Time Series Data Research Articles

A hybrid machine learning forecasting model for photovoltaic power

The increasing use of photovoltaic (PV) power generation presents a significant opportunity for global energy transformation. However, accurately forecasting PV power remains a challenge. This study proposes a hybrid approach that combines variational mode decomposition (VMD), whale optimization algorithm (WOA), and long short-term memory neural network (LSTM) to forecast photovoltaic (PV) power accurately. The model decomposes the time series of PV power using VMD to address the non-stationary nature of the time series. The VMD parameters are optimized using WOA. Subsequently, and the PV power time series data is then decomposed using the optimized VMD parameters to obtain multiple intrinsic mode functions (IMFs) components and a residual component. These components are then reconstructed with meteorological parameters to obtain the reconstructed IMF components and residuals. Finally, multiple LSTM sub-models are built, with each of them taking the IMF components and residual from the previous reconstruction as inputs. The sub-models are optimized using the WOA method to determine their hyperparameters and then constructed with these optimized hyperparameters. The predicted values of each IMF and residual are output and added for sequence reconstruction to derive the final predicted value of PV power. The model's effectiveness was verified for one-hour-ahead forecasting at the 1.8 MW solar system in Yulara, central Australia. The test results show that the proposed model outperforms other benchmark models, with mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and R-squared value (R2) of 15.247 kW, 19.753 kW, 4.405 % and 0.997, respectively. Compared to the LSTM, MAE, RMSE, and MAPE decreased by 84.942 %, 86.746 %, and 82.611 %, respectively, while R2 increased by 23.438 %. The proposed model has better predictive performance for both stable power changes and large fluctuations, essential for effectively integrating renewable energy sources into the power grid.

Decoupling representation contrastive learning for carbon emission prediction and analysis based on time series

Carbon emissions have become particularly urgent with the acceleration of industrialization. Currently, AI-based carbon emission modeling provides essential support for solving the problem of predicting, managing, and optimizing carbon emissions. However, there are still challenges in accurately predicting carbon dioxide emissions and establishing an appropriate carbon emission regulatory model to manage carbon dioxide emissions effectively. Firstly, this paper introduces a framework for learning seasonal and trend representations called DeTF (Decoupling representation for Time and Frequency domain of time series). The framework is designed for time series data of CO2 emissions used for power generation from 1973 to 2023. Secondly, we use various data enhancement techniques to improve the robustness of the learned representations. Finally, the prediction results establish a tripartite evolutionary game relationship between the state, regulatory agencies, and enterprises. We use MSE and MAE as evaluation metrics, and our model overall outperforms current state-of-the-art end-to-end algorithms. It outperforms the best performing end-to-end prediction method by 27.08% (MSE) in the prediction results. Besides, the time series prediction results are innovatively combined with the tripartite game model to analyze the main factors determining the optimal strategy.

LSTM network optimization and task network construction based on heuristic algorithm

This work aims to advance the security management of complex networks to better align with evolving societal needs. The work employs the Ant Colony Optimization algorithm in conjunction with Long Short-Term Memory neural networks to reconstruct and optimize task networks derived from time series data. Additionally, a trend-based noise smoothing scheme is introduced to mitigate data noise effectively. The approach entails a thorough analysis of historical data, followed by applying trend-based noise smoothing, rendering the processed data more scientifically robust. Subsequently, the network reconstruction problem for time series data originating from one-dimensional dynamic equations is addressed using an algorithm based on the principles of Stochastic Gradient Descent (SGD). This algorithm decomposes time series data into smaller samples and yields optimal learning outcomes in conjunction with an adaptive learning rate SGD approach. Experimental results corroborate the remarkable fidelity of the weight matrix reconstructed by this algorithm to the true weight matrix. Moreover, the algorithm exhibits efficient convergence with increasing data volume, manifesting shorter time requirements per iteration while ensuring the attainment of optimal solutions. When the sample size remains constant, the algorithm’s execution time is directly proportional to the square of the number of nodes. Conversely, as the sample size scales, the SGD algorithm capitalizes on the availability of more information, resulting in improved learning outcomes. Notably, when the noise standard deviation is 0.01, models predicated on SGD and the Least-Squares Method (LSM) demonstrate reduced errors compared to instances with a noise standard deviation of 0.1, highlighting the sensitivity of LSM to noise. The proposed methodology offers valuable insights for advancing research in complex network studies.

