Quantitative evaluation of motif sets in time series

Multivariate time series (MTS) data are ubiquitous in science and daily life, and how to measure their similarity is a core part of MTS analyzing process. Many of the research efforts in this context have focused on proposing novel similarity measures for the underlying data. However, with the countless techniques to estimate similarity between MTS, this field suffers from a lack of comparative studies using quantitative and large scale evaluations. In order to provide a comprehensive validation, an extensive evaluation of similarity measures for MTS clustering were conducted. The 14 well-known similarity measures with their variants and testing their effectiveness on 23 MTS datasets coming from a wide variety of application domains were re-implemented. In this paper, an overview of these different techniques is given and the empirical comparison regarding their effectiveness based on agglomerative clustering task is presented. Furthermore, the statistical significance tests were used to derive meaningful conclusions. It has been found that all of similarity measures are equivalent, in terms of clustering F-measure, and there is no significant difference between similarity measures based on our datasets. The results provide a comparative background between similarity measures to find the most proper method in terms of performance and computation time in this field.

The number of Landsat time-series applications has grown substantially because of its approximately 50-year history and relatively high spatial resolution for observing long term changes in the Earth’s surface. However, missing observations (i.e., gaps) caused by clouds and cloud shadows, orbit and sensing geometry, and sensor issues have broadly limited the development of Landsat time-series applications. Due to the large area and temporal and spatial irregularity of time-series gaps, it is difficult to find an efficient and highly precise method to fill them. The Missing Observation Prediction based on Spectral-Temporal Metrics (MOPSTM) method has been proposed and delivered good performance in filling large-area gaps of single-date Landsat images. However, it can be less practical for a time series longer than one year due to the lack of mechanics that exclude dissimilar data in time series (e.g., different phenology or changes in land cover). To solve this problem, this study proposes a new gap-filling method, Spectral Temporal Information for Missing Data Reconstruction (STIMDR), and examines its performance in Landsat reflectance time series. Two groups of experiments, including 2000 × 2000 pixel Landsat single-date images and Landsat time series acquired from four sites (Kenya, Finland, Germany, and China), were performed to test the new method. We simulated artificial gaps to evaluate predicted pixel values with real observations. Quantitative and qualitative evaluations of gap-filled images through comparisons with other state-of-the-art methods confirmed the more robust and accurate performance of the proposed method. In addition, the proposed method was also able to fill gaps contaminated by extreme cloud cover for a period (e.g., winter in high-latitude areas). A down-stream task of random forest supervised classification through both gap-filled simulated datasets and the original valid datasets verified that STIMDR-generated products are relevant to the user community for land cover applications.

Abstract. Time series imagery containing high-dimensional temporal features are conducive to improving classification accuracy. With the plenty accumulation of historical images, the inclusion of time series data becomes available to utilize, but it is difficult to avoid missing values caused by cloud cover. Meanwhile, seeking a large amount of training labels for long time series also makes data collection troublesome. In this study, we proposed a semi-supervised convolutional long short-term memory neural network (Semi-LSTM) in long time series which achieves an accurate and automated land cover classification with a small proportion of labels. Three main contributions of this work are summarized as follows: i) the proposed method achieve an excellent classification via a small group of labels in long time series data, and reducing dependence of training labels; ii) it is a robust algorithm in accuracy for the influence of noise, and reduces the requirements of sequential data for cloudless and lossless images; and iii) it makes full advantage of spectral-spatial-temporal features, especially expanding time context information to enhance classification accuracy. Finally, the proposed network is validated on time series imagery from Landsat 8. All quantitative analyses and evaluation indicators of the experimental results demonstrate competitive performance in the suggested modes.

