Regular Time Series Research Articles

Unsupervised clustering of longitudinal clinical measurements in electronic health records.

Longitudinal electronic health records (EHR) can be utilized to identify patterns of disease development and progression in real-world settings. Unsupervised temporal matching algorithms are being repurposed to EHR from signal processing- and protein-sequence alignment tasks where they have shown immense promise for gaining insight into disease. The robustness of these algorithms for classifying EHR clinical data remains to be determined. Timeseries compiled from clinical measurements, such as blood pressure, have far more irregularity in sampling and missingness than the data for which these algorithms were developed, necessitating a systematic evaluation of these methods. We applied 30 state-of-the-art unsupervised machine learning algorithms to 6,912 systematically generated simulated clinical datasets across five parameters. These algorithms included eight temporal matching algorithms with fourteen partitional and eight fuzzy clustering methods. Nemenyi tests were used to determine differences in accuracy using the Adjusted Rand Index (ARI). Dynamic time warping and its lower-bound variants had the highest accuracies across all cohorts (median ARI>0.70). All 30 methods were better at discriminating classes with differences in magnitude compared to differences in trajectory shapes. Missingness impacted accuracies only when classes were different by trajectory shape. The method with the highest ARI was then used to cluster a large pediatric metabolic syndrome (MetS) cohort (N = 43,426). We identified three unique childhood BMI patterns with high average cluster consensus (>70%). The algorithm identified a cluster with consistently high BMI which had the greatest risk of MetS, consistent with prior literature (OR = 4.87, 95% CI: 3.93-6.12). While these algorithms have been shown to have similar accuracies for regular timeseries, their accuracies in clinical applications vary substantially in discriminating differences in shape and especially with moderate to high missingness (>10%). This systematic assessment also shows that the most robust algorithms tested here can derive meaningful insights from longitudinal clinical data.

Novel efficient reservoir computing methodologies for regular and irregular time series classification

AbstractTime series is a data structure prevalent in a wide range of fields such as healthcare, finance and meteorology. It goes without saying that analyzing time series data holds the key to gaining insight into our day-to-day observations. Among the vast spectrum of time series analysis, time series classification offers the unique opportunity to classify the sequences into their respective categories for the sake of automated detection. To this end, two types of mainstream approaches, recurrent neural networks and distance-based methods, have been commonly employed to address this specific problem. Despite their enormous success, methods like Long Short-Term Memory networks typically require high computational resources. It is largely as a consequence of the nature of backpropagation, driving the search for some backpropagation-free alternatives. Reservoir computing is an instance of recurrent neural networks that is known for its efficiency in processing time series sequences. Therefore, in this article, we will develop two reservoir computing based methods that can effectively deal with regular and irregular time series with minimal computational cost, both while achieving a desirable level of classification accuracy.

Fund transfer fraud detection: Analyzing irregular transactions and customer relationships with self-attention and graph neural networks

This paper presents a method for identifying fraudulent fund transfers using real bank data, analyzing customer information, transactional activities, and customer relationships. The preprocessing step transforms high-dimensional, irregular transaction time series into regular time series, then further compresses them in a latent space using a self-attention-based autoencoder. To address the scarcity of fraudulent data samples and mitigate training issues caused by data imbalance, various deep generative models, including the conditional variational autoencoder and Wasserstein generative adversarial network, are applied to generate additional fraudulent raw data and augment fraud samples in latent space. The reparameterization trick is integrated into the encoder–decoder structure to boost the model’s generative capabilities. Additionally, a Graph Neural Network (GNN) is used to model customer relationships. The proposed approach utilizes end-to-end learning, integrating the autoencoder’s reconstruction loss, KL divergence loss (when reparameterization trick is applied), and classification loss for fraud detection. To optimize computational resources, neighborhood sampling for GNN is combined with mini-batch training for the autoencoder, improving both training efficiency and model reliability. Comprehensive experiments demonstrate the effectiveness of the proposed fusion network, highlighting the importance of each component and preprocessing step. For example, the areas under the precision–recall curves for fraud detection show notable improvements in our model. For suspicious transactions identified by the bank’s rules, other models range from 0.66% to 22.15%, while our model reached 27%. For non-suspicious transactions, other models range from 2.53% to 22.00%, with our model achieving 22.90%. This model has potential for wider applications in anomaly detection, particularly in datasets with irregular time series and complex customer relationships.

