Interpolation Of Time Series Research Articles

Linearly interpolating missing values in time series helps little for land cover classification using recurrent or attention networks

Satellite time series data, widely used for land cover classification, often contain missing values due to cloud contamination, which can negatively affect classification. Numerous strategies have been developed to reconstruct the missing values to produce regular time series for machine learning classifiers, among which the compositing followed by the linear interpolation is most widely used. However, the classification improvement of linear interpolation for land cover classification has not been examined. Recently developed deep learning models such as long short term memory (LSTM) and Transformer allow such examination as they can classify time series with missing values. In this study, we compared the time series composites with missing values (without linear interpolation) and the linearly interpolated time series composites (without missing values) for land cover classification. About 18 thousand Harmonized Landsat Sentinel-2 (HLS) images acquired over Amur River Basin of China (890,308 km2) in 2021 were composited to 14 16-day periods. Two time series composites were classified, i.e., (i) the 16-day composites without interpolation that have on average 15.35% 16-day periods with missing values and (ii) the linearly interpolated 16-day composites with no missing values. The classifications showed that (1) between classifications with and without linear interpolation there was < 0.2% overall accuracy differences for the bidirectional LSTM (Bi-LSTM) and < 0.5% for the Transformer both of which were smaller than model training randomness; and (2) the computation time can be saved using composites without linear interpolation. The findings suggested that it is unnecessary to use the time-consuming linear interpolation in Bi-LSTM and Transformer-based land cover classifications. The findings were confirmed by experiments for sensitivity to the number of cloud-free composites and to different classification legends using crop type classifications. It implied the linear interpolation algorithm cannot reconstruct reliable time series for land cover classifications and historical use of such method is more about mitigating the inability of traditional classifiers to handle missing values rather than improving classifications. Linear interpolation is not necessary for LSTM and Transformer with capability to handle missing values. The training datasets and developed codes in this study are made publicly available.

Multimodal sensor fusion models for real-time exercise repetition counting with IMU sensors and respiration data

This study introduces an automated exercise repetition counting model for a variety of exercises. Although external devices such as fitness trackers and smart watches are capable of tracking exercise progress, they are still incapable of recording all pertinent information essential for comprehensive exercise tracking, such as the number of repetitions.To address this limitation, we propose a deep learning model that utilizes multimodal sensor and respiration audio data obtained from wearable devices, specifically smart earbuds that record IMU sensors and collect surrounding sounds. A diverse dataset of sensor data and respiratory audio data are collected by leveraging these smart earbuds during 30 different types of exercises, which enables the study to develop a comprehensive and accurate multimodal deep learning model that can be applied to a wide range of physical activities. Advanced techniques such as data augmentation and time-series interpolation are also employed to address the challenges of working with large and complex datasets.The proposed deep learning model, which incorporates multimodal sensor data and advanced data processing techniques, can be utilized to promote more effective and personalized exercise plans, ultimately leading to improved health outcomes for individuals who seek to maintain an active and healthy lifestyle.

Interpolation of GNSS Position Time Series Using GBDT, XGBoost, and RF Machine Learning Algorithms and Models Error Analysis

The global navigation satellite system (GNSS) position time series provides essential data for geodynamic and geophysical studies. Interpolation of the GNSS position time series is necessary because missing data will produce inaccurate conclusions made from the studies. The spatio-temporal correlations between GNSS reference stations cannot be considered when using traditional interpolation methods. This paper examines the use of machine learning models to reflect the spatio-temporal correlation among GNSS reference stations. To form the machine learning problem, the time series to be interpolated are treated as output values, and the time series from the remaining GNSS reference stations are used as input data. Specifically, three machine learning algorithms (i.e., the gradient boosting decision tree (GBDT), eXtreme gradient boosting (XGBoost), and random forest (RF)) are utilized to perform interpolation with the time series data from five GNSS reference stations in North China. The results of the interpolation of discrete points indicate that the three machine learning models achieve similar interpolation precision in the Up component, which is 45% better than the traditional cubic spline interpolation precision. The results of the interpolation of continuous missing data indicate that seasonal oscillations caused by thermal expansion effects in summer significantly affect the interpolation precision. Meanwhile, we improved the interpolation precision of the three models by adding data from five stations which have high correlation with the initial five GNSS reference stations. The interpolated time series for the North, East, and Up (NEU) are examined by principal component analysis (PCA), and the results show that the GBDT and RF models perform interpolation better than the XGBoost model.

