Multivariate Spatiotemporal Data Research Articles

Modelling multivariate spatio-temporal data with identifiable variational autoencoders

Modelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are found, they can be modelled univariately. Blind source separation aims to recover the latent components by estimating the unknown linear or nonlinear unmixing transformation based on the observed data only. In this paper, we extend recently introduced identifiable variational autoencoder to the nonlinear nonstationary spatio-temporal blind source separation setting and demonstrate its performance using comprehensive simulation studies. Additionally, we introduce two alternative methods for the latent dimension estimation, which is a crucial task in order to obtain the correct latent representation. Finally, we illustrate the proposed methods using a meteorological application, where we estimate the latent dimension and the latent components, interpret the components, and show how nonstationarity can be accounted and prediction accuracy can be improved by using the proposed nonlinear blind source separation method as a preprocessing method.

Correction: Visual analytics of economic features for multivariate spatio-temporal GDP data

Correction: Visual analytics of economic features for multivariate spatio-temporal GDP data

Deep generation network for multivariate spatio-temporal data based on separated attention

The multivariate spatio-temporal data contains complex spatio-temporal background and channel coupling information. Effective extraction of these features is crucial for data generation. In this paper, a separated multiple attention network is proposed, which can capture the correlation of multiple types of variables in the same space-time, different spaces at the same time, and different times in the same space. Meanwhile, a new multiscale loss processing method based on homoscedasticity uncertainty and the assumption of gaussian loss distribution is proposed to balance the numerical scale of each channel loss in training. The experiment shows that our method has better performance and robustness than the classical machine learning model and higher computational efficiency than the physical model. It can generate multivariate intermittent spatial-temporal fields with a maximum lead time of 3 days and multivariate continuous spatial-temporal fields with a maximum lead time of 7 days.

Attention-Driven Active Sensing With Hybrid Neural Network for Environmental Field Mapping

In environmental monitoring programs, mobile robots have been widely deployed for remote sensing, with the end objective of monitoring and mapping out environmental fields. Complex characteristics and correlations in natural phenomena make it challenging to establish a reliable framework for mobile sensing and field mapping. Furthermore, constraints of onboard resources will limit the ability of mobile robots to cover a large area. This article focuses on the active sensing problem in environmental field mapping and particularly exploits the use of intrinsic interactions among multivariate spatiotemporal data. A novel deep neural network of a hybrid CNN-RNN model is employed to learn the monitored multivariate spatiotemporal field. Specifically, a set of attention mechanisms is designed and embedded in the network, which is able to adaptively capture parameterwise dependencies among the monitored heterogeneous parameters and spatial correlations in geolocations of a surveyed field. The weights of inferred attention facilitate explicit interpretation of the driving parameters and geolocations. Some subregions of interest in the surveyed field are specified by their spatial attention distribution and are actively sensed by following the proposed coverage path planner. Experiments are carried out using a real-world dataset with multisource environmental imagery from a remote sensing program. Experimental results are obtained, which demonstrate the superior mapping performance of the proposed systematical methodology compared to baseline methods. Furthermore, the proposed model is able to quantitatively reveal the driving monitored parameters and geolocations in a regression process. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the need for a practical and systematic approach for reconstruction and planning to execute robotic active sensing (AS) in environmental field mapping. Field robotic applications are not maneuverable in comparison with indoor scenarios due to severe conflict between the need for long execution endurance in the field and the very limited onboard resources. Traditional AS planners normally use statistical model-based informative metrics, which may lead to model misspecification in real-world phenomena. The developed framework in this article yields a novel attention-driven metric to guide AS and mapping. It relies on an attention-based hybrid neural network that reveals the driving variables in terms of the heterogeneities and complexities in a natural environment. The high-priority regions are maximized in a coverage path depending on the inferred spatial attention distribution while maintaining the travel cost of the sensing robots within an available energy budget. Experiments using a remote sensing dataset validate the reliable performance of the proposed framework, in environmental field mapping.

AirLens: Multi‐Level Visual Exploration of Air Quality Evolution in Urban Agglomerations

AbstractThe precise prevention and control of air pollution is a great challenge faced by environmental experts in recent years. Understanding the air quality evolution in the urban agglomeration is important for coordinated control of air pollution. However, the complex pollutant interactions between different cities lead to the collaborative evolution of air quality. The existing statistical and machine learning methods cannot well support the comprehensive analysis of the dynamic air quality evolution. In this study, we propose AirLens, an interactive visual analytics system that can help domain experts explore and understand the air quality evolution in the urban agglomeration from multiple levels and multiple aspects. To facilitate the cognition of the complex multivariate spatiotemporal data, we first propose a multi‐run clustering strategy with a novel glyph design for summarizing and understanding the typical pollutant patterns effectively. On this basis, the system supports the multi‐level exploration of air quality evolution, namely, the overall level, stage level and detail level. Frequent pattern mining, city community extraction and useful filters are integrated into the system for discovering significant information comprehensively. The case study and positive feedback from domain experts demonstrate the effectiveness and usability of AirLens.

