Dynamic Time Warping Analysis Research Articles

Temporal dynamics of depressive symptoms and cognitive decline in the oldest old: dynamic time warp analysis of the Leiden 85-plus study.

The prevalence of depressive symptoms and cognitive decline increases with age. We investigated their temporal dynamics in individuals aged 85 and older across a 5-year follow-up period. Participants were selected from the Leiden 85-plus study and were eligible if at least three follow-up measurements were available (325 of 599 participants). Depressive symptoms were assessed at baseline and at yearly assessments during a follow-up period of up to 5years, using the 15-item Geriatric Depression Scale (GDS-15). Cognitive decline was measured through various tests, including the Mini Mental State Exam, Stroop test, Letter Digit Coding test and immediate and delayed recall. A novel method, dynamic time warping analysis, was employed to model their temporal dynamics within individuals, in undirected and directed time-lag analyses, to ascertain whether depressive symptoms precede cognitive decline in group-level aggregated results or vice versa. The 325 participants were all 85years of age at baseline; 68% were female, and 45% received intermediate to higher education. Depressive symptoms and cognitive functioning significantly covaried in time, and directed analyses showed that depressive symptoms preceded most of the constituents of cognitive impairment in the oldest old. Of the GDS-15 symptoms, those with the strongest outstrength, indicating changes in these symptoms preceded subsequent changes in other symptoms, were worthlessness, hopelessness, low happiness, dropping activities/interests, and low satisfaction with life (all P's < 0.01). Depressive symptoms preceded cognitive impairment in a population based sample of the oldest old.

An investigation of the price discovery role of futures markets: A dynamic time warping analysis of the United States corn markets

AbstractFutures markets are critical to price discovery and often dominate spot markets. We analyze the linkages between daily corn futures and spot prices in the United States using dynamic time warping. This nonparametric pattern recognition technique has several advantages over traditional time series methods. First, it can detect multiple changes in the lead‐lag associations between the two prices within short intervals; the duration with which one series leads or lags another is not assumed to be fixed. Second, the method can be applied to time series without regard to their stationarity properties. This greatly expands the scope of this method to accommodate a wide range of time series. Third, it lends itself well to studying small samples, which econometricians encounter routinely. Fourth, the results are presented intelligibly using intuitive visualizations. Our results show that futures markets are critical to price discovery; nevertheless, spot markets dominate futures markets intermittently. We discuss the results in detail, setting them in the proper context. [EconLit Citations: C14, C32, Q02, Q11].

Automated Computer-Assisted Medical Decision-Making System Based on Morphological Shape and Skin Thickness Analysis for Asymmetry Detection in Mammographic Images.

Breast cancer is a significant health concern for women, emphasizing the need for early detection. This research focuses on developing a computer system for asymmetry detection in mammographic images, employing two critical approaches: Dynamic Time Warping (DTW) for shape analysis and the Growing Seed Region (GSR) method for breast skin segmentation. The methodology involves processing mammograms in DICOM format. In the morphological study, a centroid-based mask is computed using extracted images from DICOM files. Distances between the centroid and the breast perimeter are then calculated to assess similarity through Dynamic Time Warping analysis. For skin thickness asymmetry identification, a seed is initially set on skin pixels and expanded based on intensity and depth similarities. The DTW analysis achieves an accuracy of 83%, correctly identifying 23 possible asymmetry cases out of 20 ground truth cases. The GRS method is validated using Average Symmetric Surface Distance and Relative Volumetric metrics, yielding similarities of 90.47% and 66.66%, respectively, for asymmetry cases compared to 182 ground truth segmented images, successfully identifying 35 patients with potential skin asymmetry. Additionally, a Graphical User Interface is designed to facilitate the insertion of DICOM files and provide visual representations of asymmetrical findings for validation and accessibility by physicians.

On the linkages between energy and agricultural commodity prices: A dynamic time warping analysis

We use dynamic time warping, a non-parametric pattern recognition method, to study interlinkages between major energy and agricultural commodity prices. Cluster analysis is conducted to group commodity prices based on their behavioral likeness by maximizing the differences between groups while minimizing the differences within groups. Two clusters emerge: one comprises the prices of crude oil and six major agricultural commodities, whereas the other contains coal and natural gas prices. Regarding lead-lag associations, oil prices generally lag crop prices; however, there are periods during which the former lead the latter. Furthermore, the duration with which oil prices lead or lag crop prices changes frequently.

