Time Series Analysis Algorithm Research Articles

Comparative Study of Time Series Analysis Algorithms Suitable for Short-Term Forecasting in Implementing Demand Response Based on AMI

This paper compares four time series forecasting algorithms—ARIMA, SARIMA, LSTM, and SVM—suitable for short-term load forecasting using Advanced Metering Infrastructure (AMI) data. The primary focus is on evaluating the applicability and performance of these forecasting models in predicting electricity consumption patterns, which is a critical component for implementing effective demand response (DR) strategies. The study provides a comprehensive analysis of the predictive accuracy, computational efficiency, and scalability of each algorithm using a dataset of real-time electricity consumption collected from AMI systems over a designated period. Through extensive experiments, we demonstrate that each algorithm has distinct strengths and weaknesses depending on the characteristics of the dataset. Specifically, SVM exhibited superior performance in handling nonlinear patterns and high volatility, while SARIMA effectively captured seasonal trends. LSTM showed potential in modeling complex temporal dependencies but was sensitive to hyperparameter settings and required a substantial amount of training data. This research offers practical guidelines for selecting the optimal forecasting model based on data characteristics and application needs, contributing to the development of more efficient and dynamic energy management strategies. The findings highlight the importance of integrating advanced forecasting techniques into smart grid systems to enhance the reliability and responsiveness of DR programs. This study lays a solid foundation for future research on integrating these forecasting models into real-world AMI applications to support effective demand response and grid stability.

Dynamic pricing and demand forecasting: Integrating time-series analysis, regression models, machine learning, and competitive analysis

Abstract. Dynamic pricing is a critical strategy for businesses seeking to optimize revenue and stay competitive in fluctuating markets. This paper explores the integration of various demand forecasting techniques, including time-series analysis, regression models, and machine learning algorithms, with competitive analysis methodologies to enhance dynamic pricing strategies. Time-series analysis focuses on decomposing data into trend, seasonality, and random fluctuations, using ARIMA models for accurate demand prediction. Regression models delve into the complexities of variable interactions, extending beyond linear relationships to include advanced techniques like Ridge, Lasso, and Elastic Net regression. Machine learning algorithms, such as decision trees, random forests, gradient boosting, and neural networks, revolutionize demand forecasting by uncovering complex patterns in large datasets. Competitive analysis incorporates market scanning, price elasticity estimation, and competitor behavior modeling to inform dynamic pricing decisions. Optimization algorithms, including linear programming, genetic algorithms, and simulated annealing, are employed to refine pricing strategies, while revenue management techniques like yield management and overbooking ensure maximum revenue from perishable goods and services. This comprehensive approach enables businesses to dynamically adjust prices in real-time, maintaining competitiveness and maximizing profitability in an ever-evolving market landscape.

An Empirical Algorithm for Estimating the Absorption of Colored Dissolved Organic Matter from Sentinel-2 (MSI) and Landsat-8 (OLI) Observations of Coastal Waters

Sentinel-2/MSI and Landsat-8/OLI sensors enable the mapping of ocean color-related bio-optical parameters of surface coastal and inland waters. While many algorithms have been developed to estimate the Chlorophyll-a concentration, Chl-a, and the suspended particulate matter, SPM, from OLI and MSI data, the absorption by colored dissolved organic matter, acdom, a key parameter to monitor the concentration of dissolved organic matter, has received less attention. Herein we present an inverse model (hereafter referred to as AquaCDOM) for estimating acdom at the wavelength 412 nm (acdom (412)), within the surface layer of coastal waters, from measurements of ocean remote sensing reflectance, Rrs (λ), for these two high spatial resolution (around 20 m) sensors. Combined with a water class-based approach, several empirical algorithms were tested on a mixed dataset of synthetic and in situ data collected from global coastal waters. The selection of the final algorithms was performed with an independent validation dataset, using in situ, synthetic, and satellite Rrs (λ) measurements, but also by testing their respective sensitivity to typical noise introduced by atmospheric correction algorithms. It was found that the proposed algorithms could estimate acdom (412) with a median absolute percentage difference of ~30% and a median bias of 0.002 m−1 from the in situ and synthetic datasets. While similar performances have been shown with two other algorithms based on different methodological developments, we have shown that AquaCDOM is much less sensitive to atmospheric correction uncertainties, mainly due to the use of band ratios in its formulation. After the application of the top-of-atmosphere gains and of the same atmospheric correction algorithm, excellent agreement has been found between the OLI- and MSI-derived acdom (412) values for various coastal areas, enabling the application of these algorithms for time series analysis. An example application of our algorithms for the time series analysis of acdom (412) is provided for a coastal transect in the south of Vietnam.