Discovering optimally representative dynamical locations (ORDL) in big multivariate spatiotemporal data: A case study of precipitation in Australia from space to ground sensors

We develop a method for discovering a set of optimally representative dynamical locations (ORDL), a small subset of observed locations that are the most informative of the dynamics of a real complex system, as embodied in big spatiotemporal data. We achieve this through a two-pronged approach: (a) by reducing the multivariate time series data into a small set of time series with minimal loss of information on the dynamics of the system, (b) by exploiting the best that remote sensing and in-situ observations can offer. In the former, we extend the recently proposed empirical dynamical quantiles for univariate time series to multivariate data using a directional statistical depth measure and principal eigen-decomposition method. In the latter, we perform data fusion to leverage remotely sensed precipitation from multiple satellite platforms in addition to ground-based rain gauges to improve overall accuracy and spatial coverage. We demonstrate our method in the context of precipitation data over 2003–2021 for Australia. Of the six states, the location, ranking and number of ORDL suggest that Queensland has seen the most significant variability in precipitation while that in Victoria has remained relatively stable. Finally, this study has uncovered ungauged locations in data-sparse regions of Australia where the installation of future rain gauges can optimally represent precipitation dynamics in the region under a changing climate.

Rapid detection of hot-spots via tensor decomposition with applications to crime rate data

ABSTRACT In many real-world applications of monitoring multivariate spatio-temporal data that are non-stationary over time, one is often interested in detecting hot-spots with spatial sparsity and temporal consistency, instead of detecting system-wise changes as in traditional statistical process control (SPC) literature. In this paper, we propose an efficient method to detect hot-spots through tensor decomposition, and our method has three steps. First, we fit the observed data into a Smooth Sparse Decomposition Tensor (SSD-Tensor) model that serves as a dimension reduction and de-noising technique: it is an additive model decomposing the original data into: smooth but non-stationary global mean, sparse local anomalies, and random noises. Next, we estimate model parameters by the penalized framework that includes Least Absolute Shrinkage and Selection Operator (LASSO) and fused LASSO penalty. An efficient recursive optimization algorithm is developed based on Fast Iterative Shrinkage Thresholding Algorithm (FISTA). Finally, we apply a Cumulative Sum (CUSUM) Control Chart to monitor model residuals after removing global means, which helps to detect when and where hot-spots occur. To demonstrate the usefulness of our proposed SSD-Tensor method, we compare it with several other methods including scan statistics, LASSO-based, PCA-based, T2-based control chart in extensive numerical simulation studies and a real crime rate dataset.

Unsupervised Anomaly Detection in Multivariate Spatio-Temporal Data Using Deep Learning: Early Detection of COVID-19 Outbreak in Italy.

Unsupervised anomaly detection for spatio-temporal data has extensive use in a wide variety of applications such as earth science, traffic monitoring, fraud and disease outbreak detection. Most real-world time series data have a spatial dimension as an additional context which is often expressed in terms of coordinates of the region of interest (such as latitude - longitude information). However, existing techniques are limited to handle spatial and temporal contextual attributes in an integrated and meaningful way considering both spatial and temporal dependency between observations. In this paper, a hybrid deep learning framework is proposed to solve the unsupervised anomaly detection problem in multivariate spatio-temporal data. The proposed framework works with unlabeled data and no prior knowledge about anomalies are assumed. As a case study, we use the public COVID-19 data provided by the Italian Department of Civil Protection. Northern Italy regions’ COVID-19 data are used to train the framework; and then any abnormal trends or upswings in COVID-19 data of central and southern Italian regions are detected. The proposed framework detects early signals of the COVID-19 outbreak in test regions based on the reconstruction error. For performance comparison, we perform a detailed evaluation of 15 algorithms on the COVID-19 Italy dataset including the state-of-the-art deep learning architectures. Experimental results show that our framework shows significant improvement on unsupervised anomaly detection performance even in data scarce and high contamination ratio scenarios (where the ratio of anomalies in the data set is more than 5%). It achieves the earliest detection of COVID-19 outbreak and shows better performance on tracking the peaks of the COVID-19 pandemic in test regions. As the timeliness of detection is quite important in the fight against any outbreak, our framework provides useful insight to suppress the resurgence of local novel coronavirus outbreaks as early as possible.

