Cluster Analysis Of Time Series Research Articles

Affinity Coefficient for Clustering Autoregressive Moving Average Models

In various fields, such as economics, finance, bioinformatics, geology, and medicine, namely, in the cases of electroencephalogram, electrocardiogram, and biotechnology, cluster analysis of time series is necessary. The first step in cluster applications is to establish a similarity/dissimilarity coefficient between time series. This article introduces an extension of the affinity coefficient for the autoregressive expansions of the invertible autoregressive moving average models to measure their similarity between them. An application of the affinity coefficient between time series was developed and implemented in R. Cluster analysis is performed with the corresponding distance for the estimated simulated autoregressive moving average of order one. The primary findings indicate that processes with similar forecast functions are grouped (in the same cluster) as expected concerning the affinity coefficient. It was also possible to conclude that this affinity coefficient is very sensitive to the behavior changes of the forecast functions: processes with small different forecast functions appear to be well separated in different clusters. Moreover, if the two processes have at least an infinite number of π- weights with a symmetric signal, the affinity value is also symmetric.

Energy landscape analysis and time-series clustering analysis of patient state multistability related to rheumatoid arthritis drug treatment: The KURAMA cohort study.

Rheumatoid arthritis causes joint inflammation due to immune abnormalities, resulting in joint pain and swelling. In recent years, there have been considerable advancements in the treatment of this disease. However, only approximately 60% of patients achieve remission. Patients with multifactorial diseases shift between states from day to day. Patients may remain in a good or poor state with few or no transitions, or they may switch between states frequently. The visualization of time-dependent state transitions, based on the evaluation axis of stable/unstable states, may provide useful information for achieving rheumatoid arthritis treatment goals. Energy landscape analysis can be used to quantitatively determine the stability/instability of each state in terms of energy. Time-series clustering is another method used to classify transitions into different groups to identify potential patterns within a time-series dataset. The objective of this study was to utilize energy landscape analysis and time-series clustering to evaluate multidimensional time-series data in terms of multistability. We profiled each patient's state transitions during treatment using energy landscape analysis and time-series clustering. Energy landscape analysis divided state transitions into two patterns: "good stability leading to remission" and "poor stability leading to treatment dead-end." The number of patients whose disease status improved increased markedly until approximately 6 months after treatment initiation and then plateaued after 1 year. Time-series clustering grouped patients into three clusters: "toward good stability," "toward poor stability," and "unstable." Patients in the "unstable" cluster are considered to have clinical courses that are difficult to predict; therefore, these patients should be treated with more care. Early disease detection and treatment initiation are important. The evaluation of state multistability enables us to understand a patient's current state in the context of overall state transitions related to rheumatoid arthritis drug treatment and to predict future state transitions.

Rethinking new venture growth: A time series cluster analysis of biotech startups’ heterogeneous growth trajectories

Startups are crucial job creators and drivers of economic growth. Research on startups has predominantly targeted high-growth startups, while a comprehensive understanding of alternative growth journeys remains limited. Addressing this gap, we employ the theory of early firm growth and the time-calibrated theory of entrepreneurial action to examine 416 biotech startups. We use time series cluster analysis to unveil four heterogeneous new venture growth trajectories. These are characterized by unique timings, paces, and sequences of financial, human, and innovative resource-related activities. This study contributes to new venture growth research, particularly in science-based high-tech startups, with its nuanced understanding of diverse growth pathways, including intriguing notions of early failure, growth reversal, and high and moderate steady growth.

Characteristics of changes in plasma proteome profiling after sleeve gastrectomy.

Bariatric surgery (BS), recognized as the most effective intervention for morbid obesity and associated metabolic comorbidities, encompasses both weight loss-dependent and weight loss-independent mechanisms to exert its metabolic benefits. In this study, we employed plasma proteomics technology, a recently developed mass spectrometric approach, to quantitatively assess 632 circulating proteins in a longitudinal cohort of 9 individuals who underwent sleeve gastrectomy (SG). Through time series clustering and Gene Ontology (GO) enrichment analysis, we observed that complement activation, proteolysis, and negative regulation of triglyceride catabolic process were the primary biological processes enriched in down-regulated proteins. Conversely, up-regulated differentially expressed proteins (DEPs) were significantly associated with negative regulation of peptidase activity, fibrinolysis, keratinocyte migration, and acute-phase response. Notably, we identified seven proteins (ApoD, BCHE, CNDP1, AFM, ITIH3, SERPINF1, FCN3) that demonstrated significant alterations at 1-, 3-, and 6-month intervals post SG, compared to baseline. These proteins play essential roles in metabolism, immune and inflammatory responses, as well as oxidative stress. Consequently, they hold promising potential as therapeutic targets for combating obesity and its associated comorbidities.