Gap-filling of land surface temperature in arid regions by combining Landsat 8 and 9 imageries

Abstract Land surface temperature (LST) is an important factor in land monitoring studies, but due to the presence of clouds, dust and sensor issues, there are missing values. The aims of this research are to determine the optimal parameters for the reconstruction of Landsat-LST images, required in many applications, by the harmonic analysis of time series algorithm (HANTS) and to investigate the possibility of improving LST reconstruction accuracy using Landsat 8 and 9 images simultaneously. For these aims, 91 Landsat 8 and 9 images with 100 m spatial resolution in 2022 and 2023 are employed, covering Yazd-Ardakan plain in Iran. Three methods are used for evaluation. In method one, a part of LST image is considered as a gap and is compared with the initial value after reconstruction. In method two, on a cloudy day and a cloudless day, surface temperature values are measured using thermometers at fifty points in plain lands, and the difference between gap-filled satellite measurements and ground measurements is calculated. In method three, all the reconstructed LST images are compared with the original images. In method one, the root mean square error (RMSE) of reconstructed LST reduces by 1.3°C when using the combined Landsat 8 and 9 images. In method two, RMSEs of reconstructed LST images are 6.1°C when using Landsat 8 and 5.4°C when using the combined Landsat 8 and 9. Method three shows that 41% of the study region has RMSE of less than 2°C when using only Landsat 8, while this value becomes 72% when combining Landsat 8 and 9. In general, the combined use of Landsat 8 and 9 LST images improves the accuracy of reconstruction using HANTS. The findings of this research are crucial for regional applications and remote monitoring of surface temperature in areas with limited weather stations.

Clustering and Classification of Time Series Sound Data

This scientific article addresses two critical tasks in data analysis—time series classification and clustering, particularly focusing on heart sound recordings. One of the main challenges in analyzing time series lies in the difficulty of comparing different series due to their variability in length, shape, and amplitude. Various algorithms were employed to tackle these tasks, including the Long Short-Term Memory (LSTM), KNN, recurrent neural network for classification and the K-means and DBSCAN methods for clustering. The study emphasizes the effectiveness of these methods in solving classification and clustering problems involving time series data containing heart sound recordings. The results indicate that LSTM is a powerful tool for time series classification due to its ability to retain contextual information over time. In contrast, KNN demonstrated high accuracy and speed in classification, though its limitations became apparent with larger datasets. For clustering tasks, the K-means method proved to be more effective than DBSCAN, showing higher clustering quality based on metrics such as silhouette score, Rand score, and others. The data used in this research were obtained from the UCR Time Series Archive, which includes heart sound recordings from various categories: normal sounds, murmurs, additional heart sounds, artifacts, and extra systolic rhythms. The analysis of results demonstrated that the chosen classification and clustering methods could be effectively used for diagnosing heart diseases. Furthermore, this research opens up new opportunities for further improvement in data processing and analysis methods, particularly in developing new medical diagnostic tools. Thus, this work illustrates the effectiveness of machine learning algorithms for time series analysis and their significance in improving cardiovascular disease diagnosis.