Reconstruction of dense time series high spatial resolution NDVI data using a spatiotemporal optimal weighted combination estimation model based on Sentinel-2 and MODIS

A regular, dense time series of the normalized difference vegetation index (NDVI) is a crucial remote sensing parameter that provides insights into the growth status of plants across different temporal and spatial scales. However, the production of high-resolution, equal-interval, and dense-time-series NDVI products currently faces technical challenges, limiting their application in agriculture and forestry-related fields. This study proposes a new method for reconstructing a dense Sentinel-2 NDVI time series based on the spatiotemporal optimal weighted combination estimation model (SOWCEM). The SOWCEM is developed using state-of-the-art spatial and temporal reconstruction algorithms. This model considers the distribution characteristics of errors in spatiotemporal dimensions, allowing for adaptive determination of the optimal combination weight at the pixel level. Then, the reconstructed regular dense-time-series NDVI data covering the region for five days/time are evaluated through a comparative analysis. The experimental results demonstrate that the regional NDVI reconstruction image based on the SOWCEM algorithm has a determination coefficient (R2) of 0.9082, a root mean square error (RMSE) of 0.0403, and a comprehensive overall error (ERGAS) of 5.7726. Compared with single spatiotemporal dimension models, the SOWCEM algorithm shows an average improvement of 5.78% in R2, while the RMSE and ERGAS decrease by 6.5% and 6.86%, respectively. Moreover, the stability and robustness of the models are also enhanced. These results indicate that the SOWCEM algorithm can effectively achieve a high-quality fusion reconstruction of regional images, significantly enhancing the accuracy of high-spatial-resolution NDVI dense temporal spectral reconstruction. Furthermore, it exhibits clear superiority and good applicability. This algorithmic framework provides a feasible approach for the dense reconstruction of high-spatial-resolution regular time-series NDVI data, enabling more accurate and efficient high-resolution NDVI remote sensing monitoring services in related field applications. The core code of SOWCEM is available at https://github.com/GISerZkun/SOWCEM.

An Artificial Neural Network Predicts Gender Differences of Motor and Non-Motor Symptoms of Patients with Advanced Parkinson's Disease under Levodopa-Carbidopa Intestinal Gel.

Background and Objectives: Currently, no tool exists to predict clinical outcomes in patients with advanced Parkinson's disease (PD) under levodopa-carbidopa intestinal gel (LCIG) treatment. The aim of this study was to develop a novel deep neural network model to predict the clinical outcomes of patients with advanced PD after two years of LCIG therapy. Materials and Methods: This was a longitudinal, 24-month observational study of 59 patients with advanced PD in a multicenter registry under LCIG treatment from September 2019 to September 2021, including 43 movement disorder centers. The data set includes 649 measurements of patients, which make an irregular time series, and they are turned into regular time series during the preprocessing phase. Motor status was assessed with the Unified Parkinson's Disease Rating Scale (UPDRS) Parts III (off) and IV. The NMS was assessed by the NMS Questionnaire (NMSQ) and the Geriatric Depression Scale (GDS), the quality of life by PDQ-39, and severity by Hoehn and Yahr (HY). Multivariate linear regression, ARIMA, SARIMA, and Long Short-Term Memory-Recurrent NeuralNetwork (LSTM-RNN) models were used. Results: LCIG significantly improved dyskinesia duration and quality of life, with men experiencing a 19% and women a 10% greater improvement, respectively. Multivariate linear regression models showed that UPDRS-III decreased by 1.5 and 4.39 units per one-unit increase in the PDQ-39 and UPDRS-IV indexes, respectively. Although the ARIMA-(2,0,2) model is the best one with AIC criterion 101.8 and validation criteria MAE = 0.25, RMSE = 0.59, and RS = 0.49, it failed to predict PD patients' features over a long period of time. Among all the time series models, the LSTM-RNN model predicts these clinical characteristics with the highest accuracy (MAE = 0.057, RMSE = 0.079, RS = 0.0053, mean square error = 0.0069). Conclusions: The LSTM-RNN model predicts, with the highest accuracy, gender-dependent clinical outcomes in patients with advanced PD after two years of LCIG therapy.