Multivariate Pointwise Information-Driven Data Sampling and Visualization.

With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large-scale multivariate spatiotemporal data sets while preserving the important data properties so that the reduced data can answer domain-specific queries involving multiple variables with sufficient accuracy. While analyzing complex scientific events, domain experts often analyze and visualize two or more variables together to obtain a better understanding of the characteristics of the data features. Therefore, data summarization techniques are required to analyze multi-variable relationships in detail and then perform data reduction such that the important features involving multiple variables are preserved in the reduced data. To achieve this, in this work, we propose a data sub-sampling algorithm for performing statistical data summarization that leverages pointwise information theoretic measures to quantify the statistical association of data points considering multiple variables and generates a sub-sampled data that preserves the statistical association among multi-variables. Using such reduced sampled data, we show that multivariate feature query and analysis can be done effectively. The efficacy of the proposed multivariate association driven sampling algorithm is presented by applying it on several scientific data sets.

Multivariate Spatio-temporal Solar Generation Forecasting: A Unified Approach to Deal With Communication Failure and Invisible Sites

Short-term prediction of multivariate dynamical processes evolving over time when data are partially observable is a challenging task. The power from solar resources has reached grid parity and must be predicted based on real-time observations available up to the current time step to ensure efficient power systems operation. However, solar data in the form of a time series generated by a network of sensors are not always available. Invisi-ble solar sites and communication failure are two causes that leave the energy management data acquisition system with an incomplete solar time series, thus leading to inaccurate forecasts. This paper addresses the impact of partially observable measurements on short-term solar power prediction. We present a low-rank tensor learning scheme to predict six-hour-ahead solar power generation. We use actual multivariate spatio-temporal National Renewable Energy Laboratory solar data in the state of Kansas presented in the form of tensors along with a photovoltaic power conversion model. A design of experiments experimental framework has been proposed to evaluate single and joint effects of spatio-temporal partially observable sites and the regulating parameters on forecasting accuracy. Numerical results show the capability of the framework to uncover detailed insight into the forecasting model behavior.

Variable-Based Spatiotemporal Trajectory Data Visualization Illustrated

As a frontier research topic in the field of scientific visualization, trajectory data visualization extracts valuable patterns and knowledge from trajectory data for decision support via spatiotemporal trajectory visualization techniques. We propose the concept of multivariate trajectory data and interpret two categories of attributes that are based on geographical space and abstract space. Properly analyzing multivariate trajectory data depends on many factors such as visualization task and data sparsity. Therefore, we generalize rich interactions to explore the evolution of trajectory events and transform the issue into a more intelligibly perceptual task, which derives our discussion regarding advantages and limitations of the analytical methods. This review endeavors to provide a quick and thorough cognition and comprehension with regard to fundamental features and numerous outcomes in visual analytics for trajectory data, seeks to promote comparisons and criticisms about the descriptive framework for multivariate spatiotemporal trajectory data visualization, and aims to encourage the exploration of emerging methods and techniques.

Low-quality multivariate spatio-temporal serial data preprocessing

As the accumulation of spatio-temporal data, the low-quality problems of multivariate spatio-temporal data become clear and mainly present that numerous missing data, high noise of time series and great different spatial scale of spatiotemporal data. Aimed at the low-quality problems of multivariate spatio-temporal series, we propose three methods to process them, firstly, using improved non-local means (NLM) algorithm and nonlinear regression analysis method to achieve incomplete data imputation; secondly, using NLM algorithm to deal with Gaussian white noise in time series; thirdly, using the Gaussian pyramid method to zoom the spatial scale for multivariate spatial data. Besides, we compare with traditional methods using quantitative evaluation indices to measure the performance, including K-nearest and wavelet threshold. The experimental simulations indicate that the interpolating accuracy of the two proposed algorithms are higher than K-nearest neighbor algorithm and the effect of denoising using NLM algorithm is obviously better than wavelet threshold method. The experiment results further indicate that the Gaussian pyramid method effectively achieves spatial scale transformation of multivariate spatial data and keeps the local detail characteristics of spatial data with better visual expression effect.