Public interest trends for Covid-19 and alignment with the disease trajectory: A time-series analysis of national-level data.

Data from web search engines have become a valuable adjunct in epidemiology and public health, specifically during epidemics. We aimed to explore the concordance of web search popularity for Covid-19 across 6 Western nations (United Kingdom, United States, France, Italy, Spain and Germany) and how timeline changes align with the pandemic waves, Covid-19 mortality, and incident case trajectories. We used the Google Trends tool for web-search popularity, and "Our World in Data" on Covid-19 reported cases, deaths, and administrative responses (measured by stringency index) to analyze country-level data. The Google Trends tool provides spatiotemporal data, scaled to a range of <1 (lowest relative popularity) to 100 (highest relative popularity), for the selected search terms, timeframe, and region. We used "coronavirus" and "covid" as search terms and set the timeframe up to November 12, 2022. We obtained multiple consecutive samples using the same terms to validate against sampling bias. We consolidated national-level incident cases and deaths weekly and transformed them to a range between 0 to 100 through the min-max normalization algorithm. We calculated the concordance of relative popularity rankings between regions, using the non-parametric Kendall's W, which maps concordance between 0 (lack of agreement) to 1 (perfect match). We used a dynamic time-warping algorithm to explore the similarity between Covid-19 relative popularity, mortality, and incident case trajectories. This methodology can recognize the similarity of shapes between time-series through a distance optimization process. The peak popularity was recorded on March 2020, to be followed by a decline below 20% in the subsequent three months and a long-standing period of variation around that level. At the end of 2021, public interest spiked shortly to fade away to a low level of around 10%. This pattern was highly concordant across the six regions (Kendal's W 0.88, p< .001). In dynamic time warping analysis, national-level public interest yielded a high similarity with the Covid-19 mortality trajectory (Similarity indices range 0.60-0.79). Instead, public interest was less similar with incident cases (0.50-0.76) and stringency index trajectories (0.33-0.64). We demonstrated that public interest is better intertwined with population mortality, rather than incident case trajectory and administrative responses. As the public interest in Covid-19 gradually subsides, these observations could help predict future public interest in pandemic events.

Big data networks: Dynamic Time Warping as a statistical tool for network analysis using Ecological Momentary Assessment data

IntroductionIn recent research, psychological disorders have been increasingly defined as complex dynamic systems in which symptoms are interconnected and influence each other, thereby forming symptom networks. This paradigm shift calls for the analysis and interpretation of relationships between symptoms that are complex, potentially non-linear, and dynamic. Dynamic Time Warping (DTW) is used to measure similarity in temporal sequences, and has recently been found effective in modelling psychopathology symptom networks.ObjectivesWe aim to demonstrate that DTW could also be used to model the network structure in Ecological Momentary Assessment (EMA) data.Methods355 participants of the Netherlands Study of Depression and Anxiety (NESDA), of which 100 with and 255 without current disorder, completed EMA assessments of 20 symptoms (e.g., feeling sad, tired, satisfied) five times a day for two weeks. DTW analysis was performed on the group level, comparing participants suffering from mood disorders to healthy controls. DTW distances were visualized as an undirected symptom network, in which we adjusted for the average symptom severity per item per person.ResultsDTW analysis of close to half a million symptom scores yielded six symptom dimensions based on their aggregated similarity of changes over time within the participants. Surprisingly, negative affect symptom networks were found to be less strongly connected in those currently suffering from mood disorders than in controls, whereas the network density of (reverse-coded) positive affect symptoms was more closely connected in this group. This is contrary to the results of previous studies, where negative affect-related symptom networks of those with mood disorders were found to be more strongly interconnected.ConclusionsDTW is a promising new technique for analyzing EMA data and modeling dynamic symptom networks at both the individual and group levels. Using EMA data, symptom networks and dimensions can be modeled with great structural and temporal detail. Incorporating the temporal symptom dynamics may highlight the importance of the independent trajectories of negative mood symptoms.Disclosure of InterestNone Declared

Deep learning assessment of syllable affiliation of intervocalic consonants.

