A spatiotemporal ensemble machine learning framework for generating land use / land cover time-series maps for Europe (2000 – 2019) based on LUCAS, CORINE and GLAD Landsat

A seamless spatiotemporal machine learning framework for automated prediction, uncertainty assessment, and analysis of long-term LULC dynamics is presented. The framework includes: (1) harmonization and preprocessing of high-resolution spatial and spatiotemporal input datasets (GLAD Landsat, NPP/VIIRS) including 5~million harmonized LUCAS and CORINE Land Cover-derived training samples, (2) model building based on spatial k-fold cross-validation and hyper-parameter optimization, (3) prediction of the most probable class, class probabilities and uncertainty per pixel, (4) LULC change analysis on time-series of produced maps. The spatiotemporal ensemble model consists of a random forest, gradient boosted tree classifier, and a artificial neural network, with a logistic regressor as meta-learner. The results show that the most important variables for mapping LULC in Europe are: seasonal aggregates of Landsat green and near-infrared bands, multiple Landsat-derived spectral indices, long-term surface water probability, and elevation. Spatial cross-validation of the model indicates consistent performance across multiple years with overall accuracy (weighted F1-score) of 0.49, 0.63, and 0.83 when predicting 44 (level-3), 14 (level-2), and 5 classes (level-1). The spatiotemporal model outperforms spatial models on known-year classification by 2.7% and unknown-year classification by 3.5%. Results of the accuracy assessment using 48,365 independent test samples shows 87% match with the validation points. Results of time-series analysis (time-series of LULC probabilities and NDVI images) suggest forest loss in large parts of Sweden, the Alps, and Scotland. An advantage of using spatiotemporal ML is that the fitted model can be used to predict LULC in years that were not included in its training dataset, allowing generalization to past and future periods, e.g. to predict land cover for years prior to 2000 and beyond 2020. The generated land cover time-series data stack (ODSE-LULC), including the training points, is publicly available via the Open Data Science (ODS)-Europe Viewer. Functions used to prepare data and run modeling are available via the eumap library for python.

Statistical analysis of random walks on network

This paper describes an investigation of analytical formulas for parameters in random walks. Random walks are used to model situations in which an object moves in a sequence of steps in randomly chosen directions. Given a graph and a starting point, we select a neighbor of it at random, and move to this neighbor; then we select a neighbor of this point at random, and move to it etc. It is a fundamental dynamic process that arise in many models in mathematics, physics, informatics and can be used to model random processes inherent to many important applications. Different aspects of the theory of random walks on graphs are surveyed. In particular, estimates on the important parameters of hitting time, commute time, cover time are discussed in various works. In some papers, authors have derived an analytical expression for the distribution of the cover time for a random walk over an arbitrary graph that was tested for small values of n. However, this work will show the simplified analytical expressions for distribution of hitting time, commute time, cover time for bigger values of n. Moreover, this work will present the probability mass function and the cumulative distribution function for hitting time, commute time.

Time Series Analysis of Climatic Variables in Peninsular Spain. Trends and Forecasting Models for Data between 20th and 21st Centuries

Time series of mean monthly temperature and total monthly precipitation are two of the climatic variables most easily obtained from weather station records. There are many studies analyzing historical series of these variables, particularly in the Spanish territory. In this study, the series of these two variables in 47 stations of the provincial capitals of mainland Spain were analyzed. The series cover time periods from the 1940s to 2013; the studies reviewed in mainland Spain go up to 2008. ARIMA models were used to represent their variation. In the preliminary phase of description and identification of the model, a study to detect possible trends in the series was carried out in an isolated manner. Significant trends were found in 15 of the temperature series, and there were trends in precipitation in only five of them. The results obtained for the trends are discussed with reference to those of other, more detailed studies in the different regions, confirming whether the same trend was maintained over time. With the ARIMA models obtained, 12-month predictions were made by measuring errors with the observed data. More than 50% of the series of both were modeled. Predictions with these models could be useful in different aspects of seasonal job planning, such as wildfires, pests and diseases, and agricultural crops.

The power of two choices for random walks

We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the controller to significantly accelerate the hitting and cover times in several natural graph classes. In particular, we show that the cover time becomes linear in the number n of vertices on discrete tori and bounded degree trees, of order $${\mathcal O}(n\log \log n)$$ on bounded degree expanders, and of order $${\mathcal O}(n{(\log \log n)^2})$$ on the Erdős–Rényi random graph in a certain sparsely connected regime. We also consider the algorithmic question of computing an optimal strategy and prove a dichotomy in efficiency between computing strategies for hitting and cover times.

A spatiotemporal ensemble machine learning framework for generating land use / land cover time-series maps for Europe (2000 – 2019) based on LUCAS, CORINE and GLAD Landsat

A seamless spatiotemporal machine learning framework for automated prediction, uncertainty assessment, and analysis of land use / land cover (LULC) dynamics is presented. The framework includes: (1) harmonization and preprocessing of high-resolution spatial and spatiotemporal covariate datasets (GLAD Landsat, NPP/VIIRS) including 5 million harmonized LUCAS and CORINE Land Cover-derived training samples, (2) model building based on spatial k-fold cross-validation and hyper-parameter optimization, (3) prediction of the most probable class, class probabilities and uncertainty per pixel, (4) LULC change analysis on time-series of produced maps. The spatiotemporal ensemble model was fitted by combining random forest, gradient boosted trees, and artificial neural network, with logistic regressor as meta-learner. The results show that the most important covariates for mapping LULC in Europe are: seasonal aggregates of Landsat green and near-infrared bands, multiple Landsat-derived spectral indices, and elevation. Spatial cross-validation of the model indicates consistent performance across multiple years with 62%, 70%, and 87% accuracy when predicting 33 (level-3), 14 (level-2), and 5 classes (level-1); with artificial surface classes such as 'airports' and 'railroads' showing the lowest match with validation points. The spatiotemporal model outperforms spatial models on known-year classification by 2.7% and unknown-year classification by 3.5%. Results of the accuracy assessment using 48,365 independent test samples shows 87% match with the validation points. Results of time-series analysis (time-series of LULC probabilities and NDVI images) suggest gradual deforestation trends in large parts of Sweden, the Alps, and Scotland. An advantage of using spatiotemporal ML is that the fitted model can be used to predict LULC in years that were not included in its training dataset, allowing generalization to past and future periods, e.g. to predict land cover for years prior to 2000 and beyond 2020. The generated land cover time-series data stack (ODSE-LULC), including the training points, is publicly available via the Open Data Science (ODS)-Europe Viewer.

THE NEAREST UNVISITED VERTEX WALK ON RANDOM GRAPHS

We revisit an old topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and ball-covering (metric entropy) measures. For some familiar models of random graphs, this connection allows the order of magnitude of the cover time to be deduced from first passage percolation estimates. Establishing sharper results seems a challenging problem.