A dataset of monthly VCI and TCI drought indices at a resolution of 1km in the Yellow River Basin (2003–2021)

The Yellow River Basin is located in the arid, semi-arid climate zone and semi-humid climate zones. According to the statistics of the Second National Comprehensive Water Resources Planning, its annual average water resources total 71.94 billion m3, accounting for 2.5% of the country's total water resources. However, it is the most severely affected by drought among the major river basins in China, and ecological protection faces severe challenges. With the global climate change, the drought problem in the Yellow River Basin has attracted more and more attention. Based on MODIS vegetation index products (MYD13A2, V6) and surface temperature radiation products (MYD11A2, V6). The dataset is obtained by approaches including projection conversion, cloud removal, mosaic clipping, time series interpolation and SG filter smoothing and other preprocessing. Using the calculation method proposed by Kogan in 1995, the VCI and TCI indices were calculated according to the corresponding MODIS products, respectively, and the monthly 1km resolution VCI and TCI drought index datasets in the Yellow River Basin from 2003 to 2021 were generated. Through data sharing, it is expected to provide important data support for drought monitoring and research in the Yellow River Basin under the background of global change.

Grassland mowing event detection using combined optical, SAR, and weather time series

The European Union’s Common Agricultural Policy (CAP) and the Habitats Directive aim to improve biodiversity in agricultural landscapes. Both policies require enormous monitoring, which can be facilitated by remote sensing. Use intensity, measured by mowing frequency is an important indicator of biodiversity in permanent grasslands. The frequency and timing of mowing can be determined using satellite remote sensing because photosynthetically active biomass changes rapidly in response to mowing. However, the rapid regrowth of grasses requires very dense satellite time series for reliable detection. Radar time series can complement optical time series and fill in cloud-related gaps to overcome this problem. Additional weather data can support the detection of grassland mowing events, as mowing events are associated with specific meteorological conditions. However, previous studies have not fully exploited both potentials or different machine learning approaches for mowing event detection.This study presents a new transferable two-step approach to detect grassland mowing events using combined optical and SAR data and additional weather data. First, we filled cloud-related gaps in optical time series using a supervised machine learning regression with optical and SAR data. We then classified time series sequences of optical, SAR and weather data into mown and unmown using four different machine learning algorithms. We used time series of NDVI and EVI (combined Sentinel-2 and Landsat 8), SAR backscatter, six-day interferometric coherence, backscatter radar vegetation index, backscatter cross-ratio (Sentinel-1), and temperature and precipitation sums. Our test sites are distributed across Germany and cover the entire gradient of grassland use intensities.Mowing events could be detected with F1 values of up to 89%, first cut with up to 94%. Our results show no structural advantage of infilling time series with machine learning over linearly interpolated time series. The combined Sentinel-2 and Landsat-8 time series provided dense time series with mostly median gaps less than 20 days, which proved sufficient to reliably detect mowing events. SAR data were not essential for mowing event detection in our study, but weather data improved classification results for models trained on all areas and years. However, when the model was transferred to unknown years or areas that were not used for training, SAR data improved detection accuracy, whereas weather data degrade it. Models trained on all years but not all study sites detected mowing events with an accuracy of up to F1 = 76%. Models trained with all regions but not all years detected mowing events in untrained years with F1 up to 80%.