Estimating the productivity of US agriculture: The Fisher total factor productivity index for time series data with unknown prices

AbstractIn this paper, we propose a straightforward way to estimate the Fisher ideal total factor productivity (TFP) index (FI) in cases where price information is unavailable, using ‘shadow prices’ derived from data envelopment analysis (DEA). A Monte Carlo experiment shows that the shadow price Fisher ideal TFP index (SPFI) can effectively estimate the ‘true’ FI with relatively small (and stable) errors. The empirical application to the US agriculture sector (1948–2017) further suggests that the SPFI is a (superior) alternative to the traditional Malmquist DEA, especially in dealing with unbalanced panel or time series data when price data are unknown.

An efficient CNN-transformer hybrid approach for water turbine unit failure prediction

Water Turbine Unit is the core equipment of water power generation. It is the most important research object in hydroelectric power. The analysis of daily monitoring data of Water Turbines can evaluate its running state and avoid the loss caused by failure. In this paper, A hybrid neural network architecture which CNN combines Transformer is proposed to evaluate the health state of water turbines based on multivariate long time series data. It has two core components: (i) dilated convolution applies to capture low-level and local semantic information, then the output of convolutional layers is divided into subseries-level patches by time, these patches are regarded as input tokens of Transformer layers; (ii) utilizing self-attention of Transformer to extract high-level and global semantic information. Patching design naturally has benefit as follow: (i) local semantic information is retained in Transformer input tokens and high-level semantic confirm to common sense of human understanding through low-level construction; (ii) the length of Transformer input sequence is greatly shorted and attention can be more concentrated compared with point-wise form. Meanwhile, the computation and memory usage reduces at the same time. The experimental result indicates that the hybrid architecture can achieves excellent performance in time series understanding.

Interpretable baseflow segmentation and prediction based on numerical experiments and deep learning

Baseflow is a crucial water source in the inland river basins of high-cold mountainous region, playing a significant role in maintaining runoff stability. It is challenging to select the most suitable baseflow separation method in data-scarce high-cold mountainous region and to evaluate effects of climate factors and underlying surface changes on baseflow variability and seasonal distribution characteristics. Here we attempt to address how meteorological factors and underlying surface changes affect baseflow using the Grey Wolf Optimizer Digital Filter Method (GWO-DFM) for rapid baseflow separation and the Long Short-Term Memory (LSTM) neural network model for baseflow prediction, clarifying interpretability of the LSTM model in baseflow forecasting. The proposed method was successfully implemented using a 63-year time series (1958–2020) of flow data from the Tai Lan River (TLR) basin in the high-cold mountainous region, along with 21 years of ERA5-land meteorological data and MODIS data (2000–2020). The results indicate that: (1) GWO-DFM can rapidly identify the optimal filtering parameters. It employs the arithmetic average of three methods, namely Chapman, Chapman-Maxwell and Eckhardt filter, as the best baseflow separation approach for the TLR basin. Additionally, the baseflow significantly increases after the second mutation of the baseflow rate. (2) Baseflow sources are mainly influenced by precipitation infiltration, glacier frozen soil layers, and seasonal ponding. (3) Solar radiation, temperature, precipitation, and NDVI are the primary factors influencing baseflow changes, with Nash-Sutcliffe efficiency coefficients exceeding 0.78 in both the LSTM model training and prediction periods. (4) Changes in baseflow are most influenced by solar radiation, temperature, and NDVI. This study systematically analyzes the changes in baseflow and response mechanisms in high-cold mountainous region, contributing to the management of water resources in mountainous basins under changing environmental conditions.

A time-resolved multi-omics atlas of transcriptional regulation in response to high-altitude hypoxia across whole-body tissues

High-altitude hypoxia acclimatization requires whole-body physiological regulation in highland immigrants, but the underlying genetic mechanism has not been clarified. Here we use sheep as an animal model for low-to-high altitude translocation. We generate multi-omics data including whole-genome sequences, time-resolved bulk RNA-Seq, ATAC-Seq and single-cell RNA-Seq from multiple tissues as well as phenotypic data from 20 bio-indicators. We characterize transcriptional changes of all genes in each tissue, and examine multi-tissue temporal dynamics and transcriptional interactions among genes. Particularly, we identify critical functional genes regulating the short response to hypoxia in each tissue (e.g., PARG in the cerebellum and HMOX1 in the colon). We further identify TAD-constrained cis-regulatory elements, which suppress the transcriptional activity of most genes under hypoxia. Phenotypic and transcriptional evidence indicate that antenatal hypoxia could improve hypoxia tolerance in offspring. Furthermore, we provide time-series expression data of candidate genes associated with human mountain sickness (e.g., BMPR2) and high-altitude adaptation (e.g., HIF1A). Our study provides valuable resources and insights for future hypoxia-related studies in mammals.