Pengelompokan Provinsi di Indonesia Menggunakan Time Series Clustering pada Sektor Ekspor Nonmigas

Indonesia's export activities are dominated by non-oil and gas exports consisting of four sectors, namely the processing industry, agriculture, mining, and others. The government must pay attention to non-oil and gas exports for each province because exports can play an essential role in a country's economic growth. This study was conducted to cluster provinces in Indonesia using time series clustering in the non-oil and gas export sector based on data patterns concerning Dynamic Time Warping (DTW) distance. The sectors used in this study are the manufacturing industry sector and the agricultural sector in 34 Indonesian provinces in the period 2017 - 2021. Time series clustering analysis uses the average linkage method with DTW distance and the selection of the optimum number of clusters using the silhouette coefficient method. The results of the analysis in the processing industry sector resulted in 3 optimum clusters, namely cluster 1 consisting of 1 province that has high processing industry exports, cluster 2 consisting of 8 provinces that have medium processing industry exports, and cluster 3 consisting of 25 provinces that have low processing industry exports. As for the agricultural sector, it produces 2 optimum clusters, namely cluster 1 consisting of 5 provinces that have high agricultural industry exports, and cluster 2 consisting of 29 provinces that have low agricultural industry exports. The clustering results in the processing industry sector and the agricultural sectors have a silhouette coefficient value of 0.778 and 0.798, so it is said to have a strong cluster structure.

Prosocial responses in disasters: Zooming out to neighboring regions and uncovering the impact of socioeconomic and built environment features

In recent years, with the escalation of extreme climate events worldwide, prosocial responses from community members, volunteers, and organizations are becoming increasingly important to alleviate the impact of disasters. Nevertheless, the potential for prosocial responses from neighboring regions not immediately impacted by disaster has received limited attention, and particularly, very little is known about the interrelationship between prosocial responses and different socioeconomic and built environment features. This study investigated prosocial responses in regions of Florida not immediately impacted (FNII) during Hurricane Ian in 2022, using Twitter data and empirically assessed their interrelationship with various socioeconomic and built environment features. The correlation results revealed that prosocial responses and sentiments are interrelated with socioeconomic and built environment features and vary on spatial and temporal scales in regions of FNII. Specifically, the findings showed that communities with higher socioeconomic status and improved built environment facilities exhibited more prosocial responses. Moreover, the best-performed regression model, with an R2 value of 0.931, can precisely predict prosocial response-related tweets using socioeconomic and built environment features. Finally, the time series clustering analysis sheds light on socioeconomic and built environment disparities that impact prosocial responses; notably, counties with more advanced educational attainment display increased prosocial responses.

Predicting CKD progression using time-series clustering and light gradient boosting machines

Predicting the transition of kidney function in chronic kidney disease is difficult as specific symptoms are lacking and often overlooked, and progress occurs due to complicating factors. In this study, we applied time-series cluster analysis and a light gradient boosting machine to predict the trajectories of kidney function in non-dialysis dependent chronic kidney disease patients with baseline estimated glomerular filtration rate (GFR) ≥ 45 mL/min/1.73 m2. Based on 5-year changes in estimated GFR, participants were stratified into groups with similar trajectories by cluster analysis. Next, we applied the light gradient boosting machine algorithm and Shapley addictive explanation to develop a prediction model for clusters and identify important parameters for prediction. Data from 780 participants were available for analysis. Participants were classified into five classes (Class 1: n = 78, mean [± standard deviation] estimated GFR 100 ± 19.3 mL/min/1.73 m2; Class 2: n = 176, 76.0 ± 9.3 mL/min/1.73 m2; Class 3: n = 191, 59.8 ± 5.9 mL/min/1.73 m2; Class 4: n = 261, 52.7 ± 4.6 mL/min/1.73 m2; and Class 5: n = 74, 53.5 ± 12.0 mL/min/1.73 m2). Declines in estimated GFR were 8.9% in Class 1, 12.2% in Class 2, 4.9% in Class 3, 12.0% in Class 4, and 45.1% in Class 5 during the 5-year period. The accuracy of prediction was 0.675, and the top three most important Shapley addictive explanation values were 1.61 for baseline estimated GFR, 0.12 for hemoglobin, and 0.11 for body mass index. The estimated GFR transition of patients with preserved chronic kidney disease mostly depended on baseline estimated GFR, and the borderline for estimated GFR trajectory was nearly 50 mL/min/1.73 m2.