Assessing decadal- to centennial-scale nonstationary variability in meteorological drought trends

Abstract. There are indications that the reference climatology underlying meteorological drought has shown nonstationarity at seasonal, decadal, and centennial timescales, impacting the calculation of drought indices and potentially having ecological and economic consequences. Analyzing these trends in meteorological drought climatology beyond 100 years, a time frame which exceeds the available period of observation data, contributes to a better understanding of the nonstationary changes, ultimately determining whether they are within the range of natural variability or outside this range. To accomplish this, our study introduces a novel approach to integrate unevenly scaled tree-ring proxy data from the North American Seasonal Precipitation Atlas (NASPA) with instrumental precipitation datasets by first temporally downscaling the proxy data to produce a regular time series and then modeling climate nonstationarity while simultaneously correcting model-induced bias. This new modeling approach was applied to 14 sites across the continental United States using the 3-month standardized precipitation index (SPI) as a basis. The findings showed that certain locations have experienced recent rapid shifts towards drier or wetter conditions during the instrumental period compared to the past 1000 years, with drying trends generally found in the west and wetting trends in the east. This study also found that seasonal shifts have occurred in some regions recently, with seasonality changes most notable for southern gauges. We expect that our new approach provides a foundation for incorporating various datasets to examine nonstationary variability in long-term precipitation climatology and to confirm the spatial patterns noted here in greater detail.

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.

Vegetation classification in a subtropical region with Sentinel-2 time series data and deep learning

ABSTRACT Preparing regular time series optical remote sensing data is a difficult task due to the influences of frequently cloudy and rainy days. The irregular data and their forms severely limit the data’s ability to be analyzed and modeled for vegetation classification. However, how irregular time series data affect vegetation classification in deep learning models is poorly understood. To address these questions, this research preprocessed the 2019–2021 time series of Sentinel-2 in both unequal and equal intervals, and transformed them into an image through recurrence plot for each pixel. The initial one-dimension time series (1DTS) and recurrence plot data were then used as input data for three deep learning methods (i.e. Conv1D model based on one-dimensional convolution, GoogLeNet model based on two-dimensional convolution, and CGNet model which fused Conv1D and GoogLeNet) for vegetation classification, respectively. The class separability of the features generated by each model was evaluated and the importance of spectral and temporal features was further examined through gradient backpropagation. The equal-interval time series data significantly improved the classification accuracy with 0.04, 0.13, and 0.09 for Conv1D, GoogLeNet, and CGNet, respectively. The CGNet achieved the highest classification accuracy, indicating that the information from 1DTS and recurrence plot can be a good complementary for vegetation classification. The importance of spectral bands and time showed that the Sentinel-2 red edge-1 spectral band played a critical role in the identification of eucalyptus, loquat, and honey pomelo, but the importance order of bands varied in different vegetation types in GoogLeNet. The time importance varied across different vegetation types but is similar in these deep learning models. This study quantified the impacts of organizational form (1DTS and recurrence plot) of time series data on different models. This research is valuable for us to choose appropriate data structures and efficient deep learning models for vegetation classification.