The time-series GF-1 WFV data monitoring of sugarcane using a Random Forest Algorithm in South China

Abstract. There is large distribution of sugarcane growth in south China which is play an important role of sugar industry. Remote sensing technology is used in sugarcane monitoring for large areas. However, the optical satellite data coverage is influenced by the rainy weather especially in the grand growth period of sugarcane. GF-1 WFV has widely swath 800km and short revisit time which is ideal data for this study area. In this paper, the random forest model was chosen to get a precise classification result of sugarcane based on time-series band value and 5 spectral indexes image is 89.73% and the Kappa coefficient is 0.65 which is satisfied the overall extraction of sugarcane for large area is the southern China. Furthermore, the decision tree classification was chosen as a comparative experience research.

Short-term power load forecasting for integrated energy system based on a residual and attentive LSTM-TCN hybrid network

In the context of Integrated Energy System (IES), accurate short-term power demand forecasting is crucial for ensuring system reliability, optimizing operational efficiency through resource allocation, and supporting effective real-time decision-making in energy management. However, achieving high forecasting accuracy faces significant challenges due to the inherent complexity and stochastic nature of IES’s short-term load profiles, resulting from diverse consumption patterns among end-users and the intricate coupling within the network of interconnected energy sources. To address this issue, a dedicated Short-Term Power Load Forecasting (STPLF) framework for IES is proposed, which relies on a newly developed hybrid deep learning architecture. The framework seamlessly combines Long Short-Term Memory (LSTM) with Temporal Convolutional Network (TCN), enhanced by an attention mechanism module. By merging these methodologies, the network leverages the parallel processing prowess of TCN alongside LSTM’s ability to retain long-range temporal information, thus enabling it to dynamically concentrate on relevant sections of time series data. This synergy leads to improved prediction accuracy and broader applicability. Furthermore, the integration of residual connections within the network structure serves to deepen its learning capabilities and enhance overall performance. Ultimately, results from a real case study of a user-level IES demonstrate that the Mean Absolute Percentage Error (MAPE) of the proposed framework on the test set is 2.35%. This error rate is lower than the averages of traditional methods (3.43%) and uncombined single submodules (2.80%).

A comparative study of mass balance in the Lambert Glacier and Amery Ice Shelf along the Chinese inland traverse during 2019–2023 using altimetry, gravity, and in-situ observations

Abstract. The new photon-counting laser altimetry satellite ICESat-2 was successfully launched on September 15, 2018 with an unprecedented ice surface elevation measurement accuracy of 2–4 cm. It is meaningful for accurately estimating volumetric changes in the Antarctic Ice Sheet. Cross-validation of different types of data, especially comparison with in-situ data, is important for the ice sheet mass balance results of a new satellite. This paper proposes an elevation-difference method of grid elevation change rate model, based on ICESat-2 ATL11 elevation time series data, to distinguish the linear change trend of ice sheet surface elevation from the elevation change resulting from periodic precipitation. In order to compare the estimated elevation-change rate with the flux computed from in-situ snow stake velocity measurements and GRACE-FO gravity survey data, we made corrections for firn air content, elastic, and glacier isostatic adjustment. Based on the ATL11 data from 2019 to 2023, our results show that the ice sheet change in Basin 11 along the CHINARE traverse is from ~0.019 m yr−1 to ~0.121 m yr−1, and the mass balance in the upstream of the traverse in Basin 11 is ~1.9±0.2 Gt yr−1. It is comparable to ~2.4±1.2 Gt yr−1 from GRACE-FO during the same time period. Furthermore, the flux across traverse-11.9±1.1 Gt yr−1 is comparable to that of ~-9.7±0.9 Gt yr−1 across the same flux gate during 1997–2009 which is calculated based on GNSS-derived ice velocity observations, considering the time period difference and uncertainties.