Smart watch for early heart attack detection and emergency assistance using IoT

This research introduces a Smart Watch equipped with advanced physiological monitoring capabilities for the early detection of heart attacks and automatic initiation of emergency assistance. Cardiovascular diseases, particularly heart attacks, are a leading cause of global mortality. Rapid response during a heart attack significantly improves patient outcomes, emphasizing the need for innovative solutions. The proposed Smart Watch integrates a combination of sensors, including ECG (Electrocardiogram) and PPG (Photoplethysmography), to continuously monitor the user's heart rate, rhythm, and other relevant physiological parameters. Machine learning (Time Series Analysis algorithm) is employed to analyse the collected data in real-time, identifying patterns indicative of a potential heart attack.Upon detecting abnormal cardiac activity, the Smart Watch triggers an immediate response by connecting to a dedicated mobile application. The application utilizes built-in communication features to establish a connection with emergency services, providing vital information about the user's condition, location, and medical history. Simultaneously, the Smart Watch alerts predefined emergency contacts, ensuring a swift response from friends or family members.

Traditional matric potential thresholds underestimate soil moisture at field capacity across Oklahoma

AbstractField capacity is a dubious soil physical property, but its use continues because of its perceived value for representing a soil's capacity to store water. Appropriate field capacity estimates can be useful for interpreting data from soil moisture sensors, including those in large‐scale monitoring networks, but suitable methods for defining field capacity in this context are unclear. Motivated by the desire to determine optimal field capacity values for the Oklahoma Mesonet, our objectives were (1) to develop and apply an automated time series analysis algorithm to estimate volumetric soil water content at field capacity and corresponding matric potential and (2) to compare the resulting water contents to those calculated from traditional matric potential thresholds (−33 and −10 kPa). Across 118 Oklahoma Mesonet sites and three soil depths (5, 25, and 60 cm), a matric potential threshold of −10 kPa underestimated field capacity water content by 0.010–0.014 cm cm−3 (3–4%) on average, and a threshold of −33 kPa underestimated it for every site and depth by 0.055–0.078 cm cm−3 (16%−22%) on average. Median matric potentials corresponding to field capacity were −7.6 kPa at the 5‐cm depth, −7.2 kPa at the 25‐cm depth, and −7.3 kPa at the 60‐cm depth. The algorithm developed here can be used to estimate field capacity wherever adequate data are available, and for sites where soil water retention properties are known, matric potentials at field capacity can also be estimated. Using a matric potential of −33 kPa as a standard threshold to represent field capacity is not scientifically justified and should be discontinued.

Machine learning-based understanding of aquatic animal behaviour in high-turbidity waters

Inspired by the ambitions envisioned in the Fourth Industrial Revolution for aquaculture, also known as Aquaculture 4.0, the aquaculture (marine animal farming) industry is seeking to adopt data-driven Artificial Intelligence (AI) to help significantly improve business operations. One of the major barriers is the manual annotation of animal behaviour data, which is a time-consuming task that demands high levels of concentration from biologists. To address this challenge, this paper proposes novel automatic animal behaviour monitoring tailored for industrial scenarios. Our approach introduces a real-time machine-learning-based instance segmentation system that is specialised for underwater environments, where large groups of shrimp are farmed. The implemented system achieves an accuracy rate of 89% at 30 frames per second (fps) and can accurately detect shrimp in high-density areas under poor lighting conditions and high turbidity waters, despite the challenges of occlusion and overlapping. A key innovation of our method is the implementation of a new density cluster algorithm for time series and video analysis. This approach provides a more efficient and accurate way of monitoring animal behaviour, significantly saving time and effort for biologists and advancing the capabilities of automated aquaculture systems.

Streamflow in the United States: Characteristics, trends, regime shifts, and extremes

Long-term streamflow observations contain essential information for understanding hydrological changes and managing water resources. A continental-scale dataset or analysis of temporal streamflow change is still lacking across hydrologic gauges in the Conterminous United States (CONUS). Here, we compiled 70 years of streamflow records from 1951 to 2021 at ~ 8000 hydrologic stations across the CONUS and characterized temporal trends, regime shifts, and extreme events using a Bayesian time series analysis algorithm. We found that the occurrences of sudden streamflow changes (e.g., regime shifts and extreme events) have been increasing with time across the CONUS. In addition, we derived 181 streamflow indicators that are valuable for hydrological and biological applications, such as the duration and frequency of high or low streamflow events. The Mississippi River Basin, especially the middle and lower parts, was a hot spot of high-frequency high-flow events. Overall, we anticipate the dataset generated here offers valuable information for understanding and quantifying changes in water resources across the CONUS.

