescent photoelectric detection system were determined. The research results showed that the fluorescence photoelectric detection system can effectively identify the detection data of TATP, H2O2, acetone, acetonitrile, ethanol, ethyl acetate, and petroleum ether. The detection limit of 0.01 mg/mL of TATP and 0.0046 mg/mL of H2O2 was less than 10 ppb. The time series similarity measurement method improves the analytical capabilities of fluorescence photoelectric detection technology.

Methane Emissions in Boreal Forest Fire Regions: Assessment of Five Biomass-Burning Emission Inventories Based on Carbon Sensing Satellites

Greenhouse gases such as CH4 generated by forest fires have a significant impact on atmospheric methane concentrations and terrestrial vegetation methane budgets. Verification in conjunction with “top-down” satellite remote sensing observation has become a vital way to verify biomass-burning emission inventories and accurately assess greenhouse gases while looking into the limitations in reliability and quantification of existing “bottom-up” biomass-burning emission inventories. Therefore, we considered boreal forest fire regions as an example while combining five biomass-burning emission inventories and CH4 indicators of atmospheric concentration satellite observation data. By introducing numerical comparison, correlation analysis and trend consistency analysis methods, we explained the lag effect between emissions and atmospheric concentration changes and evaluated a more reliable emission inventory using time series similarity measurement methods. The results indicated that total methane emissions from five biomass-burning emission inventories differed by a factor of 2.9 in our study area, ranging from 2.02 to 5.84 Tg for methane. The time trends of the five inventories showed good consistency, with the Quick Fire Emissions Dataset version 2.5 (QFED2.5) having a higher correlation coefficient (above 0.8) with the other four datasets. By comparing the consistency between the inventories and satellite data, a lagging effect was found to be present between the changes in atmospheric concentration and gas emissions caused by forest fires on a seasonal scale. After eliminating lagging effects and combining time series similarity measures, the QFED2.5 (Euclidean distance = 0.14) was found to have the highest similarity to satellite data. In contrast, Global Fire Emissions Database version 4.1 with small fires (GFED4.1s) and Global Fire Assimilation System version 1.2 (GFAS1.2) had larger Euclidean distances of 0.52 and 0.4, respectively, which meant that they had lower similarity to satellite data. Therefore, QFED2.5 was found to be more reliable while having higher application accuracy compared to the other four datasets in our study area. This study further provided a better understanding of the key role of forest fire emissions in atmospheric CH4 concentrations and offered reference for selecting appropriate biomass burning emission inventory datasets for bottom-up inventory estimation studies.

Research on Interactive Children's Teaching Mode Driven by Artificial Intelligence Technology

This paper designs an interactive system of intelligent robots for children's education, which includes interactive desktop devices and interactive robot devices. Teaching and interactive content can be displayed through the display surface of the interactive desktop device. A user manipulates the display surface via gesture manipulation or teaching tools. Interactive desktop devices perform interactive information gathering. A new time series similarity measurement method is given. The display surface and the interactive robotic device provide interactive feedback to the user through sounds, images, and lights. The guidance and interactive operation of the interactive robot on the display surface enhances the effect of the interactive operation. The effectiveness of this method is verified by simulation experiments.

Constrained DTW preserving shapelets for explainable time-series clustering

The analysis of time series is becoming ever more popular due to the proliferation of sensors. A well-known similarity measure for time-series is Dynamic Time Warping (DTW), which does not respect the axioms of a metric. These, however, can be reintroduced through Learning DTW-Preserving Shapelets (LDPS). This article extends LDPS and presents constrained DTW-preserving shapelets (CDPS). CDPS directs the time-series representation to captures the user’s interpretation of the data by considering a limited amount of user knowledge in the from of must-link- cannot link constraints. Subsequently, unconstrained algorithms can be used to generate a clustering that respects the constraints without explicit knowledge of them. Out-of-sample data can be transformed into this space, overcoming the limitations of traditional transductive constrained-clustering algorithms. Furthermore, several Shapelet Cluster Explanation (SCE) approaches are proposed that explain the clustering and can simplify the representation while preserving clustering performance. State-of-the-art performance is demonstrated on multiple time-series datasets and an open-source implementation will be made publicly available upon acceptance.

Evaluation of advanced time series similarity measures for object-based cropland mapping

ABSTRACT With more and more high-resolution remote-sensing data becoming available, satellite image time series (SITS) analysis is often used to map crops at the pixel level. Although the object-based image analysis paradigm has proven superior to pixel-based image analysis for overcoming salt-and-pepper effects, object-based time series crop classification is still rare. Except for time-weighted dynamic time warping (TWDTW), other time series similarity measuring algorithms popular in the signal processing domain, such as shape-based distance (SBD) and global alignment kernel (GAK), remain poorly explored at the object level. Accordingly, this study aimed to explore better object-based time series classification frameworks by investigating similarity measures, including SBD, GAK and TWDTW, and thus experiments were designed to analyse the response of these methods to various parameters, including crop types, time series density, processing efficiency and so on. The results show that GAK is superior to SBD and TWDTW in general. Specifically, GAK performs better than TWDTW with the limited available images, e.g. in cloudy and rainy climate regions. Also, GAK outperforms SBD in identifying crops with a complex phenological pattern, such as alfalfa. Furthermore, TWDTW has the lowest processing efficiency. This study addresses the scarcity of similarity measurement methods in the object-based time series paradigm, and it is expected that this study could provide some guidance for the selection of cropland mapping methods.