Bangladesh towards green growth: a review of environmental sustainability indicators

Pursuing green growth is crucial for Bangladesh to transition from an unsustainable economic trajectory to a more sustainable and inclusive one. Bangladesh is picked for this study because of impending and severe economic and environmental threats. This study intends to review the present scenario of various environmental sustainability-related indicators in Bangladesh, focusing on renewable energy consumption, freshwater resources, water productivity, CO2 emissions, energy intensity, air pollution, and natural resource rents. The World Bank database has been utilized to obtain secondary time series data of Bangladesh spanning from 2000 to 2020. As a descriptive study, cross-sectional and observational research methods as well as descriptive statistics and figures are used to elucidate the secondary data. Data demonstrate that Bangladesh now generates 41.16% of its energy from renewables, despite considerable variability. Regardless of the variation in freshwater availability, averaging at 708.19 cubic meters per capita, efficient water productivity remains consistent, indicating a robust water management system. The country demonstrates a relatively low carbon footprint, emitting 0.35 metric tons of CO2 per capita, alongside varying energy intensity levels, highlighting the need for enhanced efficiency measures. While pervasive PM2.5 air pollution poses a significant health risk, Bangladesh's reliance on natural resource rents underscores the importance of sustainable resource management practices for long-term economic stability. The observations of this study might assist in the formulation of policies of water management systems, air pollution control initiatives, and conservation of ecology to promote Bangladesh's long-term sustainability objectives and formulate policies.

Development of an Artificial Intelligence-Based Predictive Anomaly Detection System to Nuclear Power Plant

Abstract In a large-scale plant such as a nuclear power plant, thousands of process values are measured for the purpose of monitoring the plant performance and the system health. It is difficult for plant operators to constantly monitor all of the process values. We present a data-driven method to comprehensively monitor a large number of process values and detect early signs of anomalies, including unknown events, with few false positives. In order to learn the complex changing internal state of a nuclear power plant and accurately predict the normal process values, we have developed a two-stage auto-encoder (TSAE), a type of neural network, composed of a time window auto-encoder and a deviation auto-encoder. TSAE realizes to detect anomalous signals during the plant transient conditions by collecting time-series data and learning the nonlinear temporal correlation among them. In the actual plant, some process values which are physically uncorrelated with each other happen to behave similarly (pseudo-correlation). Learning the pseudo-correlation by the algorithm causes false positives because the predicted values of unrelated process values are incorrectly correlated. Therefore, Toshiba has proposed the model classification concept of separating the process values into two groups based on physical correlation and applied a model structure of TSAE. As a result, it becomes possible to learn only with the process values that are physically correlated and enhance the performance of prediction/detection. We assessed the improved TSAE with simulated process values of a nuclear power plant and showed excellent performances with early detection and few false positives.

ECG-image-kit: a synthetic image generation toolbox to facilitate deep learning-based electrocardiogram digitization

Abstract Objective: Cardiovascular diseases are a major cause of mortality globally, and electrocardiograms (ECGs) are crucial for diagnosing them. Traditionally, ECGs are stored in printed formats. However, these printouts, even when scanned, are incompatible with advanced ECG diagnosis software that require time-series data. Digitizing ECG images is vital for training machine learning models in ECG diagnosis, leveraging the extensive global archives collected over decades. Deep learning models for image processing are promising in this regard, although the lack of clinical ECG archives with reference time-series data is challenging. Data augmentation techniques using realistic generative data models provide a solution.

Approach: We introduce ECG-Image-Kit, an open-source toolbox for generating synthetic multi-lead ECG images with realistic artifacts from time-series data, aimed at automating the conversion of scanned ECG images to ECG data points. The tool synthesizes ECG images from real time-series data, applying distortions like text artifacts, wrinkles, and creases on a standard ECG paper background.

Main results: As a case study, we used ECG-Image-Kit to create a dataset of 21,801 ECG images from the PhysioNet QT database. We developed and trained a combination of a traditional computer vision and deep neural network model on this dataset to convert synthetic images into time-series data for evaluation. We assessed digitization quality by calculating the signal-to-noise ratio (SNR) and compared clinical parameters like QRS width, RR, and QT intervals recovered from this pipeline, with the ground truth extracted from ECG time-series. The results show that this deep learning pipeline accurately digitizes paper ECGs, maintaining clinical parameters, and highlights a generative approach to digitization.

Significance: The toolbox has broad applications, including model development for ECG image digitization and classification. The toolbox currently supports data augmentation for the 2024 PhysioNet Challenge, focusing on digitizing and classifying paper ECG images.