In English, a sentence like "He made out our intentions." could be misperceived as "He may doubt our intentions." because the coda /d/ sounds like it has become the onset of the next syllable. The nature and occurrence condition of this resyllabification phenomenon are unclear, however. Previous empirical studies mainly relied on listener judgment, limited acoustic evidence, such as voice onset time, or average formant values to determine the occurrence of resyllabification. This study tested the hypothesis that resyllabification is a coarticulatory reorganisation that realigns the coda consonant with the vowel of the next syllable. Deep learning in conjunction with dynamic time warping (DTW) was used to assess syllable affiliation of intervocalic consonants. The results suggest that convolutional neural network- and recurrent neural network-based models can detect cases of resyllabification using Mel-frequency spectrograms. DTW analysis shows that neural network inferred resyllabified sequences are acoustically more similar to their onset counterparts than their canonical productions. A binary classifier further suggests that, similar to the genuine onsets, the inferred resyllabified coda consonants are coarticulated with the following vowel. These results are interpreted with an account of resyllabification as a speech-rate-dependent coarticulatory reorganisation mechanism in speech.

A wind speed vector-wind power curve modeling method based on data denoising algorithm and the improved Transformer

• A wind power curve modeling method based on improved Transformer is proposed. • The CEEMDAN algorithm is introduced for data denoising. • Multivariate combined with DTW analysis optimizes the network input. • Convolution combined with multi-head attention enhances information mining. • A multi-dimensional evaluation mechanism is established to evaluate the model. The complex nonlinear relationship between the wind speed and the wind power, and the singularity of wind speed information leads to the lack of accuracy of current wind power curve modeling. To address the problem, this paper presents a high-precision wind power curve modeling method based on the wind speed vector, including the wind speeds and wind directions at different heights of the wind measuring tower. First, considering the stochastic fluctuation of the wind speed vectors and wind power sequences, complementary ensemble empirical modal decomposition with adaptive noise (CEEMDAN) is used to decompose and reconstruct the high-noise data. Second, based on the reconstructed data, dynamic time warping (DTW) is adopted to analyze the lagged causality between current wind power and historical wind speed series. In order to better mine the rules, the improved Transformer network is proposed with two convolutional layers and multi-head attention mechanisms to develop the wind speed vector-wind power curve model. Finally, through comparative experiments with the mainstream methods, the advancement of the proposed wind power curve modeling method is verified from the perspective of modeling error and its distribution

Capturing Cognitive Events Embedded in the Real World Using Mobile Electroencephalography and Eye-Tracking

The study of cognitive processes underlying natural behaviors implies departing from computerized paradigms and artificial experimental probes. The present study aims to assess the feasibility of capturing neural markers (P300 ERPs) of cognitive processes evoked in response to the identification of task-relevant objects embedded in a real-world environment. To this end, EEG and eye-tracking data were recorded while participants attended stimuli presented on a tablet and while they searched for books in a library. Initial analyses of the library data revealed that P300-like features shifted in time. A Dynamic Time Warping analysis confirmed the presence of P300 ERP in the library condition. Library data were then lag-corrected based on cross-correlation coefficients. Together, these approaches uncovered P300 ERP responses in the library recordings. These findings highlight the relevance of scalable experimental designs, joint brain and body recordings, and template-matching analyses to capture cognitive events during natural behaviors.

Deterioration of postural control due to the increase of similarity between center of pressure and smooth-pursuit eye movements during standing on one leg.

Upright postural control is regulated by afferent and efferent/reafferent visual mechanisms. There are two types of efferent and conjugate eye movements: saccades and smooth pursuits. Although postural control is improved by saccades, the effects of smooth pursuits on postural control are still debated, because the difficulties of postural and visual tasks differ in the previous research. Additionally, the mechanisms that interfere with postural control and smooth pursuit are not fully understood. To address these issues, we examined the effects of different patterns of smooth-pursuit eye movement on the path length of the center of pressure (COP) displacement under bipedal and unipedal standing conditions. The relative frequency and amplitude of the COP displacement were remarkably increased when uniform linear visual targets were presented during unipedal standing. In addition, dynamic time warping analysis demonstrated that the similarity between the displacement of the COP and eye movements was increased by the presentation of uniform linear visual targets with orientation selectivity during unipedal standing but not during bipedal standing. In contrast, the attenuation of similarity between the displacement of the COP and eye movements significantly decreased the path length, relative frequency, and amplitude of the COP displacement. Our results indicate that postural stability is deteriorated by the increase of similarity between the displacement of the COP and smooth-pursuit eye movements under unstable conditions.