Multivariate Time-Series Cluster Analysis for Multiple Functional Domains to Identify Recovery Patterns of Patients With Fragility Hip Fracture After Surgery

Multivariate Time-Series Cluster Analysis for Multiple Functional Domains to Identify Recovery Patterns of Patients With Fragility Hip Fracture After Surgery

Finding Patterns in the Dynamics of Protest Campaigns: Computational Modeling and Empirical Analysis

In most of current papers devoted to the analysis of protest-repression nexus,the research design misses the dynamic nature of this nexus, which seems methodologically incorrect. The analysis of the dynamics allows us to identify the role of various factors influencing the course of this conflict. The variety of different dynamics of the number of protesters and the dynamics of the use of repression gives rise to a variety of scenarios for the development of a protest campaign. In this regard, this paper raises the question of identifying dynamic patterns. At the same time, we consider both empirical scenarios that have already taken place in real protests, as well as “ideal”, i.e. arising in theory and capable of serving as guidelines in the analysis of real ones. To obtain “ideal” scenarios, a theoretical and mathematical model was developed with various strategies for the reactions of the authorities to the protesters, which we implemented into the existing computational model of protest mobilization. Based on the data obtained in the course of computer simulations, firstly, by linear and logistic regressions, the effects of various decision-making mechanisms on the survival of protests were evaluated, and, secondly, using various methods of time series cluster analysis, we discovered a number of patterns. For verification, the same methods of cluster analysis were applied repeatedly on empirical data.

Statistical Analysis of the Socio-Economic Situation in St. Petersburg in the Context of Crises

Purpose of the study. Statistical research of the socio-economic development issues of the region acquires special significance in crisis situations. Statistical methods make it possible to quantify the current situation, identify the impact of crisis phenomena and forecast the development of the region. In the analysis of socio-economic development, both economic characteristics (GDP, production and distribution) and direct indicators of the standard of living of the population (unemployment level, personal income and wages) are the key ones. The purpose of this paper is to statistically assess the impact of crisis situations on the socio-economic situation in St. Petersburg.Materials and methods. The information base for the study was official data from the Federal State Statistics Service. The paper uses methods of time series analysis, cluster analysis and analysis of structural changes.Results. Based on the results of the study, the main periods in the dynamics of the main socio-economic indexes were identified. Special attention is paid to studying the structure of GRP of St. Petersburg. Emphasis is placed on comparing the dynamics of regional indexes with data for the federal district and the Russian Federation as a whole. The features of the city’s development are considered using cluster analysis according to the current range of factors for different time periods. An assessment of the achievement of key planned indexes is given and a comprehensive index is proposed for assessing the development of the dynamics of the socio-economic development of the region. Particular attention is paid to analyzing the impact of crisis situations on the socio-economic status of the region and assessing the degree of their impact.Conclusion. Based on the results of the analysis, recommendations were given for the development of the region, which can be used in the implementation of socio-economic policy. Particular attention is paid to indexes of living standards.

An air combat maneuver pattern extraction based on time series segmentation and clustering analysis

Target maneuver recognition is a prerequisite for air combat situation awareness, trajectory prediction, threat assessment and maneuver decision. To get rid of the dependence of the current target maneuver recognition method on empirical criteria and sample data, and automatically and adaptively complete the task of extracting the target maneuver pattern, in this paper, an air combat maneuver pattern extraction based on time series segmentation and clustering analysis is proposed by combining autoencoder, G-G clustering algorithm and the selective ensemble clustering analysis algorithm. Firstly, the autoencoder is used to extract key features of maneuvering trajectory to remove the impacts of redundant variables and reduce the data dimension; Then, taking the time information into account, the segmentation of Maneuver characteristic time series is realized with the improved FSTS-AEGG algorithm, and a large number of maneuver primitives are extracted; Finally, the maneuver primitives are grouped into some categories by using the selective ensemble multiple time series clustering algorithm, which can prove that each class represents a maneuver action. The maneuver pattern extraction method is applied to small scale air combat trajectory and can recognize and correctly partition at least 71.3% of maneuver actions，indicating that the method is effective and satisfies the requirements for engineering accuracy. In addition, this method can provide data support for various target maneuvering recognition methods proposed in the literature, greatly reduce the workload and improve the recognition accuracy.