A Novel Improved Variational Mode Decomposition-Temporal Convolutional Network-Gated Recurrent Unit with Multi-Head Attention Mechanism for Enhanced Photovoltaic Power Forecasting

Photovoltaic (PV) power forecasting plays a crucial role in optimizing renewable energy integration into the grid, necessitating accurate predictions to mitigate the inherent variability of solar energy generation. We propose a novel forecasting model that combines improved variational mode decomposition (IVMD) with the temporal convolutional network-gated recurrent unit (TCN-GRU) architecture, enriched with a multi-head attention mechanism. By focusing on four key environmental factors influencing PV output, the proposed IVMD-TCN-GRU framework targets a significant research gap in renewable energy forecasting methodologies. Initially, leveraging the sparrow search algorithm (SSA), we optimize the parameters of VMD, including the mode component K-value and penalty factor, based on the minimum envelope entropy principle. The optimized VMD then decomposes PV power, while the TCN-GRU model harnesses TCN’s proficiency in learning local temporal features and GRU’s capability in rapidly modeling sequence data, while leveraging multi-head attention to better utilize the global correlation information within sequence data. Through this design, the model adeptly captures the correlations within time series data, demonstrating superior performance in prediction tasks. Subsequently, the SSA is employed to optimize GRU parameters, and the decomposed PV power mode components and environmental feature attributes are inputted into the TCN-GRU neural network. This facilitates dynamic temporal modeling of multivariate feature sequences. Finally, the predicted values of each component are summed to realize PV power forecasting. Validation using real data from a PV station corroborates that the novel model demonstrates a substantial reduction in RMSE and MAE of up to 55.1% and 54.5%, respectively, particularly evident in instances of pronounced photovoltaic power fluctuations during inclement weather conditions. The proposed method exhibits marked improvements in accuracy compared to traditional PV power prediction methods, underscoring its significance in enhancing forecasting precision and ensuring the secure scheduling and stable operation of power systems.

Bipartite networks represent causality better than simple networks: evidence, algorithms, and applications

A network, whose nodes are genes and whose directed edges represent positive or negative influences of a regulatory gene and its targets, is often used as a representation of causality. To infer a network, researchers often develop a machine learning model and then evaluate the model based on its match with experimentally verified “gold standard” edges. The desired result of such a model is a network that may extend the gold standard edges. Since networks are a form of visual representation, one can compare their utility with architectural or machine blueprints. Blueprints are clearly useful because they provide precise guidance to builders in construction. If the primary role of gene regulatory networks is to characterize causality, then such networks should be good tools of prediction because prediction is the actionable benefit of knowing causality. But are they? In this paper, we compare prediction quality based on “gold standard” regulatory edges from previous experimental work with non-linear models inferred from time series data across four different species. We show that the same non-linear machine learning models have better predictive performance, with improvements from 5.3% to 25.3% in terms of the reduction in the root mean square error (RMSE) compared with the same models based on the gold standard edges. Having established that networks fail to characterize causality properly, we suggest that causality research should focus on four goals: (i) predictive accuracy; (ii) a parsimonious enumeration of predictive regulatory genes for each target gene g; (iii) the identification of disjoint sets of predictive regulatory genes for each target g of roughly equal accuracy; and (iv) the construction of a bipartite network (whose node types are genes and models) representation of causality. We provide algorithms for all goals.

Automated Cropland Fallow Algorithm (ACFA) for the Northern Great Plains of USA

ABSTRACT Cropland fallowing is choosing not to plant a crop during a season when a crop is normally planted. It is an important component of many crop rotations and can improve soil moisture and health. Knowing which fields are fallow is critical to assess crop productivity and crop water productivity, needed for food security assessments. The annual spatial extent of cropland fallows is poorly understood within the United States (U.S.). The U.S. Department of Agriculture Cropland Data Layer does provide cropland fallow areas; however, at a significantly lower confidence than their cropland classes. This study developed a methodology to map cropland fallows within the Northern Great Plains region of the U.S. using an easily implementable decision tree algorithm leveraging training and validation data from wet (2019), normal (2015), and dry (2017) precipitation years to account for climatic variability. The decision trees automated cropland fallow algorithm (ACFA) was coded on a cloud platform utilizing remotely sensed, time-series data from the years 2010–2019 to separate cropland fallows from other land cover/land use classes. Overall accuracies varied between 96%-98%. Producer’s and user’s accuracies of cropland fallow class varied between 70-87%.