Establishing relationships among patterns in stock market data

MODIS time series data have been widely used in the research of regional and global ecosystems and climate change. For vegetation monitoring, vegetation indices such as NDVI (normalized difference vegetation index), EVI (enhanced vegetation index) and NBR (normalized burn ratio), are usually derived from MODIS reflectance data. However, noise usually makes it difficult to generate reliable time series of vegetation indices. Although some methods have been developed for reconstructing NDVI time series data, they still suffer from some limitations. First, there is no reliable approach for detecting and dealing with low-quality data, resulting in poor outcomes. Second, no effective evaluation of the fidelity of the corrected data to the original data has been discussed. For these reasons, we developed a new time series reconstruction approach, named Fixing Invalid Value (FIV) method. The proposed method assumes that the noise in surface reflectance data stems from invalid data, such as clouds, ice, and missing values. The FIV method first uses the spatially and temporally neighboring pixels to estimate the invalid values and then applies morphology operations to remove the residual noise. Finally, the Savitzky-Golay (S-G) filter is employed to generate the final results. The FIV method is tested on 8-day composite MODIS surface reflectance time series data from 2001 to 2012 in Jiangxi and Fujian provinces, China. The results show that the FIV method outperforms the conventional S-G filter and the HANTS method both in terms of visual inspection and quantitative evaluation. Furthermore, the fidelity evaluation reveals that the proposed FIV method produces high-quality time series data under all weather conditions.

The Landsat archive is one of the richest Earth observation datasets available and provides long-term data at fairly high temporal and spatial resolution globally. Temporal aggregation is frequently used to condense single observations into a more digestible feature space that provides spatially gap-free data to fulfill demands of many processing strategies that rely on homogeneous data coverage across a large area, e.g., machine learning-based land cover classification. Spectral Temporal Metrics (STMs) represent a conceptually simple feature space wherein multiple observations are temporally aggregated by statistical functions. The quality and inter-annual consistency of STMs is affected by data availability, including usable clear-sky observations that vary in time and space due to satellite lifecycles, sensor failures, changes of observation modes, climate regimes, orbital overlaps, as well as inter-annual variability of cloud cover. However, the relationship between data availability and STM consistency between years is still poorly understood, especially as differences in STMs between years can both result from inter-annual variability in data availability, as well as inter-annual variability of land surfaces. In this study, we systematically quantify the effect of inter-annual data availability on annual STMs for the years 1984–2019, while completely controlling for inter-annual land surface changes. Our results are expected to help assess where on Earth, and in what periods, specific metrics can be used or should be avoided when multi-annual consistency is required. We synthesized a global, nearly gap-free reference time series at daily temporal resolution from MODIS data. This “baseline” was subsequently degraded with actual annual Landsat mission observation scenarios resulting in synthetic annual time series that only differ with respect to data availability. Based on the differences between STMs generated from the baseline, and STMs computed from the degraded time series, we statistically quantified the accuracy, precision, and uncertainty (APU) for various STMs across the Landsat spectral bands. We compared the performance against a reasonable specification, i.e., a tolerated error. We aggregated APU metrics along climate zones annually to carve out regional and temporal differences. We found that huge regional differences exist, with the highest quality and consistency in arid climates (i.e., APU within specification). Errors in fully humid snow climates are high, yet systematic (biased but repeatable), whereas equatorial and temperate climates are characterized by unbiased but uncertain metrics, where accuracy or precision and uncertainty can exceed specification by a factor of three or more. Quality generally increased with time as a response to improved observation modes and data storage commitment, e.g., uncertainty improved from one sensor availability period to the next in >90% of all climate zones for the near infrared average – with the exception of the Landsat 7 scanline corrector failure in 2003 where quality decreased again in 62% of climate zones. We also derived and tested different measures of STM quality and found that the seasonal distribution of clear-sky observations is more important than the number of observations, e.g., the near infrared standard deviation's accuracy can be explained with an R2 of 0.55, and 0.78 by the number of observations, and maximum time between subsequent observations in Cfb climates, respectively. Furthermore, our findings revealed how many observations, or how short the largest gap between consecutive observations must be to still produce reliable metrics (e.g., a maximum gaps of 42–45 days to obtain tolerated uncertainty of the near infrared average and standard deviation in Cfb climates), which has substantial implications for the design of downstream applications relying on multi-annual STM. This study provides the tools for a global and systematic assessment of inter-annual STM consistency while controlling for land-surface dynamics and thereby paves the way for a systematic error quantification in Level 3 products.