A new efficient ALignment-driven Neural Network for Mortality Prediction from Irregular Multivariate Time Series data

The irregularity of the time interval between observations in and across the stream is a key factor that leads to a drop in performance when classical machine learning or deep learning models are used for a downstream task requiring multivariate time series. Indeed, irregular multivariate time series not only increase the rate of missing values but also lead to data sparsity, which consequently makes the data almost unleverageable and/or ineffective for models. To tackle this scorching challenge, most of the pioneering approaches apply imputation or interpolation in their core, which might lead to embedding data with noise. To especially address this irregular multivariate time series issue, we introduce, in this paper, a new deep neural network model called ALignment-driven Neural Network. The innovative idea of our model is to transform the irregular multivariate time series into pseudo-aligned (or pseudo-regular) latent values. The latter are shown as a matrix, where the coefficients are the latent values of each feature at user-defined reference time points that are evenly spaced. They are obtained through a duplication process driven by an exponential decay mechanism. The obtained output is then passed to a Recurrent Neural Network model, which is undoubtedly the must-use model for regular time series data. To show that our model added value, we looked at the Intensive Care Unit mortality prediction task. In this unit, the physiological measurements used to make decisions have a problem with time irregularity. Leveraging the publicly available MIMIC-III, we compare the performance of our model to that of flagship models. In addition, we also performed extensive ablation studies to highlight the importance of specific components in our model. Interestingly enough, whenever data is collected 24 and 48 h after a patient’s admission, we outperform our pioneering competitors, i.e., +1.1% and +1.5% for the AUC score, +2.3% and +2.4% for the AUPRC score and +0.6% and +1.7% for the F1-score.

Correlation of satellite-based LAI and actual crop yield

The main objective of this article was to investigate the correlation between actual crop yield and Sentinel-2 Leaf Area Index (LAI) for the further possibility of predict model creating. To do so, the following steps have been done. Step 1 – the dataset of actual crop yield was collected for 2364 fields in Ukraine represented with maize, soy, sunflower, winter wheat, winter rapeseed and winter barley. Step 2 – the dataset of Sentinel-2 LAI was collected for 2016-2018 period according to the actual crop yield available. Step 3 – LAI preprocessing (spatial averaging, temporal interpolation/extrapolation to fill the time series gaps, smoothing time series dynamics, temporal averaging). In order to accomplish the process of filling the gaps for the LAI time series, the regular time series dynamics of LAI with a 1-day interval were created using 4 methods: linear interpolation, spline interpolation, LOCF (Last Observation Carried Forward) and ARIMA (AutoRegressive Integrated Moving Average). The time series smoothing process have been accomplish using the local polynomial regression (LOESS) function with different degrees of smoothing. The LAI dynamics preprocessing step did not strongly affect the improvement of the correlation coefficients. Thus, the smoothing process for the time series LAI dynamics at the 0.1 degree of smoothing according to the LOCF and ARIMA gap-filling methods of improved correlation coefficients by 0.01 on average. Step 4 – actual yield values were related to preprocessed satellite-based LAI (correlation of actual yields and LAI). A strong relationship was not indicated (with averaged by vegetation periods correlation coefficient of 0.4 for maize, 0.52 – soy, 0.39 – sunflower, 0.86 – winter barley, 0.54 – winter rapeseed and 0.5 – winter wheat). Since the reliability of obtained correlation coefficients also depends on how many observed data points were in the sample, the hypothesis test of the "significance of the correlation coefficient" has been performed and shows the significance level of p &lt; 0.05 for all crops except winter barley (there is insufficient evidence to conclude that high correlation coefficient of 0.86 for this crop is significant). The average correlation coefficient for all crops is about 0.5 (p &lt; 0.05) which is considered low/moderate. Thus, an attempt to create a linear crop yield prediction model using only Leaf Area Index (LAI) derived from Sentinel-2 will not be effective (based on the cases considered).