Improved deep-learning rotor fault diagnosis based on multi vibration sensors and recurrence plots

Deep learning techniques are increasingly applied to time series data, offering promising results in various fields. Deep learning techniques can handle data from multiple sensors to detect anomalies in an industrial environment. This paper proposes a new method of anomaly detection based on a multilayer image representation of different vibration sensors’ recurrence plots. Each sensor’s recurrence plot forms a layer. The performance and reliability of our method were assessed using an experimental database collected under different load conditions and with different types of rotor anomalies. Experiment results demonstrate the effectiveness of GoogLeNet using individual and multi-layered recurrence plots to find rotor faults in an induction motors.

Empowering Pakistan’s Economy: The Role of Health and Education in Shaping Labor Force Participation and Economic Growth

The labor force is a crucial factor in conducting economic activities, especially in labor-surplus countries like Pakistan. In this study, we explore the impact of labor force participation (LF) on economic growth (EG), with an emphasis on how this impact depends on the levels of health and education expenditures. We analyze time series data from Pakistan spanning from 1980 to 2022, using ARDL (Autoregressive Distributed Lag), ECM (Error Correction Model) and Granger causality techniques for empirical analysis. The ARDL results indicate that LF significantly boosts EG, both in the short and long run. Furthermore, the estimations reveal that better facilities for health and education strengthen the positive effects of LF on EG. This suggests a complementary relationship between health, education, and LF in driving EG. Moreover, our findings highlight the temporal significance of health and education: Health plays a more crucial role in the short run, while education’s impact is more substantial in the long run. Furthermore, the Granger causality results indicate that LF, health, and education significantly contribute to EG. It is advisable for the government to prioritize investments in the health and education sectors. This approach can empower individuals to actively and effectively participate in economic activities, eventually contributing to the overall economic output of the nation.

The impact of fiscal shocks on economic growth and income inequality in Ghana: is there a trade-off?

PurposeThe study examines the impact of fiscal policy shocks on economic growth and income inequality in Ghana. This has become necessary because of the interdependence between growth and income inequality and the role fiscal policy plays in this relationship in the development process of a country. Thus, a study that investigates how government expenditure shock and tax revenue shock influence the relationship between economic growth and income inequality could assist policymakers to adopt the best policy mix to ensure income equity and sustained economic growth in Ghana.Design/methodology/approachIt employs sacrifice ratio from structural VAR model using quarterly time series data from 1996 to 2019 on Ghana.FindingsOur results show that government expenditure shock impacts economic growth, exchange rate and education positively and significantly in the long run. Also, tax revenue shock has a positive impact on income inequality, economic growth and education. The findings further show that there exists a trade-off between economic growth and income inequality in the long run.Originality/valueThe relationships between fiscal policy shocks, economic growth and income inequality have been extensively discussed among scholars. Understanding how these three macroeconomic variables are determined and their interrelationships are crucial for policymakers. This is because fiscal policy aids in both economic growth and income inequality. In the empirical literature, the emphasis has been on independently estimating the growth effects of fiscal policy or the distribution effects of fiscal policy, leaving out the existence of possible trade-off between economic growth and income inequality following a fiscal shock. To the best of our knowledge, no empirical study has been done on Ghana to empirically examine the trade-off between economic growth and income inequality as we do in this paper.

Biclustering analysis on tree-shaped time-series single cell gene expression data of Caenorhabditis elegans

BackgroundIn recent years, gene clustering analysis has become a widely used tool for studying gene functions, efficiently categorizing genes with similar expression patterns to aid in identifying gene functions. Caenorhabditis elegans is commonly used in embryonic research due to its consistent cell lineage from fertilized egg to adulthood. Biologists use 4D confocal imaging to observe gene expression dynamics at the single-cell level. However, on one hand, the observed tree-shaped time-series datasets have characteristics such as non-pairwise data points between different individuals. On the other hand, the influence of cell type heterogeneity should also be considered during clustering, aiming to obtain more biologically significant clustering results.ResultsA biclustering model is proposed for tree-shaped single-cell gene expression data of Caenorhabditis elegans. Detailedly, a tree-shaped piecewise polynomial function is first employed to fit non-pairwise gene expression time series data. Then, four factors are considered in the objective function, including Pearson correlation coefficients capturing gene correlations, p-values from the Kolmogorov-Smirnov test measuring the similarity between cells, as well as gene expression size and bicluster overlapping size. After that, Genetic Algorithm is utilized to optimize the function.ConclusionThe results on the small-scale dataset analysis validate the feasibility and effectiveness of our model and are superior to existing classical biclustering models. Besides, gene enrichment analysis is employed to assess the results on the complete real dataset analysis, confirming that the discovered biclustering results hold significant biological relevance.