Network structure of time-varying depressive symptoms through dynamic time warp analysis in late-life depression.

ObjectivesLate‐life major depressive disorder (MDD) can be conceptualized as a complex dynamic system. However, it is not straightforward how to analyze the covarying depressive symptoms over time in case of sparse panel data. Dynamic time warping (DTW) analysis may yield symptom networks and dimensions both at the patient and group level.MethodsIn the Netherlands Study of Depression in Older People (NESDO) depressive symptoms were assessed every 6 months using the 30‐item Inventory of Depressive Symptomatology (IDS) with up to 13 assessments per participant. Our sample consisted of 182 persons, aged ≥ 60 years, with an IDS total score of 26 or higher at baseline. Symptom networks dimensions, and centrality metrics were analyzed using DTW and Distatis analyses.ResultsThe mean age was 69.8 years (SD 7.1), with 69.0% females, and a mean IDS score of 38.0 (SD = 8.7). DTW enabled visualization of an idiographic symptom network in a single NESDO participant. In the group‐level nomothetic approach, four depressive symptom dimensions were identified: “core symptoms”, “lethargy/somatic”, “sleep”, and “appetite/atypical”. Items of the “internalizing symptoms” dimension had the highest centrality, whose symptom changes over time were most similar to those changes of other symptoms.ConclusionsDTW revealed symptom networks and dimensions based on the within‐person symptom changes in older MDD patients. Its centrality metrics signal the most influential symptoms, which may aid personalized care.

SCALING THE 14C-EXCURSION SIGNAL IN MULTIPLE TREE-RING SERIES WITH DYNAMIC TIME WARPING

ABSTRACTA signal of rapid changes in 14C production is logged in annual series of 14C derived from tree rings, which can be associated with diverse effects of cosmic-ray fluxes, including solar burst and supernova events. These 14C signatures may vary in time and space. The intensity and structure of the 14C signal is multifaced, which complicates understanding of the forcing and attribution of the underlying astrophysical events. It was suggested that Δ14C in 1052/53 CE and 1054/55 CE signatures at a 4‰–6‰ range over two years could be caused by the Crab Nebula supernova (SN1054) or/and solar perturbation. The temporal incoherence of the signals in published 14C series is investigated with dynamic time warping (DTW), novel approach for matching time-behavioral patterns in multiple 14C datasets. DTW analysis of four 14C signatures from tree rings of California, Finland and England suggests that 14C spikes between 1052 CE and 1055 CE can be caused by a single event. The flickering fingerprint may result from cross-dating inconformity. Cross-checking of tree-ring records from distant locations is impossible sometimes due to large difference in environmental conditions limiting tree growth. The methodology helps to align the signals and can be applied to other 14C datasets.

Comparability of Heart Rate Turbulence Methodology: 15 Intervals Suffice to Calculate Turbulence Slope - A Methodological Analysis Using PhysioNet Data of 1074 Patients.

Heart rate turbulence (HRT) is a characteristic heart rate pattern triggered by a ventricular premature contraction (VPC). It can be used to assess autonomic function and health risk for various conditions, e.g., coronary artery disease or cardiomyopathy. While comparability is essential for scientific analysis, especially for research focusing on clinical application, the methodology of HRT still varies widely in the literature. Particularly, the ECG measurement and parameter calculation of HRT differs, including the calculation of turbulence slope (TS). In this article, we focus on common variations in the number of intervals after the VPC that are used to calculate TS (#TSRR) posing two questions: 1) Does a change in #TSRR introduce noticeable changes in HRT parameter values and classification? and 2) Do larger values of turbulence timing (TT) enabled by a larger #TSRR still represent distinct HRT? We compiled a free-access data set of 1,080 annotated long-term ECGs provided by Physionet. HRT parameter values and risk classes were determined both with #TSRR 15 and 20. A standard local tachogram was created by averaging the tachograms of only the files with the best heart rate variability values. The shape of this standard VPC sequence was compared to all VPC sequences grouped by their TT value using dynamic time warping (DTW) in order to identify HRT shapes. When calculated with different #TSRR, our results show only a little difference between the number of files with enough valid VPC sequences to calculate HRT (<1%) and files with different risk classes (5 and 6% for HRT0-2 and HRTA-C, respectively). In the DTW analysis, the difference between averaged sequences with a specific TT and the standard sequence increased with increasing TT. Our analysis suggests that HRT occurs in the early intervals after the VPC and TS calculated from late intervals reflects common heart rate variability rather than a distinct response to the VPC. Even though the differences in classification are marginal, this can lead to problems in clinical application and scientific research. Therefore, we recommend uniformly using #TSRR 15 in HRT analysis.