Detection of motor imagery based on short-term entropy of time–frequency representations

BackgroundMotor imagery is a cognitive process of imagining a performance of a motor task without employing the actual movement of muscles. It is often used in rehabilitation and utilized in assistive technologies to control a brain–computer interface (BCI). This paper provides a comparison of different time–frequency representations (TFR) and their Rényi and Shannon entropies for sensorimotor rhythm (SMR) based motor imagery control signals in electroencephalographic (EEG) data. The motor imagery task was guided by visual guidance, visual and vibrotactile (somatosensory) guidance or visual cue only.ResultsWhen using TFR-based entropy features as an input for classification of different interaction intentions, higher accuracies were achieved (up to 99.87%) in comparison to regular time-series amplitude features (for which accuracy was up to 85.91%), which is an increase when compared to existing methods. In particular, the highest accuracy was achieved for the classification of the motor imagery versus the baseline (rest state) when using Shannon entropy with Reassigned Pseudo Wigner–Ville time–frequency representation.ConclusionsOur findings suggest that the quantity of useful classifiable motor imagery information (entropy output) changes during the period of motor imagery in comparison to baseline period; as a result, there is an increase in the accuracy and F1 score of classification when using entropy features in comparison to the accuracy and the F1 of classification when using amplitude features, hence, it is manifested as an improvement of the ability to detect motor imagery.

Repose time patterns of debris‐flow events in alpine catchments

AbstractThe omnipresent threat of natural hazards in mountainous regions has led to a risk culture which requires knowledge about the frequency of the considered hazardous process. Observations suggest that the frequency of debris‐flow events in a single catchment is, besides climatic thresholds, also controlled by its geological, lithological and geomorphological characteristics. Based on investigations of debris‐flow event frequencies from 47 headwater catchments, our results support the classification of recurrence intervals as irregular, clustered or regular, originally proposed by Zimmermann et al. in 1997 (Eclogae Geologicae Helvetiae, 90(3), 415–420). However, instead of using geomorphological characteristics, our classification relies on quantitative analyses considering potential dependencies between events based on their inter‐event (repose) times. By employing a modified dynamic threshold concept with respect to debris‐flow initiation, we show that for irregular frequencies neither climatic nor geomorphological thresholds are altered by the last debris‐flow event. For regular and clustered time series, however, mutual dependency between events is reasonable and therefore prompts dynamic changes of climatic as well as geomorphological thresholds.

Fine Structure of Vertical Density Distribution in the Black Sea and Its Relationship with Vertical Turbulent Exchange

This paper is concerned with the analysis of the long-term regular time series of current velocity and conductivity, temperature, and depth (CTD) profiles, measured with the moored autonomous profiler Aqualog over the upper part of the continental slope at a fixed geographical location in the Northeastern Black Sea. This study focuses on the fine structure of the density profiles to show that the fine-structure Cox number (C) is a power function of the Richardson number (Ri). A similar inverse power relationship with the same exponent was found earlier for the coefficient of vertical turbulent mass exchange (Kρ) and Ri. Based on those results, the analysis indicated a statistically significant correlation between C and Kρ, which suggests that the estimations of Kρ could be conducted from the CTD data only.

Monetary policy uncertainty, monetary policy surprises and stock returns

We study the effects of monetary policy surprises on stock returns under low and high monetary policy uncertainty in the U.S. using the Panel Smooth Transition Regression (PSTR) model to identify the uncertainty regimes. Monetary policy surprises are unexpected changes in the Federal Funds Rate (FFR) on Federal Open Market Committee (FOMC) announcement days, where the mimicking portfolio method is used to obtain a regular time series with surprises since the announcements occur on an irregular basis. Using data for the period 1994–2008, we find a negative relationship between monetary policy surprises and stock returns under both uncertainty regimes but a less pronounced relationship between surprises and returns when uncertainty is low. Hence, it is more important to hedge against unexpected stock market volatility when the uncertainty in monetary policy is high compared to when uncertainty is low.