Optical images of the Earth at very high spatial resolutions (VHR, typically < 5 m) are seeing rapid growth in volumes over the past 5 years, due in part to the fast-expanding constellations of CubeSats. Special preprocessing of these VHR images is required to ensure their geometric and radiometric consistency for quantitative analyses for a wide range of Earth and environmental sciences and applications. Here we describe a hierarchical normalization framework (HiNF) to achieve and evaluate geometric and radiometric normalization of these VHR images towards producing analysis ready data (ARD) of optical CubeSat images. We demonstrated HiNF at a spatially heterogeneous and temporally dynamic wetland site in northeastern Germany by generating a stack of temporally consistent ~ biweekly 5-m images over 8 years (2013–2020) at visible and near infrared bands (VNIR). The HiNF combined images from rigorously calibrated multispectral sensors onboard large satellites (Landsat-7/8 and Sentinel-2) and less well calibrated sensors onboard RapidEye (SmallSats) and PlanetScope (CubeSats). A two-stage radiometric normalization procedure produced two levels of image normalization and resulted in more normalized images that passed the quality control in time series compared to common one-stage procedures. The outcome of this novel procedure allows for downstream applications to balance between the quality and the quantity of available normalized CubeSat images in a time series. The HiNF provides a new approach to quantitative evaluations of radiometric normalizations using daily MODIS imagery as bridging benchmark data. The quantitative evaluations showed the HiNF resulted in greater normalization efficacy in the visible bands than in the NIR over the predominantly wetland area. The two normalization levels yielded statistically similar efficacy for the NIR band and the widely-used normalized difference vegetation index according to the Chow test (at significance level of 0.05) but less so for the visible bands. The HiNF facilitates generating ARD of optical CubeSat images and assuring their qualities through its demonstrated efficacy and its quantitative evaluation approach. Such ARD-quality time series of VHR images from CubeSats allow for improved analyses and quantitative applications of this new stream of multispectral images at spatial scales that are better related to ground measurements and environmental management in terrestrial ecosystems.

Image Distortion Correction in fMRI: A Quantitative Evaluation

This paper presents a search engine system for sensor time series data and metadata in the context of building management. It takes natural language queries as input and retrieves sensor time series data, ranks them with respect to their relevance to a given query, and visualizes the results as graphs. In addition, the system allows users to interact with the search results: they can define events of interest in the visualized results and search across sensor data for time series with similar shape, i.e. the search by example scheme. We leverage both a feature based cosine similarity model and DTW to find similar time series and rank them by relevance. Our quantitative evaluations and user studies demonstrate the value of this system for managing building sensor data.

Remote sensing image super-resolution (SR) plays an important role by supplementing the lack of original high-resolution (HR) images in the study scenarios of large spatial areas or long time series. However, due to the lack of imagery information in low-resolution (LR) images, single-image super-resolution (SISR) is an inherently ill-posed problem. Especially, it is difficult to reconstruct the fine textures of HR images at large upscaling factors (e.g., four times). In this work, based on Google Earth HR images, we explore the potential of the reference-based super-resolution (RefSR) method on remote sensing images, utilizing rich texture information from HR reference (Ref) images to reconstruct the details in LR images. This method can use existing HR images to help reconstruct the LR images of long time series or a specific time. We build a reference-based remote sensing SR data set (RRSSRD). Furthermore, by adopting the generative adversarial network (GAN), we propose a novel end-to-end reference-based remote sensing GAN (RRSGAN) for SR. RRSGAN can extract the Ref features and align them to the LR features. Eventually, the texture information in the Ref features can be transferred to the reconstructed HR images. In contrast to the existing RefSR methods, we propose a gradient-assisted feature alignment method that adopts the deformable convolutions to align the Ref and LR features and a relevance attention module (RAM) to improve the robustness of the model in different scenarios (e.g., land cover changes and cloud coverage). The experimental results demonstrate that RRSGAN is robust and outperforms the state-of-the-art SISR and RefSR methods in both quantitative evaluation and visual results, which indicates the great potential of the RefSR method for remote sensing tasks. Our code and data are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/dongrunmin/RRSGAN</uri> .