PREDICTIVE MODELLING FOR SUGARCANE PRODUCTION: A COMPREHENSIVE COMPARISON OF ARIMA AND MACHINE LEARNING ALGORITHMS

Accurate prediction of sugarcane yield is essential for trade, economic planning, and sustainable agriculture in India. This study addressed the challenge of forecasting sugarcane yield by evaluating the effectiveness of time series modelling and machine learning algorithms. Leveraging data spanning from 2001 to 2020, the research focuses on predicting the sugarcane yield for the subsequent years. The problem statement revolves around the need for precise yield predictions to inform decision-making in the agricultural sector. Methods employed included the utilization of Autoregressive Integrated Moving Average (ARIMA) for time series analysis and machine learning algorithms such as Random Forest (RF), Support Vector Machine (SVM), and Gradient Boosting Machine (GBM). The analysis encompassed sugarcane yield data spanning multiple years, with predictions extending for a specified duration. Through analysis of temporal patterns and dependencies within the sugarcane yield time series data using Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), the study optimized the predictive models. Results indicated that ARIMA outperformed machine learning algorithms, exhibiting superior performance with a root meansquare error of 36700.68 anda minimumAICvalue of 456.7. The study emphasizes the significance of accurate yield predictions for agricultural planning and decision-making, highlighting the implications for sustainable crop management and the fortification of Indian sugar industry.The study affirms the importance of informed decisions facilitated by accurate yield predictions in resilient agricultural sector. Overall, this study contributes to the advancement of sugarcane yield prediction, offers practical insights for stakeholders and policymakers in India's agricultural landscape.

Global Potato Production Forecasting Based on Time Series Analysis and Advanced Waterwheel Plant Optimization Algorithm

Global Potato Production Forecasting Based on Time Series Analysis and Advanced Waterwheel Plant Optimization Algorithm

Forecasting Student Employment Trends in Colleges and Universities Education Using Time Series Analysis Algorithms

Student employment trends in colleges have been evolving, with a notable shift towards internships, co-op programs, and other experiential learning opportunities. Colleges are increasingly emphasizing the importance of gaining practical work experience alongside academic studies to enhance students' employability. This trend reflects the growing demand from employers for graduates who possess not only theoretical knowledge but also relevant skills and hands-on experience. This study investigates student employment trends within Colleges and Universities education through the application of time series analysis algorithms. Utilizing historical data spanning five years from 2019 to 2023, the study examines the dynamics of student employment rates and explores the effectiveness of forecasting methodologies, including ARIMA and Ranking with ARIMA (R-ARIMA). The findings reveal a consistent upward trend in student employment rates over the study period, indicating a favorable environment for student career opportunities within higher education institutions. Moreover, the accuracy of forecasting models is demonstrated through the close alignment between predicted and observed employment rates. Optimal ARIMA configurations are identified, providing insights for strategic planning and resource allocation to support student career development and success. The findings reveal a consistent upward trend in student employment rates over the study period, with the percentage of employed students increasing annually. For instance, the student employment rate rises from 65% in 2019 to 77% in 2023. This indicates a favourable environment for student career opportunities within higher education institutions. Moreover, the accuracy of forecasting models is demonstrated through the close alignment between predicted and observed employment rates. Optimal ARIMA configurations are identified, with the best-performing model achieving an AIC score of 95.3 and a BIC score of 99.8. These configurations provide insights for strategic planning and resource allocation to support student career development and success.

Application of Time Series Analysis and Regression Algorithm in Assessing the Effectiveness of Monetary Policy in the Era of Digital Economy

Monetary policy is the series of actions to manage country's money supply and to attain economic growth. An objection to using interest rates in monetary policy is that the use of interest rates has the problem of time uncertainty. Therefore, this research introduces Conditional Autoregressive Value-at-Risk and Henry Gas Solubility Optimization (Caviar-HGSO) with Deep Long Short Term Memory (DeepLSTM) to monetary policy forecasting to demonstrate its effectiveness. Here, Caviar-HGSO is a hybrid of Caviar and HGSO used to tune DeepLSTM weights. The HGSO algorithm follows the wind state to balance exploration and exploitation in search space while avoiding local optimization. A Caviar model estimates the parameter over time by autoregressive process and determine a parameter by regression analysis. The advantages of these two optimization algorithms lead to better monetary policy forecasts. The experimental results show that Caviar-HGSO_DeepLSTM performs better regarding MAE, MSE, and RMSE, namely 0.438, 0.103, and 0.351.