Diabetes Reshapes the Circadian Transcriptome Profile in Murine Retina.

Diabetic retinopathy (DR) is a common complication of diabetes and has a high prevalence. Dysregulation of circadian rhythmicity is associated with the development of DR. This research aimed to investigate rhythmical transcriptome alterations in the retina of diabetic mice. C57BL/6J mice were used to establish a diabetes model by intraperitoneal injection of streptozotocin (STZ). After 12 weeks, retinas were collected continuously at 4-hour intervals over 1day. Total RNA was extracted from normal and STZ-treated retinas and RNA sequencing was performed. Meta2d algorithm, Kyoto Encyclopedia of Genes, Phase Set Enrichment Analysis, and time-series cluster analysis were used to identify, analyze and annotate the composition, phase, and molecular functions of rhythmic transcripts in retinas. The retina exhibited powerful transcriptome rhythmicity. STZ-induced diabetes markedly modified the transcriptome characteristics of the circadian transcriptome in the retina, including composition, phase, and amplitude. Moreover, the diabetic mice led to re-organized temporal and clustering enrichment pathways in space and time and affected core clock machinery. Diabetes impairs the circadian rhythm of the transcriptomic profile of retinas. This study offers new perspectives on the negative effects of diabetes on the retina, which may provide important information for the development of new treatments for DR.

Groundwater monitoring and specific yield estimation using time-lapse electrical resistivity imaging and machine learning

This paper presents an alternative method for monitoring groundwater levels and estimating specific yields of an unconfined aquifer under different seasonal conditions. The approach employs the Time-Lapse Electrical Resistivity Imaging (TL-ERI) method and machine learning-based time series clustering. A TL-ERI survey was conducted at ten sites (WS01-WS10 sites) throughout the dry and wet seasons, with five-time measurements collected for each site, in the Taichung-Nantou Basin along the Wu River, Central Taiwan. The obtained resistivity raw data was inverted and converted into normalized water content values using Archie’s law, followed by applying the Van Genuchten (VG) model for the Soil Water Characteristic Curve to estimate the Groundwater Level (GWL), and estimated the theoretical specific yield (Sy) by computing the difference between the saturated and residual water contents of the fitted VG model. In addition, the specific yield capacity (Sc), representing the nature of the storage capacity in the aquifer, was also calculated. The results showed that this approach was able to estimate those hydrogeological parameters. The spatial distribution of the GWL reveals that during the dry-wet seasons from February to July, there was a high GWL that extended from southeast to northwest. Conversely, during the wet-dry seasons from July to October, the high GWL shrank, which can be attributed to recharge variations from rainfall events. The determined spatial distribution of Sy and Sc fall within the range of 0.03–0.24 and 0.14–0.25, respectively. To quantitatively establish areas of similar groundwater level changes along with the VG model parameter variations during the study period, a Time series Clustering analysis (TSC) was performed by utilizing Hierarchical Agglomerative Clustering (HAC). The findings suggest that the WS03 site is a promising area for further investigation due to its highest Sc value with a slight change in groundwater levels during the dry and wet seasons. This study brings an advanced development of the geoelectrical method to estimate regional hydrogeological parameters in an area with limited available groundwater observation wells, in different seasonal conditions for groundwater management purposes.

Physical Activity Pattern of Adults With Metabolic Syndrome Risk Factors: Time-Series Cluster Analysis.

Physical activity plays a crucial role in maintaining a healthy lifestyle, and wrist-worn wearables, such as smartwatches and smart bands, have become popular tools for measuring activity levels in daily life. However, studies on physical activity using wearable devices have limitations; for example, these studies often rely on a single device model or use improper clustering methods to analyze the wearable data that are extracted from wearable devices. This study aimed to identify methods suitable for analyzing wearable data and determining daily physical activity patterns. This study also explored the association between these physical activity patterns and health risk factors. People aged >30 years who had metabolic syndrome risk factors and were using their own wrist-worn devices were included in this study. We collected personal health data through a web-based survey and measured physical activity levels using wrist-worn wearables over the course of 1 week. The Time-Series Anytime Density Peak (TADPole) clustering method, which is a novel time-series method proposed recently, was used to identify the physical activity patterns of study participants. Additionally, we defined physical activity pattern groups based on the similarity of physical activity patterns between weekdays and weekends. We used the χ2 or Fisher exact test for categorical variables and the 2-tailed t test for numerical variables to find significant differences between physical activity pattern groups. Logistic regression models were used to analyze the relationship between activity patterns and health risk factors. A total of 47 participants were included in the analysis, generating a total of 329 person-days of data. We identified 2 different types of physical activity patterns (early bird pattern and night owl pattern) for weekdays and weekends. The physical activity levels of early birds were less than that of night owls on both weekdays and weekends. Additionally, participants were categorized into stable and shifting groups based on the similarity of physical activity patterns between weekdays and weekends. The physical activity pattern groups showed significant differences depending on age (P=.004) and daily energy expenditure (P<.001 for weekdays; P=.003 for weekends). Logistic regression analysis revealed a significant association between older age (≥40 y) and shifting physical activity patterns (odds ratio 8.68, 95% CI 1.95-48.85; P=.007). This study overcomes the limitations of previous studies by using various models of wrist-worn wearables and a novel time-series clustering method. Our findings suggested that age significantly influenced physical activity patterns. It also suggests a potential role of the TADPole clustering method in the analysis of large and multidimensional data, such as wearable data.