Visual analytics of economic features for multivariate spatio-temporal GDP data

Many prevalent visualization packages can be used to visualize the GDP data from different perspectives. However, it is difficult to integrate these visualizations and provide a comprehensive analysis to assist users get deeper insights into the various economic features of GDP data, due to its spatio-temporal and multidimensional attributes. In this paper, we propose a visualization tool for the analysis of spatio-temporal multidimensional GDP data, aiming at the combination of the extraction of economic clusters in a time period and the track of dynamic feature evolutions across time periods. MDS is first employed to reduce the multiple dimensions of GDP data, in which the attributes used to achieve similarity matrix are selected interactively by users, according to their requirements. The 2D coordinates obtained by MDS are further clustered based on a hierarchical clustering scheme, allowing the analysts to visually capture the economic features of interest in a time period. We also design a temporal visualization to visually present the dynamic changes of clusters, which largely helps users track the various evolutions of economic features. In addition, stability is defined to evaluate the disorder of clusters between adjacent time periods and used to map meaningful colors to different glyphs in the visualizations. A rich set of interactions are further provided to help users highlight and explore economic features of interest. We demonstrate the usefulness of our system in two case studies based on a real-world GDP data of China.

Dynamic Network Model for Smart City Data-Loss Resilience Case Study: City-to-City Network for Crime Analytics.

Today's cities generate tremendous amounts of data, thanks to a boom in affordable smart devices and sensors. The resulting big data creates opportunities to develop diverse sets of context-aware services and systems, ensuring smart city services are optimized to the dynamic city environment. Critical resources in these smart cities will be more rapidly deployed to regions in need, and those regions predicted to have an imminent or prospective need. For example, crime data analytics may be used to optimize the distribution of police, medical, and emergency services. However, as smart city services become dependent on data, they also become susceptible to disruptions in data streams, such as data loss due to signal quality reduction or due to power loss during data collection. This paper presents a dynamic network model for improving service resilience to data loss. The network model identifies statistically significant shared temporal trends across multivariate spatiotemporal data streams and utilizes these trends to improve data prediction performance in the case of data loss. Dynamics also allow the system to respond to changes in the data streams such as the loss or addition of new information flows. The network model is demonstrated by city-based crime rates reported in Montgomery County, MD, USA. A resilient network is developed utilizing shared temporal trends between cities to provide improved crime rate prediction and robustness to data loss, compared with the use of single city-based auto-regression. A maximum improvement in performance of 7.8% for Silver Spring is found and an average improvement of 5.6% among cities with high crime rates. The model also correctly identifies all the optimal network connections, according to prediction error minimization. City-to-city distance is designated as a predictor of shared temporal trends in crime and weather is shown to be a strong predictor of crime in Montgomery County.

Multivariate spatio-temporal models for high-dimensional areal data with application to Longitudinal Employer-Household Dynamics

Many data sources report related variables of interest that are also referenced over geographic regions and time; however, there are relatively few general statistical methods that one can readily use that incorporate these multivariate spatio-temporal dependencies. Additionally, many multivariate spatio-temporal areal data sets are extremely high dimensional, which leads to practical issues when formulating statistical models. For example, we analyze Quarterly Workforce Indicators (QWI) published by the US Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) program. QWIs are available by different variables, regions, and time points, resulting in millions of tabulations. Despite their already expansive coverage, by adopting a fully Bayesian framework, the scope of the QWIs can be extended to provide estimates of missing values along with associated measures of uncertainty. Motivated by the LEHD, and other applications in federal statistics, we introduce the multivariate spatio-temporal mixed effects model (MSTM), which can be used to efficiently model high-dimensional multivariate spatio-temporal areal data sets. The proposed MSTM extends the notion of Moran's I basis functions to the multivariate spatio-temporal setting. This extension leads to several methodological contributions, including extremely effective dimension reduction, a dynamic linear model for multivariate spatio-temporal areal processes, and the reduction of a high-dimensional parameter space using a novel parameter model.

A method for discovery and analysis of temporal patterns in complex event data

Pattern analysis techniques currently common within geography tend to focus either on characterizing patterns of spatial and/or temporal recurrence of a single event type (e.g., incidence of flu cases) or on comparing sequences of a limited number of event types where relationships between events are already represented in the data (e.g., movement patterns). The availability of large amounts of multivariate spatiotemporal data, however, requires new methods for pattern analysis. Here, we present a technique for finding associations among many different event types where the associations among these varying event types are not explicitly represented in the data or known in advance. This pattern discovery method, known as T-pattern analysis, was first developed within the field of psychology for the purpose of finding patterns in personal interactions. We have adapted and extended the T-pattern method to take the unique characteristics of geographic data into account and implemented it within a geovisualization toolkit for an integrated computational-geovisual environment we call STempo. To demonstrate how T-pattern analysis can be employed in geographic research for discovering patterns in complex spatiotemporal data, we describe a case study featuring events from news reports about Yemen during the Arab Spring of 2011–2012. Using supplementary data from the Global Database of Events, Language, and Tone, we briefly summarize and reference a separate validation study, then evaluate the scalability of the T-pattern approach. We conclude with ideas for further extensions of the T-pattern technique to increase its utility for spatiotemporal analysis.