Fast fitting of neural ordinary differential equations by Bayesian neural gradient matching to infer ecological interactions from time‐series data

Abstract Inferring ecological interactions is hard because we often lack suitable parametric representations to portray them. Neural ordinary differential equations (NODEs) provide a way of estimating interactions non‐parametrically from time‐series data. NODEs, however, are slow to fit, and inferred interactions usually are not compared with the ground truth. We provide a fast NODE fitting method, Bayesian neural gradient matching (BNGM), which relies on interpolating time series with neural networks and fitting NODEs to the interpolated dynamics with Bayesian regularisation. We test the accuracy of the approach by inferring ecological interactions in time series generated by an ODE model with known interactions. We compare these results against three existing approaches for estimating ecological interactions, standard NODEs, ODE models and convergent cross‐mapping (CCM). We also infer interactions in experimentally replicated time series of a microcosm featuring an algae, flagellate and rotifer population, in the hare and lynx system, and the Maizuru Bay community featuring 11 species. Our BNGM approach allows us to reduce the fitting time of NODE systems to only a few seconds and provides accurate estimates of ecological interactions in the artificial system, as true ecological interactions are recovered with minimal error. Our benchmark analysis reveals that our approach is both faster and more accurate than standard NODEs and parametric ODEs, while CCM was found to be faster but less accurate. The analysis of the replicated time series reveals that only the strongest interactions are consistent across replicates, while the analysis of the Maizuru community shows the strong negative impact of the chameleon goby on most species of the community, and a potential indirect negative effect of temperature by favouring goby population growth. Overall, NODEs alleviate the need for a mechanistic understanding of interactions, and BNGM alleviates the heavy computational cost. This is a crucial step availing quick NODE fitting to larger systems, cross‐validation and uncertainty quantification, as well as more objective estimation of interactions, and complex context dependence, than parametric models.

A Spatiotemporally Constrained Interpolation Method for Missing Pixel Values in the Suomi-NPP VIIRS Monthly Composite Images: Taking Shanghai as an Example

The Visible Infrared Imaging Radiometer Suite Day/Night Band (VIIRS/DNB) nighttime light data is a powerful remote sensing data source. However, due to stray light pollution, there is a lack of VIIRS data in mid-high latitudes during the summer, resulting in the absence of high-precision spatiotemporal continuous datasets. In this paper, we first select nine-time series interpolation methods to interpolate the missing images. Second, we construct image pixel-level temporal continuity constraints and spatial correlation constraints and remove the pixels that do not meet the constraints, and the eliminated pixels are filled with the focal statistics tool. Finally, the accuracy of the time series interpolation method and the spatiotemporally constrained interpolation method (STCIM) proposed in this paper are evaluated from three aspects: the number of abnormal pixels (NP), the total light brightness value (TDN), and the absolute value of the difference (ADN). The results show that the images simulated by the STCIM are more accurate than the nine selected time series interpolation methods, and the image interpolation accuracy is significantly improved. Relevant research results have improved the quality of the VIIRS dataset, promoted the application research based on the VIIRS DNB long-time series night light remote sensing image, and enriched the night light remote sensing theory and method system.

Mean value splines and their use for climatological time series

AbstractA new approach of splines to examine climatological time series is introduced and different applications are shown. Instead of the classical spline‐procedure to find polynomials which fit given values at certain points (knots), a variational formulation is used here, where a cost function is minimized to obtain smooth interpolated values at arbitrary points. The innovation of the method consists in the selection of the constraint, namely the conservation of mean values within certain smoothing intervals. The methodology allows a sound derivation of the past and present climate conditions in times of climate change. It allows a refined computation of extreme values and of the probability of certain temperature thresholds. The methodology furthermore allows to detect break points in climatological time series. Finally the method leads to a consistent interpolation of time series, which are only given by mean values. Several applications of the method, using climatological time series of Vienna are shown and discussed.

Artificial Neural Network-Assisted Classification of Hearing Prognosis of Sudden Sensorineural Hearing Loss With Vertigo.