Multi-Objective Optimization with Artificial Neural Network Based Robust Paddy Yield Prediction Model

Agriculture plays a vital role in the food production process that occupies nearly one-third of the total surface of the earth. Rice is propagated from the seeds of paddy and it is a stable food almost used by fifty percent of the total world population. The extensive growth of the human population alarms us to ensure food security and the country should take proper food steps to improve the yield of food grains. This paper concentrates on improving the yield of paddy by predicting the factors that influence the growth of paddy with the help of Evolutionary Computation Techniques. Most of the researchers used to relay on historical records of meteorological parameters to predict the yield of paddy. There is a lack in analyzing the day to day impact of meteorological parameters such as direction of wind, relative humidity, Instant Wind Speed in paddy cultivation. The real time meteorological data collected and analysis the impact of weather parameters from the day of paddy sowing to till the last day of paddy harvesting with regular time series. A Robust Optimized Artificial Neural Network (ROANN) Algorithm with Genetic Algorithm (GA) and Multi Objective Particle Swarm Optimization Algorithm (MOPSO) proposed to predict the factors that to be concentrated by farmers to improve the paddy yield in cultivation. A real time paddy data collected from farmers of Tamilnadu and the meteorological parameters were matched with the cropping pattern of the farmers to construct the database. The input parameters were optimized either by using GA or MOPSO optimization algorithms to reconstruct the database. Reconstructed database optimized by using Artificial Neural Network Back Propagation Algorithm. The reason for improving the growth of paddy was identified using the output of the Neural Network. Performance metrics such as Accuracy, Error Rate etc were used to measure the performance of the proposed algorithm. Comparative analysis made between ANN with GA and ANN with MOPSO to identify the recommendations for improving the paddy yield.

Parcel-Level Mapping of Horticultural Crops in Mountain Areas Using Irregular Time Series and VHR Images Taking Qixia, China as An Example

Accurate and reliable horticultural crop classification results are an important part of agricultural management. At present, research on orchard classification based on optical images in complex mountain areas is vulnerable to the influence of cloudy weather, especially in the summer, which leads to a lack of key phenological characteristics. To solve this problem, a parcel-level orchard mapping experiment with an irregular time series was carried out in Qixia City, China. Firstly, the candidate parcels in the study area were extracted from VHR images with a spatial resolution of 0.55 m based on RCF and DABNet models. The F1 score and area-based intersection-over-union (IoU) of the parcel extraction results were calculated. When the boundary buffer radius was 1 m, the F1 score was 0.93. When the radius was 2 m, the F1 score was 0.96. The IoU was 0.872, which shows the effectiveness of the parcel extraction method. Then, based on Sentinel-2 data, the NDVI, EVI, and SAVI vegetation indexes were calculated to construct an irregular time series. A two-dimensional CNN model was used for classification. In order to verify the effectiveness of this method, the study also constructed regular time series for the study area and conducted classification experiments using the 2DCNN and LSTM as classifiers, respectively. Confusion matrices were constructed for the classification results, and the overall accuracy was calculated. The results show that the overall accuracy of the method based on irregular time series is 97.76%, with a kappa coefficient of 0.96, higher than the other experiments, which indicates that the classification method based on irregular time series is effective and can make full use of the fragmented spectral features. Finally, based on the candidate parcels and pixel-level classification results of the study area, the crop categories of the parcels were filled to achieve accurate parcel-level mapping of horticultural crops in complex mountain areas. This method can provide a theoretical reference for orchard crop mapping and serves the development of regional precision agriculture.

Corrigendum to the article “Regular multidimensional stationary time series”

In Theorem 2.1 which was the main result of the article it was implicitly assumed that for any regular ‐dimensional weakly stationary time series of rank , , there exists an analytic spectral factor of the form , where is the diagonal matrix of the positive eigenvalues of the spectral density matrix and is the sub‐unitary matrix of the corresponding eigenvectors. In fact, to the best of my knowledge, it is not known if this assumption is true or false.