Elastic similarity and distance measures for multivariate time series

This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.

Forecasting COVID‐19 cases using dynamic time warping and incremental machine learning methods

AbstractThe investment of time and resources for developing better strategies is key to dealing with future pandemics. In this work, we recreated the situation of COVID‐19 across the year 2020, when the pandemic started spreading worldwide. We conducted experiments to predict the coronavirus cases for the 50 countries with the most cases during 2020. We compared the performance of state‐of‐the‐art machine learning algorithms, such as long‐short‐term memory networks, against that of online incremental machine learning algorithms. To find the best strategy, we performed experiments to test three different approaches. In the first approach (single‐country), we trained each model using data only from the country we were predicting. In the second one (multiple‐country), we trained a model using the data from the 50 countries, and we used that model to predict each of the 50 countries. In the third experiment, we first applied clustering to calculate the nine most similar countries to the country that we were predicting. We consider two countries to be similar if the differences between the curve that represents the COVID‐19 time series are small. To do so, we used time series similarity measures (TSSM) such as Euclidean Distance (ED) and Dynamic Time Warping (DTW). TSSM return a real value that represents the distance between the points in two time series which can be interpreted as how similar they are. Then, we trained the models with the data from the nine more similar countries to the one that was predicted and the predicted one. We used the model ARIMA as a baseline for our results. Results show that the idea of using TSSM is a very effective approach. By using it with the ED, the obtained RMSE in the single‐country and multiple‐country approaches was reduced by 74.21% and 74.70%, respectively. And by using the DTW, the RMSE was reduced by 74.89% and 75.36%. The main advantage of our methodology is that it is very simple and fast to apply since it is only based on time series data, as opposed to more complex methodologies that require a deep and thorough study to consider the number of parameters involved in the spread of the virus and their corresponding values. We made our code public to allow other researchers to explore our proposed methodology.

Identification of Urban Jobs–Housing Sites Based on Online Car-Hailing Data

With the development of cities, the organization of jobs–housing space is becoming more complex, and the rapid, effective identification of both residences and workplaces is crucial to sustainable urban development. The long time series of online car-hailing data conveys a large amount of activity trajectory information about urban populations, which can represent the social functions of urban areas, including workplaces and residences. This paper constructs a jobs–housing site identification model based on human activity characteristics. This model uses a time series dataset of online car hailing that characterizes the changes in regional passenger flow and implements the similarity measure and semi-supervised learning of time series to determine the classification of urban areas. Then, the jobs–housing factor method is introduced to extract the jobs–housing characteristics of different regions, which achieves the jobs–housing site identification. Finally, the empirical analysis of Chengdu city shows that the proposed model method can effectively mine the distribution of urban jobs–housing sites. The identification results are consistent with the actual situation, and the combination of the time series similarity and the jobs–housing feature variable improves the identification effect, providing a new way of thinking about urban jobs–housing space research.

Ultra-fast meta-parameter optimization for time series similarity measures with application to nearest neighbour classification

Nearest neighbour similarity measures are widely used in many time series data analysis applications. They compute a measure of similarity between two time series. Most applications require tuning of these measures’ meta-parameters in order to achieve good performance. However, most measures have at least O(L^2) complexity, making them computationally expensive and the process of learning their meta-parameters burdensome, requiring days even for datasets containing only a few thousand series. In this paper, we propose UltraFastMPSearch, a family of algorithms to learn the meta-parameters for different types of time series distance measures. These algorithms are significantly faster than the prior state of the art. Our algorithms build upon the state of the art, exploiting the properties of a new efficient exact algorithm which supports early abandoning and pruning for most time series distance measures. We show on 128 datasets from the UCR archive that our new family of algorithms are up to an order of magnitude faster than the previous state of the art.