Spatiotemporal Evolution of Cultivated Land Use Eco-Efficiency and Its Dynamic Relationship with Landscape Pattern Change from the Perspective of Carbon Effect: A Case Study of Henan, China

Cultivated land is a vital factor in agricultural production but faces multiple challenges, including declining total area, spatial transformation, and ecological degradation. It is imperative to enhance cultivated land use eco-efficiency (CLUE). This study aimed to evaluate the CLUE that considers both carbon sequestration and emissions using the SBM model at the county level. Next, spatial autocorrelation was employed to measure CLUE’s spatial correlation. The spatial agglomeration pattern of CLUE was determined, then time-series cluster analysis was used to identify the temporal evolution patterns of CLUE in various districts and counties. Furthermore, we explored the spatiotemporal dynamic relationship between CLUE and landscape pattern changes using landscape pattern index and geographically and temporally weighted regression (GTWR), considering spatiotemporal heterogeneity, and using interaction detectors to identify the interaction between landscape pattern factors on CLUE. The results show that: (1) From 2000 to 2020, CLUE in Henan Province varied between 0.50 and 0.70 in most years, indicating potential for improvement. There are four primary temporal evolution patterns: 26 Late-development, 22 Wave-rising, 27 Fluctuation-rising, and 29 Continuous-rising types of CLUE. (2) CLUE exhibits low values in the middle and eastern regions, i.e., areas with high values are concentrated in the southern districts, counties, and western and northern regions. CLUE has a significant positive spatial correlation with HH agglomeration areas mainly concentrated in Xinyang City, and LL agglomeration areas mainly located in the eastern and central regions. (3) Overall, different landscape factors exhibit varying degrees of spatiotemporal heterogeneity in their impact on CLUE. The total area and aggregation of cultivated land have a positive effect on CLUE, with the area of the positive influence of the total area gradually expanding over time and the aggregation gradually decreasing. The complexity of cultivated land shape has a negative effect. The impact of cultivated land patch density is two-sided, with the area of negative influence gradually expanding over time. (4) The interaction between the total area, shape, and aggregation of cultivated land is enhanced. Additionally, the interaction between cultivated land patch density and other factors has changed from a weakening to a strengthening one, and the “double-edged sword” effect has gradually shifted into a one-way effect. Therefore, in the process of land consolidation, it is recommended to prioritize regularized, larger, and more concentrated cropland patches whenever possible.

Using Interactive Time-series Cluster Analysis to Relate Metabolomic Data with Perturbed Pathways

The study conducted on interactive time-series cluster analysis has shed light on the dynamic nature of the interaction that exists between metabolites and the activities that occur within living organisms. Integration of metabolomic data with pathways that had been disrupted was the method that was used to achieve this goal. We investigated the significance of metabolomics in biological systems, the fundamentals and applications of time-series cluster analysis, and the connection between metabolomic data and pathways that have been altered in the various sections of this research paper, such as the introduction, the literature review, the methodology, the results, the discussion, and the recommendations. These sections include: the introduction; the literature review; the methodology; the results; the discussion; and the recommendations. The introduction, the literature review, the methodology, the results, the discussion, and the suggestions are included in these parts.

How much food tracking during a digital weight-management program is enough to produce clinically significant weight loss?