After a natural disaster occurs, the production and sharing of damage reports are extremely important for a disaster response site. However, one of the problems is that the data shared by the damage reports cannot clearly indicate when the damage situation could be grasped because such data change day by day. Accordingly, in this study, the data of the damage reports of the Headquarters for Disaster Control are treated as unequally spaced time series data to evaluate the changing conditions of the data quantitatively. For this purpose, a case is examined for the Headquarters for Disaster Control of Fukuoka Prefecture at the time of the Northern Kyushu Heavy Rainfall event in July 2017. As a result of the examination, it is indicated that the quantitative evaluation would be possible for 1) analysis on timing when the data of the damage reports are updated, 2) analysis on the characteristics of time series of the report data, and 3) visualization of the progress of the damage report service.

Ad-hoc explanation for time series classification

The C-band Sentinel-1 satellite constellation enables the continuous monitoring of the Earth’s surface within short revisit times. Thus, it provides Synthetic Aperture Radar (SAR) time series data that can be used to detect changes over time regardless of daylight or weather conditions. Within this study, a time series classification approach is developed for the extraction of the flood extent with a focus on temporary flooded vegetation (TFV). This method is based on Sentinel-1 data, as well as auxiliary land cover information, and combines a pixel-based and an object-oriented approach. Multi-temporal characteristics and patterns are applied to generate novel times series features, which represent a basis for the developed approach. The method is tested on a study area in Namibia characterized by a large flood event in April 2017. Sentinel-1 times series were used for the period between September 2016 and July 2017. It is shown that the supplement of TFV areas to the temporary open water areas prevents the underestimation of the flood area, allowing the derivation of the entire flood extent. Furthermore, a quantitative evaluation of the generated flood mask was carried out using optical Sentinel-2 images, whereby it was shown that overall accuracy increased by 27% after the inclusion of the TFV.

As science and technology continue to advance, sci-tech journals are developing rapidly, and the quality of these journals affects the development and progress of particular subjects. Whether sci-tech journals can be evaluated and predicted comprehensively and dynamically from multiple angles based on the current qualitative and quantitative evaluations of sci-tech journals is related to a rational adjustment of journal resource allocation and development planning. In this study, we propose a time series analysis task for the comprehensive and dynamic evaluation of sci-tech journals, construct a multivariate short-time multi-series time series dataset that contains 18 journal evaluation metrics, and build models based on machine learning and deep learning methods commonly used in the field of time series analysis to carry out training and testing experiments on the dataset. We compare and analyze the experimental results to confirm the generalizability of these methods for the comprehensive dynamic evaluation of journals and find the LSTM model built on our dataset produced the best performance (MSE: 0.00037, MAE: 0.01238, accuracy based on 80% confidence: 72.442%), laying the foundation for subsequent research on this task. In addition, the dataset constructed in this study can support research on the co-analysis of multiple short time series in the field of time series analysis.

The authors propose a method for distinguishing chaos from random fractal sequences which have been difficult to discriminate from chaos. In the proposed method, the time series is predicted both in the forward direction and in the backward direction, and the accuracy of the two types of predictions is compared. They show, considering the time reversal symmetry of time series, that if the time series is chaotic and originates from a dissipative dynamical system, the accuracy is in general better for the forward prediction than for the backward prediction, whereas the accuracy is the same if the time series is a random fractal sequence. The method is also applicable to distinguishing between chaos and stationary noise. It is possible to give a quantitative evaluation of the distinction without a large amount of data or calculation.