Analysis of Economic Impact Based on Time Series Model -- Taking the GDP of Two Provinces as an Example

Time series analysis is an important branch of statistics, which is widely used in various fields, as well as in the economic field. In the economic field, a reasonable GDP forecast helps a country to set credible, substantive, and strategic goals. In recent years, Northeast China has seen an obvious decline in the national economic ranking, and the relevant GDP data of Jilin and Heilongjiang provinces are more obvious. This paper is based on time series analysis and support vector regression (SVR) algorithm to build a series model. The model was established by using 60 GDP data of Jilin Province and Heilongjiang Province from 1959 to 2022 with similar economic facts. After calculation and verification, the optimal model of Jilin Province is ARIMA (1, 1,0), the SVR with parameter C of 10 and 2 of 0.007, and the combined model with it as the main model is the optimal model of Heilongjiang Province. The GDP of the two provinces will continue to rise in the next five years, and the GDP of Jilin Province will rise faster, and the GDP gap between the two provinces will gradually narrow.

Mapping Forest Abrupt Disturbance Events in Southeastern China—Comparisons and Tradeoffs of Landsat Time Series Analysis Algorithms

Forest change monitoring is a fundamental and routine task for forest survey and planning departments, and the resulting forest change information acts as an underlying asset for sustainable forest management strategy development, ecological quality assessment, and carbon cycle research. The traditional ground-based manual monitoring of forest change has the disadvantages of high time and labor costs, low accessibility, and poor timeliness over wide regions. Remote sensing technology has become a popular approach for multi-scale forest change monitoring due to its multiple available spatial, spectral, temporal, and radiometric resolutions and wide coverage. Particularly, the free access policy of long time series archive data of Landsat (around 50 years) has triggered many automated analysis algorithms for landscape-scale forest change analysis, such as VCT, LandTrendr, BFAST, and CCDC. These automated algorithms differ in their principles, parameter settings, execution complexity, and disturbance types to be detected. Thus, selecting a suitable algorithm to satisfy the particular forest management demands is an urgent and challenging task for forest managers in a given forested area. In this study, Lishui City, Zhejiang Province, a typical plantation forest region in Southern China where forest disturbance widely and frequently exists, was selected as the study area. Based on the GEE platform, the algorithmic adaptability of VCT, LandTrendr, and CCDC in monitoring abrupt forest disturbance events was compared and assessed. The results showed that the kappa coefficients of the abrupt disturbance events detected by the three algorithms were at 0.704 (LandTrendr), 0.660 (VCT), and 0.727 (CCDC), and the corresponding overall accuracies were at 0.852, 0.830, and 0.862, respectively. The validated disturbance occurrence time consistency reached nearly 80% for the three algorithms. In light of the characteristics of forest disturbance occurrence in southeastern China as well as the algorithmic complexity, efficiency, and adaptability, LandTrendr was recommended as the most suitable one in this region or other similar regions. Overall, the forest change monitoring process based on GEE is becoming more simplified and easily implemented, and the comparisons and tradeoffs in this study provide a reference for the choice of long time series forest monitoring algorithms.

Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis.

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.