The aim of this study was to identify the levels of food-tracking adherence that best predict ≥3%, ≥5%, and ≥10% weight loss at 6 months and to identify distinctive food-tracking trajectories among participants in a 6-month, commercial digital weight-management program. This study used data from 153 participants of a single-arm trial of a commercial digital weight-management program, WeightWatchers (WW). Receiver operating characteristic (ROC) curve analysis was conducted to identify the optimum thresholds of food tracking that can predict ≥3%, ≥5%, and ≥10% weight loss at 6 months. Time series clustering analysis was performed on weekly food-tracking data to identify trajectories and compare trajectories on weight loss at 6 months. ROC analyses showed that the optimum thresholds of food tracking were 28.5% of the intervention days to achieve ≥3% weight loss (area under the curve [AUC] = 0.820, p < 0.001), 39.4% to achieve ≥5% weight loss (AUC = 0.744, p < 0.001), and 67.1% to achieve 10% weight loss (AUC = 0.712, p = 0.002). Time series clustering analyses found three food-tracking trajectories. Trajectories differed significantly in weight loss at 6 months (F = 14.1, p < 0.001). Results suggest that perfect food-tracking adherence is not necessary to achieve clinically significant weight loss.

Topology Identification of Low-Voltage Distribution Network Based on Deep Convolutional Time-Series Clustering

Accurate topology relationships of low-voltage distribution networks are important for distribution network management. However, the topological information in Geographic Information System (GIS) systems for low-voltage distribution networks is prone to errors such as omissions and false alarms, which can have a heavy impact on the effective management of the networks. In this study, a novel method for the identification of topology relationships, including the user-transformer relationship and the user-phase relationship, is proposed, which is based on Deep Convolutional Time-Series Clustering (DCTC) analysis. The proposed DCTC method fuses convolutional autoencoder and clustering layers to perform voltage feature representation and clustering in a low-dimensional feature space simultaneously. By jointly optimizing the clustering process via minimizing the sum of the reconstruction loss and clustering loss, the proposed method effectively identifies the network topology relationships. Analysis of examples shows that the proposed method is correct and effective.

Time series cluster analysis reveals individual assignment of microbiota in captive tiger (Panthera tigris) and wildebeest (Connochaetes taurinus).

Fecal microbiota variability and individuality are well studied in humans and also in farm animals (related to diet- or disease-specific influences), but very little is known for exotic zoo-housed animals. This includes a wide range of species that differ greatly in microbiota composition and variation. For example, herbivorous species show a very similar and constant fecal microbiota over time, whereas carnivorous species appear to be highly variable in fecal microbial diversity and composition. Our objective was to determine whether species-specific and individual-specific clustering patterns were observed in the fecal microbiota of wildebeest (Connochaetes taurinus) and tigers (Panthera tigris). We collected 95 fecal samples of 11 animal individuals that were each sampled over eight consecutive days and analyzed those with Illumina MiSeq sequencing of the V3-V4 region of the 16SrRNA gene. In order to identify species or individual clusters, we applied two different agglomerative hierarchical clustering algorithms - a community detection algorithm and Ward's linkage. Our results showed that both, species-specific and individual-specific clustering is possible, but more reliable results were achieved when applying dynamic time warping which finds the optimal alignment between different time series. Furthermore, the bacterial families that distinguish individuals from each other in both species included daily occurring core bacteria (e.g., Acidaminococcaceae in wildebeests or Clostridiaceae in tigers) as well as individual dependent and more fluctuating bacterial families. Our results suggest that while it is necessary to consider multiple consecutive samples per individual, it is then possible to characterize individual abundance patterns in fecal microbiota in both herbivorous and carnivorous species. This would allow establishing individual microbiota profiles of animals housed in zoos, which is a basic prerequisite to quickly detect deviations and use microbiome analysis as a non-invasive and cost-effective tool in animal welfare.

Review of Clustering Methods for Functional Data

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across various fields of sciences, including but not limited to biology, (bio)chemistry, engineering, environmental science, medical science, psychology, social science, and so on. The phenomenal growth of the application of functional data clustering indicates the urgent need for a systematic approach to develop efficient clustering methods and scalable algorithmic implementations. On the other hand, there is abundant literature on the cluster analysis of time series, trajectory data, spatio-temporal data, and so on, which are all related to functional data. Therefore, an overarching structure of existing functional data clustering methods will enable the cross-pollination of ideas across various research fields. We here conduct a comprehensive review of original clustering methods for functional data. We propose a systematic taxonomy that explores the connections and differences among the existing functional data clustering methods and relates them to the conventional multivariate clustering methods. The structure of the taxonomy is built on three main attributes of a functional data clustering method and therefore is more reliable than existing categorizations. The review aims to bridge the gap between the functional data analysis community and the clustering community and to generate new principles for functional data clustering.