Use of Dynamic Time Warping for Description of Combustion Process in a Biomass Boiler

Abstract The efficient biomass energy use is a key prerequisite for the implementation of renewable energy development strategies on a regional level. For the highly efficient energy use in the combustion process, it is necessary to properly regulate the process based on its precise description. The paper aim is to evaluate whether dynamic time warping (DTW) methods can be used for this description, as well as for the recognition of the specific operating state of a biomass boiler. For the DTW analysis, operating records of more than 10 hours of a laboratory biomass boiler (P = 25 kW) were used, including an emission analysis, for which the operating modes were intentionally alternated in order to identify the stable and transient states of boiler operation. Based on the results, it can be stated that the identical partial operating sections of the controlled variables can be reliably identified in the operating variables of boiler by means of the DTW method, since its manifestations of operating regulation showed compliance with the given operating state, and it is possible to identify a partial quantity for estimating the total operating boiler state.

Biomarker identification using dynamic time warping analysis: a longitudinal cohort study of patients with COVID-19 in a UK tertiary hospital

ObjectivesCOVID-19 is a heterogeneous disease, and many reports have described variations in demographic, biochemical and clinical features at presentation influencing overall hospital mortality. However, there is little information regarding longitudinal...

Spatial distribution of inter- and intra-crop variability using time-weighted dynamic time warping analysis from Sentinel-1 datasets

This study investigates the robustness of an advanced classification algorithm to spatially map heterogeneous, fragmented croplands using multi-temporal synthetic aperture radar (SAR) datasets. Four parameters derived from Sentinel-1 (backscatters in dual-polarization: σVHo, σVVo, cross-ratio (σVHoσVVo), and radar vegetation index (RVI)) were considered to develop temporal patterns and correlate with un-classified time-series satellite imagery using time-weighted dynamic time warping (TWDTW) algorithm. Pixel and parcel based classifications were considered to identify four crop varieties (paddy, sugarcane, cotton and vegetables) subjected to two water limiting conditions (low stress-LS, high stress-HS). In-situ data were split-sampled (30:70 ratio) between training (to develop temporal patterns) and testing (to validate classification output). Overall accuracy of pixel and parcel based classifications were 63% and 76% with a Kappa coefficient of 0.58 and 0.73 respectively. In conclusion, parcel based TWDTW algorithm conditioned by temporal signatures of RVI has effectively delineated croplands with varying irrigation treatments for yield and damage assessment modeling studies.

A Sensor-Based Data Driven Framework to Investigate PM2.5 in the Greater Detroit Area

PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> are inhalable particles with aerodynamic diameters of 2.5 micrometers or smaller. PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> concentrations require close monitoring as they impose negative effects on both human health and air quality. Monitoring PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> concentrations in the metropolitan Detroit Area is increasingly important as its residents are being disproportionately exposed to harmful air pollution due to health inequities through economic divestment, limited educational and employment opportunities. The relations between PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> and meteorological factors can be critical in understanding how particulate matter affects humans and the environment. This study utilizes PurpleAir sensors to measure PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> along with some methodological factors such as humidity and applies temporal analysis of the impact of meteorological factors on PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> concentrations and spatiotemporal analysis of PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> distributions at different locations over the Greater Detroit Area via Long Short Term Memory (LSTM) neural networks and Dynamic Time Warping (DTW) algorithms, respectively. Our findings show that although LSTMs with exogenous variables (i.e., the current values of PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> concentration, meteorological features, and weather conditions) can accurately (i.e., average RMSE of 3.2 μg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) predict levels of PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> , but there is no significant relation between the mentioned meteorological factors and PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> concentrations over the Greater Detroit Area. Furthermore, DTW analysis portraits the similarity of PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> behavioral patterns over the Greater Detroit Area.