This study aimed to determine the impact on hearing prognosis of the coherent frequency with high magnitude-squared wavelet coherence (MSWC) in video head impulse test (vHIT) among patients with sudden sensorineural hearing loss with vertigo (SSNHLV) undergoing high-dose steroid treatment. This study was a retrospective cohort study. SSNHLV patients treated at our referral center from December 2016 to December 2020 were examined. The cohort comprised 64 patients with SSNHLV undergoing high-dose steroid treatment. MSWC was measured by calculating the wavelet coherence analysis (WCA) at various frequencies from a vHIT. The hearing prognosis were analyzed using a multivariable Cox regression model and convolution neural network (CNN) of WCA. There were 64 patients with a male-to-female ratio of 1:1.67. The greater highest coherent frequency of the posterior semicircular canal (SCC) was associated with the complete recovery (CR) of hearing. After adjustment for other factors, the result remained robust (hazard ratio [HR] 2.11, 95% confidence interval [CI] 1.86-2.35). In the feature extraction with Resnet-50 and proceeding SVM in the horizontal image cropping style, the classification accuracy [STD] for (CR vs. partial + no recovery [PR + NR]), (over-sampling of CR vs. PR + NR), (extensive data extraction of CR vs. PR + NR), and (interpolation of time series of CR vs. PR + NR) were 83.6% [7.4], 92.1% [6.8], 88.9% [7.5], and 91.6% [6.4], respectively. The high coherent frequency of the posterior SCC was a significantly independent factor that was associated with good hearing prognosis in the patients who have SSNHLV. WCA may be provided with comprehensive ability in vestibulo-ocular reflex (VOR) evaluation. CNN could be utilized to classify WCA, predict treatment outcomes, and facilitate vHIT interpretation. Feature extraction in CNN with proceeding SVM and horizontal cropping style of wavelet coherence plot performed better accuracy and offered more stable model for hearing outcomes in patients with SSNHLV than pure CNN classification. Clinical and Translational Impact Statement-High coherent frequency in vHIT results in good hearing outcomes in SSNHLV and facilitates AI classification.

Measurement and characterization of infrasound waves from the March 25, 2023 thunderstorm at the near equatorial

&lt;abstract&gt; &lt;p&gt;Thunderstorm activity on March 25, 2023 provided a unique opportunity to study the mechanism of lightning events on changes in air pressure. In particular, this event made it possible to study changes in air pressure during thunderstorms using various instruments. This paper presented comprehensive results of infrasound, satellite data, weather radar and weather measurements at the ground during the storm. Observations of lightning events were confirmed using observational data from the International Space Station's Lightning Imaging Sensor (ISS LIS). This work estimated three spectral percentile values on infrasonic sensor data, time series interpolation of standard meteorology profiles, weather radar reflectivity and total radiant energy of lightning from ISS LIS observations during the day and night periods. As a result, during the investigation, it was seen that the recorded infrasound signal in the 0.6–0.8 Hertz (Hz) range was contaminated by background environmental noise, but in the 1–3 Hz band range it was consistent with the appearance of storms that produce high energy blows. Infrasound detection and electromagnetic lightning detection show good correlation up to a distance of 100 km from the infrasonic station. During a thunderstorm, the ISS LIS flight directly above the observation site detected more than 2,000 lightning events. In addition, the application of lightning detection from several independent instruments can provide a complete picture of the observed event.&lt;/p&gt; &lt;/abstract&gt;

Research on the Partition Method Based on the Observation Points of Voltage Distortion in Harmonic Optimization

With the use of a large number of power electronic equipment, the harmonics in the power grid are becoming more and more serious. There are many methods for harmonic mitigation and optimization such as Global network Optimization. When there are many nodes, the global network optimization method is more complicated. Considering the problem of large numbers of harmonic injection nodes in the power grid, this paper proposes a method of clustering the voltage distortion nodes according to correlation, and using the characteristic nodes to describe the harmonic voltage distortion in the region to mitigate harmonic voltage. This method is based on the observation data of the voltage distortion of the nodes for dynamic selection and grouping. The results show that this method meets the needs of Global network Optimization. The data processing methods used in this paper such as feature extraction methods and time series interpolation optimization can effectively reduce the data dimension, and get better optimization effect.