Similarity Measure of Time Series With Different Sampling Frequencies Based on Context Density Consistency and Dynamic Time Warping

Similarity Measure of Time Series With Different Sampling Frequencies Based on Context Density Consistency and Dynamic Time Warping

Deep attentive time warping

Similarity measures for time series are important problems for time series classification. To handle the nonlinear time distortions, Dynamic Time Warping (DTW) has been widely used. However, DTW is not learnable and suffers from a trade-off between robustness against time distortion and discriminative power. In this paper, we propose a neural network model for task-adaptive time warping. Specifically, we use the attention model, called the bipartite attention model, to develop an explicit time warping mechanism with greater distortion invariance. Unlike other learnable models using DTW for warping, our model predicts all local correspondences between two time series and is trained based on metric learning, which enables it to learn the optimal data-dependent warping for the target task. We also propose to induce pre-training of our model by DTW to improve the discriminative power. Extensive experiments demonstrate the superior effectiveness of our model over DTW and its state-of-the-art performance in online signature verification.

Information Granulation With Rectangular Information Granules and Its Application in Time-Series Similarity Measurement

Information granules can discover interpretable and meaningful relationships offering a full description for time series. This article presents an information granulation method with rectangular information granules and applies it to time-series similarity measurement. First, the fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c$</tex-math></inline-formula> -means clustering algorithm transforms the time series and its first-order difference time series to data clusters. With the maximum volume of rectangular information granules viewed as the criterion, the optimal rectangular information granules are formed using the data cluster by the principle of justifiable granularity and the gravitational search algorithm. The time-series similarity is measured by calculating the similarity between the upper and lower bounds of the optimal rectangular information granules built from the time series. Finally, an experiment is performed on a public dataset to verify the feasibility of the proposed method. The result shows that the rectangular information granulation method can capture the change characteristics of time series. The similarity measurement method can effectively evaluate the similarity of the time series belonging to different classes.

Fast Exact Dynamic Time Warping on Run-Length Encoded Time Series

Dynamic Time Warping (DTW) is a well-known similarity measure for time series. The standard dynamic programming approach to compute the DTW distance of two length-n time series, however, requires O(n^2) time, which is often too slow for real-world applications. Therefore, many heuristics have been proposed to speed up the DTW computation. These are often based on lower bounding techniques, approximating the DTW distance, or considering special input data such as binary or piecewise constant time series. In this paper, we present a first exact algorithm to compute the DTW distance of two run-length encoded time series whose running time only depends on the encoding lengths of the inputs. The worst-case running time is cubic in the encoding length. In experiments we show that our algorithm is indeed fast for time series with short encoding lengths.

Sub-Surface Defect Depth Approximation in Cold Infrared Thermography.

Detection and characterisation of hidden corrosion are considered challenging yet crucial activities in many sensitive industrial plants where preventing the loss of containment or structural reliability are paramount. In the last two decades, infrared (IR) thermography has proved to be a reliable means for inspection of corrosion or other sub-surface anomalies in low to mid thickness metallic mediums. The foundation of using IR thermography for defect detection and characterisation is based on active thermography. In this method of inspection, an external excitation source is deployed for the purpose of stimulating thermal evolutions inside objects. The presence of sub-surface defects disrupts the evolution of electromagnetic pulse inside an object. The reflection of altered pulse at the surface can be recorded through thermal camera in the form of temperature anomalies. Through authors’ previous works, cold thermography has shown that it can be a viable defect detection alternative to the most commonly used means of active thermography, known as heating. In the current work, the characterisation of defect dimensions, i.e., depth and diameter, has been explored. A simple analytical model for thermal contrast over defect is used in order to approximate the defect depth and diameter. This is achieved by comparing the similarities of the model and the experimental contrast time-series. A method of time-series similarity measurement known as dynamic time wrapping (DTW) is used to score the similarity between a pair of model and experiment time-series. The final outcome of the proposed experimental setup has revealed that there is a good potential to predict the metal loss of up to 50% in mid-thickness substrate even by deploying a less accurate nonradiometric thermal device and no advanced image processing.

Fault Diagnosis Method Based on Time Series in Autonomous Unmanned System

There are various types of autonomous unmanned systems, covering different spaces of sea, land, and air, and they are comprehensively going deep into multiple fields of national security and social life. Due to the development of technology, the scale of unmanned systems is getting larger and larger, the number of components in the system is increasing, and the operating environment of the system is also becoming more and more complex. Therefore, the probability of failure of the components of the system will also be significantly increased. In order to eliminate the impact of the fault in time, the fault diagnosis method is significant. Considering the differences of components in autonomous unmanned systems, if a specific fault diagnosis algorithm is designed for each type of component, it will bring difficulties to the coordinated control of the system. Therefore, this paper analyzes the data characteristics of unmanned autonomous system devices (such as sensors) and finds that these data have time series. Therefore, the data of different devices can be converted into time series, and a general fault diagnosis algorithm suitable for most devices can be studied. The fault diagnosis algorithm is based on the clustering algorithm. In order to improve the clustering effect, the time series of different devices are represented by Gaussian mixture clustering to reduce the computational complexity of the clustering calculation. Then, a time series similarity measurement method based on the improved Markov chain is proposed. This method can better distinguish normal samples from abnormal samples so as to classify and identify faults effectively.