Forecasting Stock Market Prices Using Machine Learning and Deep Learning Models: A Systematic Review, Performance Analysis and Discussion of Implications

The financial sector has greatly impacted the monetary well-being of consumers, traders, and financial institutions. In the current era, artificial intelligence is redefining the limits of the financial markets based on state-of-the-art machine learning and deep learning algorithms. There is extensive use of these techniques in financial instrument price prediction, market trend analysis, establishing investment opportunities, portfolio optimization, etc. Investors and traders are using machine learning and deep learning models for forecasting financial instrument movements. With the widespread adoption of AI in finance, it is imperative to summarize the recent machine learning and deep learning models, which motivated us to present this comprehensive review of the practical applications of machine learning in the financial industry. This article examines algorithms such as supervised and unsupervised machine learning algorithms, ensemble algorithms, time series analysis algorithms, and deep learning algorithms for stock price prediction and solving classification problems. The contributions of this review article are as follows: (a) it provides a description of machine learning and deep learning models used in the financial sector; (b) it provides a generic framework for stock price prediction and classification; and (c) it implements an ensemble model—“Random Forest + XG-Boost + LSTM”—for forecasting TAINIWALCHM and AGROPHOS stock prices and performs a comparative analysis with popular machine learning and deep learning models.

System dynamics monitoring using PIC micro-controller-based PLSE

The permutation largest slope entropy (PLSE) algorithm has been shown to be effective to distinguish between regular and non-regular dynamics from time series analysis. However, as it is the case for many non-linear time series analysis algorithms, such a characterization is locally made and does not allow one to capture some micro-phenomena, such as intermittency, that may occur in the system behavior. This paper presents a PIC micro-controller based implementation of the PLSE for a real-time monitoring of system dynamics. The PLSE algorithm is optimized to fit the program and data memory of low-end processors using the XC8 compiler and the MPLAB X IDE. The resulting algorithm is implemented on the PIC16F18446 and deployed on the Explorer 8 development board. The effectiveness of the developed tool is validated by considering an electrical circuit of the Duffing oscillator that can generate both periodic and chaotic dynamics. By comparing the PLSE values with the phase portraits and previous results on the Duffing oscillator circuit, the developed tool efficiently allows one to monitor the behavior of dynamical systems.

Forecast of differential settlement of structures using data of monitoring system

The article analyzes the results of observations of uneven settlement of various buildings, obtained in the course of long-term observations with the help of automated systems of deformation monitoring. The main purpose of the work is to evaluate the possibilities of predicting sedimentary processes using statistical forecasting models. Emphasis is placed on approach using time series analysis algorithms. The results of simulation using the integrated autoregressive moving average model are demonstrated. To build a forecast, data on the foundation settlement over a 5-year period were used. Predictive values obtained for 1-year and 2-year intervals are compared with the data of real observations. The comparison showed that at the chosen forecasting horizon, the deviation of the predicted settlement value from the actually observed one is comparable to the accuracy of sediment measurement by hydraulic leveling sensors. The study showed the promise of using this approach to predict the integrity of structures within the framework of an automated system of deformation monitoring.

Quantum Dynamic Mode Decomposition Algorithm for High-Dimensional Time Series Analysis

The dynamic mode decomposition (DMD) algorithm is a widely used factorization and dimensionality reduction technique in time series analysis. When analyzing high-dimensional time series, the DMD algorithm requires extremely large amounts of computational power. To accelerate the DMD algorithm, we propose a quantum-classical hybrid algorithm that we call the quantum dynamic mode decomposition (QDMD) algorithm. Given a time series X ∈ R n × ( m + 1) with n ≫ m , the QDMD algorithm first executes quantum singular value decomposition on a matrix related to X and obtains a quantum state containing the main singular values and singular vectors of the decomposed matrix, then performs a low-sampling-frequency process on the obtained quantum state and computes the low-dimensional projection of the DMD operator through the sampling results. Finally, the algorithm computes the DMD eigenvalues and prepares the amplitude-encoding states of the DMD modes using the obtained classical information and X . Considering the main variables, the complexity of the QDMD algorithm is O ~ M m polylog n / ϵ , where M = O ~ m 3 / ϵ 2 denotes the number of samples. Compared with the classical DMD algorithm, which has complexity O ~ n m 2 log 1 / ϵ , the QDMD algorithm provides an exponential acceleration of n , at the cost of greater dependence on M and ϵ . We test the effects of M on the QDMD algorithm in the specific application scenarios of data denoising, scene background extraction, and fluid dynamics analysis. We determined that the QDMD algorithm requires only a small number of samples M in specific applications, further demonstrating the quantum advantage of the QDMD algorithm in high-dimensional data analysis.