BIM-Based Pavement Management Tool for Scheduling Urban Road Maintenance

The latest advancements in road asphalt materials and construction technologies have increased the difficulty for engineers to select the appropriate pavement design solution with consideration of proper timing for maintenance planning. On the other hand, Building Information Modeling (BIM) tools allow practitioners to efficiently store and manage large amounts of data, supporting decision making in road asphalt pavement design and management. The present work focused on the elaboration of a BIM-based maintenance analysis tool for the specific evaluation of several condition indicators and the selection of proper maintenance solutions designed to include alternative materials and advanced recycling technologies. A traditional BIM workflow was integrated with additional user-defined property sets to investigate the need for maintenance at the present date and predict the degradation curve of the condition indicators through the least square interpolation of time series of data. The analysis tool also provided the selection of available pavement alternatives from a library of designed solutions based on their compliance with project-specific constraints (maximum budget, minimum useful life, and availability of secondary raw materials and in-place recycling technologies). The proposed BIM tool aims to be a practical and dynamic way to integrate maintenance planning considerations into road pavement design, encouraging the use of digital tools in the road industry and ultimately supporting a pavement maintenance decision-making process oriented towards a circular economy.

Evolving a Bayesian network model with information flow for time series interpolation of multiple ocean variables

Evolving a Bayesian network model with information flow for time series interpolation of multiple ocean variables

Maps, trends, and temperature sensitivities\u2014phenological information from and for decreasing numbers of volunteer observers

Phenology serves as a major indicator of ongoing climate change. Long-term phenological observations are critically important for tracking and communicating these changes. The phenological observation network across Germany is operated by the National Meteorological Service with a major contribution from volunteering activities. However, the number of observers has strongly decreased for the last decades, possibly resulting in increasing uncertainties when extracting reliable phenological information from map interpolation. We studied uncertainties in interpolated maps from decreasing phenological records, by comparing long-term trends based on grid-based interpolated and station-wise observed time series, as well as their correlations with temperature. Interpolated maps in spring were characterized by the largest spatial variabilities across Bavaria, Germany, with respective lowest interpolated uncertainties. Long-term phenological trends for both interpolations and observations exhibited mean advances of −0.2 to −0.3 days year−1 for spring and summer, while late autumn and winter showed a delay of around 0.1 days year−1. Throughout the year, temperature sensitivities were consistently stronger for interpolated time series than observations. Such a better representation of regional phenology by interpolation was equally supported by satellite-derived phenological indices. Nevertheless, simulation of observer numbers indicated that a decline to less than 40% leads to a strong decrease in interpolation accuracy. To better understand the risk of declining phenological observations and to motivate volunteer observers, a Shiny app is proposed to visualize spatial and temporal phenological patterns across Bavaria and their links to climate change–induced temperature changes.

A fractal interpolation approach to improve neural network predictions for difficult time series data

Deep Learning methods, such as Long Short-Term Memory (LSTM) neural networks prove capable of predicting real-life time series data. Crucial for this technique to work is a sufficient amount of data. This can either be very long time-series data or fine-grained time-series data. If the data is insufficient, in terms of length or complexity, LSTM approaches perform poorly. We propose a fractal interpolation approach to generate a more fine-grained time series out of insufficient data sets. The interpolation is dynamically adapted to the time series using a time-dependent complexity feature so that the complexity properties of the interpolated time series are related to that of the original one. Also we perform a linear interpolation with the same number of interpolation points to compare results.This paper shows that predictions of fractal interpolated and linear interpolated time series clearly outperform the ones of the original data for a test fit on unknown data. Though predictions of linear and fractal interpolated time series data perform very similar, the fractal interpolated ones outperform the linear interpolated ones on difficult time series data. Also, though the complexities of sub-intervals are tailored to match the one from the original data, the interpolated time series shows a much higher degree of persistency and (in terms of the Hurst exponent) a much higher degree of long term memory.