Time-Series Forecasting via Fuzzy-Probabilistic Approach With Evolving Clustering-Based Granulation

Time-series prediction based on information granule in which the algorithm is developed by deriving the relations existing in the granular time series, has achieved excellent success. However, the existing uncertainty in data and the computational demand of the granulation process make it difficult for these methods to accurately and efficiently achieve long-term prediction. In this article, a fuzzy-probabilistic prediction approach with evolving clustering-based granulation is proposed. First, the evolving clustering-based granulation strategy is proposed to transform the original numerical data into information granules. The granulation process is performed in an incremental way and the information granules are represented with the triplets, which can efficiently reduce the computation overhead. Then, the proposed information granule clustering is used to derive the group relations in the information granules. Based on the logical relationships of information granules in the temporal order, the information granule forecasting the integrated fuzzy and probability theory is proposed to deal with uncertainties and perform final long-term prediction. A series of experiments using publicly available time series are conducted, and the comparative analysis demonstrates that the proposed approach can achieve a better performance for regular and Big Data time series than the existing granular and numeric models for long-term prediction.

Multistate capture–recapture models for irregularly sampled data

Multistate capture-recapture data comprise individual-specific sighting histories, together with information on individuals’ states related, for example, to breeding status, infection level, or geographical location. Such data are often analysed using the Arnason–Schwarz model, where transitions between states are modelled using a discrete-time Markov chain, making the model most easily applicable to regular time series. When time intervals between capture occasions are not of equal length, more complex time-dependent constructions may be required, increasing the number of parameters to estimate, decreasing interpretability, and potentially leading to reduced precision. Here we develop a multi-state model based on a state process operating in continuous time, which can be regarded as an analogue of the discrete-time Arnason–Schwarz model for irregularly sampled data. Statistical inference is carried out by regarding the capture-recapture data as realisations from a continuous-time hidden Markov model, which allows the associated efficient algorithms to be used for maximum likelihood estimation and state decoding. To illustrate the feasibility of the modelling framework, we use a long-term survey of bottlenose dolphins where capture occasions are not regularly spaced through time. Here, we are particularly interested in seasonal effects on the movement rates of the dolphins along the Scottish east coast. The results reveal seasonal movement patterns between two core areas of their range, providing information that will inform conservation management.

A New Spatial–Temporal Depthwise Separable Convolutional Fusion Network for Generating Landsat 8-Day Surface Reflectance Time Series over Forest Regions

Landsat has provided the longest fine resolution data archive of Earth’s environment since 1972; however, one of the challenges in using Landsat data for various applications is its frequent large data gaps and heavy cloud contaminations. One pressing research topic is to generate the regular time series by integrating coarse-resolution satellite data through data fusion techniques. This study presents a novel spatiotemporal fusion (STF) method based on a depthwise separable convolutional neural network (DSC), namely, STFDSC, to generate Landsat-surface reflectance time series at 8-day intervals by fusing Landsat 30 m with high-quality Moderate Resolution Imaging Spectroradiometer (MODIS) 500 m surface reflectance data. The STFDSC method consists of three main stages: feature extraction, feature fusion and prediction. Features were first extracted from Landsat and MODIS surface reflectance changes, and the extracted multilevel features were then stacked and fused. Both low-level and middle-level features that were generally ignored in convolutional neural network (CNN)-based fusion models were included in STFDSC to avoid key information loss and thus ensure high prediction accuracy. The prediction stage generated a Landsat residual image and is combined with original Landsat data to obtain predictions of Landsat imagery at the target date. The performance of STFDSC was evaluated in the Greater Khingan Mountains (GKM) in Northeast China and the Ziwuling (ZWL) forest region in Northwest China. A comparison of STFDSC with four published fusion methods, including two classic fusion methods (FSDAF, ESTARFM) and two machine learning methods (EDCSTFN and STFNET), was also carried out. The results showed that STFDSC made stable and more accurate predictions of Landsat surface reflectance than other methods in both the GKM and ZWL regions. The root-mean-square-errors (RMSEs) of TM bands 2, 3, 4, and 7 were 0.0046, 0.0038, 0.0143, and 0.0055 in GKM, respectively, and 0.0246, 0.0176, 0.0280, and 0.0141 in ZWL, respectively; it can be potentially used for generating the global surface reflectance and other high-level land products.