Effects of visualizing uncertainty on decision-making in a target identification scenario

This paper presents an empirical study that addresses the effects the visualization of uncertainty has on decision-making. We focus our investigations on an area where uncertainty plays an important role and the decision time is limited. For that, we selected an air defense scenario, where expert operators have a few minutes to make a well-informed decision based on uncertain sensor data regarding the identity of an object and where the consequences of a late or wrong decision are severe.An approach for uncertainty visualization is proposed and tested using a prototype that supports the interactive analysis of multivariate spatio-temporal sensor data. The uncertainty visualization embeds the accuracy of the sensor data values using the thickness of the lines in the graphical representation of the sensor values. Semi-transparent filled circles represent the uncertain position, while a track quality value between 0 and 1 accounts for the quality of the estimated track for each target. Twenty-two experienced air traffic operators were divided into two groups (with and without uncertainty visualization) and carried out identification and prioritization tasks using the prototype. The results show that the group aided by visualizations of uncertainty needed significantly fewer attempts to make a final identification, and a significant difference between the groups when considering the identities and priorities assigned was observed (participants with uncertainty visualization selected higher priority values and more hostile and suspect identities). These results may show that experts put themselves in the “worst-case scenario” in the presence of uncertainty when safety is an issue. Additionally, the presentation of uncertainty neither increased the participants׳ expressed workload, nor the time needed to make a classification. However, the inclusion of the uncertainty information did not have a significant effect on the performance (true positives, false negatives and false positives) or the participants׳ expressed confidence in their decisions.

Using Simultaneous Diagonalization to Identify a Space–Time Linear Coregionalization Model

Although there are multiple methods for modeling matrix covariance functions and matrix variograms in the geostatistical literature, the linear coregionalization model is still widely used. In particular it is easy to check to ensure whether the matrix covariance function is positive definite or that the matrix variogram is conditionally negative definite. One of the difficulties in using a linear coregionalization model is in determining the number of basic structures and the corresponding covariance functions or variograms. In this paper, a new procedure is given for identifying the basic structures of the space–time linear coregionalization model and modeling the matrix variogram. This procedure is based on the near simultaneous diagonalization of the sample matrix variograms computed for a set of spatiotemporal lags. A case study using a multivariate spatiotemporal data set provided by the Environmental Protection Agency of Lombardy, Italy, illustrates how nearly simultaneous diagonalization of the empirical matrix variograms simplifies modeling of the matrix variograms. The new methodology is compared with a previous one by analyzing various indices and statistics.

Testing the covariance structure of multivariate random fields

There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.

Using treemaps for variable selection in spatio-temporal visualisation

We demonstrate and reflect upon the use of enhanced treemaps that incorporate spatial and temporal ordering for exploring a large multivariate spatio-temporal data set. The resulting data-dense views summarise and simultaneously present hundreds of space-, time-, and variable-constrained subsets of a large multivariate data set in a structure that facilitates their meaningful comparison and supports visual analysis. Interactive techniques allow localised patterns to be explored and subsets of interest selected and compared with the spatial aggregate. Spatial variation is considered through interactive raster maps and high-resolution local road maps. The techniques are developed in the context of 42.2 million records of vehicular activity in a 98 km2 area of central London and informally evaluated through a design used in the exploratory visualisation of this data set. The main advantages of our technique are the means to simultaneously display hundreds of summaries of the data and to interactively browse hundreds of variable combinations with ordering and symbolism that are consistent and appropriate for space- and time-based variables. These capabilities are difficult to achieve in the case of spatio-temporal data with categorical attributes using existing geovisualisation methods. We acknowledge limitations in the treemap representation but enhance the cognitive plausibility of this popular layout through our two-dimensional ordering algorithm and interactions. Patterns that are expected (e.g. more traffic in central London), interesting (e.g. the spatial and temporal distribution of particular vehicle types) and anomalous (e.g. low speeds on particular road sections) are detected at various scales and locations using the approach. In many cases, anomalies identify biases that may have implications for future use of the data set for analyses and applications. Ordered treemaps appear to have potential as interactive interfaces for variable selection in spatio-temporal visualisation.