Time-weighted dynamic time warping analysis for mapping interannual cropping practices changes in large-scale agro-industrial farms in Brazilian Cerrado

Methods for crop phenology detection using time series analysis have provided accurate information for large agricultural areas in shorter processing times, which can be useful for agronomic management and supply chain monitoring. Given the crop dynamics in the Brazilian Cerrado, with alternating crop type plantings, crop successions, and crop rotations, as well as climate and crop practices variation between harvest periods, these methods can be useful for detecting subtle land use and land cover changes at farm and crop field scales, improving thematic classifications and the near real-time crop monitoring. In this study, the Time-Weighted Dynamic Time Warping method was applied to recognize patterns in Moderate Resolution Imaging Spectroradiometer (MODIS) time series for land use and cover classification, identifying crop successions and rotations at crop field level in a large-scale agro-industrial agglomerate of farms located at Brazilian Cerrado. We detected and analyzed temporal cropping patterns in training samples to classify the MODIS time series and images, using a robust ground truth data set for validation. The method distinguished Cotton-fallow, Soybean-cotton, Soybean-maize, and Soybean-millet cropping patterns with an overall accuracy above 85% for all evaluated harvest periods. Seasonal variations in the crop fields, caused by interannual succession and rotation, were detected. The method demonstrated the benefit of creating a spatial vector data set for supporting decision-making in several crop management contexts, improving crop and supply chain monitoring.

Understanding personalized dynamics to inform precision medicine: a dynamic time warp analysis of 255 depressed inpatients

BackgroundMajor depressive disorder (MDD) shows large heterogeneity of symptoms between patients, but within patients, particular symptom clusters may show similar trajectories. While symptom clusters and networks have mostly been studied using cross-sectional designs, temporal dynamics of symptoms within patients may yield information that facilitates personalized medicine. Here, we aim to cluster depressive symptom dynamics through dynamic time warping (DTW) analysis.MethodsThe 17-item Hamilton Rating Scale for Depression (HRSD-17) was administered every 2 weeks for a median of 11 weeks in 255 depressed inpatients. The DTW analysis modeled the temporal dynamics of each pair of individual HRSD-17 items within each patient (i.e., 69,360 calculated “DTW distances”). Subsequently, hierarchical clustering and network models were estimated based on similarities in symptom dynamics both within each patient and at the group level.ResultsThe sample had a mean age of 51 (SD 15.4), and 64.7% were female. Clusters and networks based on symptom dynamics markedly differed across patients. At the group level, five dynamic symptom clusters emerged, which differed from a previously published cross-sectional network. Patients who showed treatment response or remission had the shortest average DTW distance, indicating denser networks with more synchronous symptom trajectories.ConclusionsSymptom dynamics over time can be clustered and visualized using DTW. DTW represents a promising new approach for studying symptom dynamics with the potential to facilitate personalized psychiatric care.

Clustering of Time Series Water Quality Data Using Dynamic Time Warping: A Case Study from the Bukhan River Water Quality Monitoring Network

It is essential to monitor water quality for river water management because river water is used for various purposes and is directly related to the health and safety of a population. Proper network installation and removal is an important part of water quality monitoring and network operation efficiency. To do this, cluster analysis based on calculated similarity between measuring stations can be used. In this study, we measured the similarities between 12 water quality monitoring stations of the Bukhan River. River water quality data always have a station-dependent time lag because water flows from upstream to downstream; therefore, we proposed a Dynamic Time Warping (DTW) algorithm that searches for the minimum distance by changing and comparing time-points, rather than using the Euclidean algorithm, which compares the same time-point. Both Euclidean and DTW algorithms were applied to nine water quality variables to identify similarities between stations, and K-medoids cluster analysis were performed based on the similarity. The Clustering Validation Index (CVI) was used to select the optimal number of clusters. Our results show that the Euclidean algorithm formed clusters by mixing mainstream and tributary stations; the mainstream stations were largely divided into three different clusters. In contrast, the DTW algorithm formed clear clusters by reflecting the characteristics of water quality and watershed. Furthermore, because the Euclidean algorithm requires the lengths of the time series to be the same, data loss was inevitable. As a result, even where clusters were the same as those obtained by DTW, the characteristics of the water quality variables in the cluster differed. The DTW analysis in this study provides useful information for understanding the similarity or difference in water parameter values between different locations. Thus, the number and location of required monitoring stations can be adjusted to improve the efficiency of field monitoring network management.