Time series interpolation and application of its methods in financial analysis

In the modern market economy conditions, financial information is very significant when evaluating the results of enterprises’ financial status and activity results. General economic, mathematical, heuristic methods are used for this type of analysis. The article analyses application opportunities for one of the mathematical research methods–time series–as well as its research instruments, discusses the place and role of interpolation methods in a financial analysis. The article reveals that interpolation methods which may be used to determined former values of an enterprise’s financial indicators or identify reasons which determined the enterprise’s financial status and activity results are the following: 1) graphic and arithmetic interpolation in a linear equation; 2) geometric interpolation based on the compound percentage formula and 3) interpolation by averaging.

Interpolating time series based on fuzzy cluster analysis problem

This study proposes the model for interpolating time series to use them to forecast effectively for future. This model is established based on the improved fuzzy clustering analysis problem, which is implemented by the Matlab procedure. The proposed model is illustrated by a data set and tested for many other datasets, especially for 3003 series in M3-Competition data. Comparing to the existing models, the proposed model always gives the best result. We also apply the proposed model in forecasting the salt peak for a coastal province of Vietnam. Examples and applications show the potential of the studied problem.

DATimeS: A machine learning time series GUI toolbox for gap-filling and vegetation phenology trends detection

Optical remotely sensed data are typically discontinuous, with missing values due to cloud cover. Consequently, gap-filling solutions are needed for accurate crop phenology characterization. The here presented Decomposition and Analysis of Time Series software (DATimeS) expands established time series interpolation methods with a diversity of advanced machine learning fitting algorithms (e.g., Gaussian Process Regression: GPR) particularly effective for the reconstruction of multiple-seasons vegetation temporal patterns. DATimeS is freely available as a powerful image time series software that generates cloud-free composite maps and captures seasonal vegetation dynamics from regular or irregular satellite time series. This work describes the main features of DATimeS, and provides a demonstration case using Sentinel-2 Leaf Area Index time series data over a Spanish site. GPR resulted as an optimum fitting algorithm with most accurate gap-filling performance and associated uncertainties. DATimeS further quantified LAI fluctuations among multiple crop seasons and provided phenological indicators for specific crop types.

(1906-5269) Interpolating time series based on fuzzy cluster analysis problem

This study proposes the model for interpolating time series to use them to forecast effectively for future. This model isestablished based on the improved fuzzy clustering analysis problem, which is implemented by the Matlab procedure.The proposed model is illustrated by a data set and tested for many other datasets, especially for 3003 series in M3-Competition data. Comparing to the existing models, the proposed model always gives the best result. We also applythe proposed model in forecasting the salt peak for a coastal province of Vietnam. Examples and applications show thepotential of the studied problem.

A Simple Similarity Index for the Comparison of Remotely Sensed Time Series with Scarce Simultaneous Acquisitions

Emergence of new state-of-the-art technologies has enabled an unprecedented amount of high spatial resolution satellite data having great potential for exploitation of extracted time series for a vast range of applications. Despite the high temporal resolution of time series, the number of real observations of optical data that can be utilized is reduced due to meteorological conditions (such as cloud or haze) prevailing at the time of acquisition. This fact has an effect on the density of the retrieved time series and subsequently on a number of coincidental observations when comparing the similarity of time series from two different data sources for which the simultaneous acquisition date is already scarce. Classical tools for assessing the similarity of such time series can prove to be difficult or even impossible because of a lack of simultaneous observations. In this paper, we propose a simple method in order to circumvent this scarcity issue. In the first step, we rely on an interpolation in order to produce artificial time series on the union of the original acquisition dates. Then, we extend the theory of the correlation coefficient (CC) estimator to these interpolated time series. After validation on synthetic data, this simple approach proved to be extremely efficient on a real case study where Sentinel-2 and PlanetScope NDVI time series on parcels in The Netherlands are compared. Indeed, compared to other methods, it reduced the number of undecided cases while also improving the power of the statistical test on the similarity between both types of time series and the precision of the estimated CC.