A generic test for the similarity of spatial data

This chapter introduces exploratory data analysis (EDA) and visualization techniques for spatial data in S-Plus and S+SpatialStats. EDA involves methods of describing data and its structure in order to formulate hypotheses and check the validity of assumptions. In general, we will be concerned with the distribution of data and violations of local and global stationarity (as defined in chapter 1)—including trends and outliers. Although a researcher uses EDA techniques throughout spatial analysis and modeling, this chapter focuses on initial explorations—before analysis has been attempted. Analysis techniques for specific types of spatial data — geostatistical data, lattice data, and spatial point patterns, will be discussed in chapters 4, 5, and 6.

Continuous technological growth and the corresponding environmental implications are triggering the enhancement of advanced environmental monitoring solutions, such as remote sensing. In this paper, we propose a new method for the spatial point patterns generation by classifying remote sensing images using convolutional neural network. To increase the accuracy, the training samples are extended by the suggested data augmentation scheme based on the similarities of images within the same part of the landscape for a limited observation time. The image patches are classified in accordance with the labels of previously classified images of the manually prepared training and test samples. This approach has improved the accuracy of image classification by 7% compared to current best practices of data augmentation. A set of image patch centers of a particular class is considered as a random point configuration, while the class labels are used as marks for every point. A marked point pattern is regarded as a combination of several subpoint patterns with the same qualitative marks. We analyze the bivariate point pattern to identify the relationships between points of different types using the features of a marked random point pattern.

Many geographical applications have to deal with spatial objects that reveal an intrinsically vague or fuzzy nature. A spatial object is fuzzy if locations exist that cannot be assigned completely to the object or to its complement. Spatial database systems and Geographical Information Systems are currently unable to cope with this kind of data. Based on an available abstract data model of fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions, this paper proposes the Spatial Plateau Algebra that provides spatial plateau data types as an executable type system for fuzzy spatial data types. Each spatial plateau object consists of a finite number of crisp counterparts that are all adjacent or disjoint to each other, are associated with different membership values, and hence form different plateaus. The formal framework and the implementation are based on well known, exact models and available implementations of crisp spatial data types. Spatial plateau set and metric operations as well as spatial plateau topological predicates on spatial plateau objects are expressed as a combination of geometric methods on the underlying crisp spatial objects. This paper offers a conceptually clean specification for implementing a database extension for fuzzy spatial objects and their operations and predicates. Further, we demonstrate the embedding of these new data types as attribute data types in a database schema as well as the incorporation of fuzzy spatial operations and predicates into a database query language.

Analysis of massive marked point patterns with stochastic partial differential equations

The longitude, latitude and depth of the hypocenter in 3-D space and the date and time of rupture makes an earthquake a “point” in a spatio-temporal point pattern, observed over a region and months, years or decades. The magnitude of earthquakes marks the point pattern, as would hypocenter depth do if only the longitude and latitude of epicenters were used for location in 2-D space. Stochastic declustering, based on a space–time ETAS model (ETAS: epidemic-type aftershock sequence), is a procedure that can be applied in the preliminary stage of an earthquake catalog data analysis. Stochastic declustering procedures have underlying assumptions, such as the time independence of the background intensity function whether the spatial framework is 2-D or 3-D, and a separate treatment of hypocenter depth from longitude and latitude when the spatial framework is 3-D. Cyclical processes in the Earth, including tides and seasonal surface water loads, can introduce periodic behavior in earthquake occurrence and related variables. The effects of ETAS-based 2-D and 3-D declustering on the outcome of periodicity analyses performed from the resulting earthquake data catalogs are studied. The research objectives and statistical challenges include the detection of periodicities for hypocenter depth in addition to monthly earthquake number, and the risk of missing observations for hypocenter depth when the monthly earthquake number after declustering is zero. A version of the method of multi-frequential periodogram analysis (MFPA) that allows for missing observations in the input temporal series is presented in detail, and applied to hypocenter depth (monthly mean and median) for central and northern California from January 2006 to December 2014. The results obtained for the 2-D and 3-D declustered catalogs are compared with those for the original catalog for this region. A semiannual periodicity in hypocenter depth is detected for the original and 2-D declustered catalogs, and fitted with the goal of relating it to periodicities found in the time series of monthly earthquake numbers. Using these results for central and northern California earthquakes, some of the assumptions on the intensity function of the spatio-temporal point process in stochastic declustering are discussed and future research perspectives are proposed.

The mammalian plasma membrane is known to contain domains with varying lipid composition and biophysical properties. However, studying these membrane lipid domains presents challenges due to their predicted morphological similarity to the bulk membrane and their scale being below the classical resolution limit of optical microscopy. To address this, we combine the solvatochromic probe di-4-ANEPPDHQ, which reports on its biophysical environment through changes in its fluorescence emission, with spectrally resolved single-molecule localisation microscopy. The resulting data comprises nanometre-precision localisation coordinates and a generalised polarisation value related to the probe’s environment – a marked point pattern. We introduce quantification algorithms based on topological data analysis (PLASMA) to detect and map nano-domains in this marked data, demonstrating their effectiveness in both artificial membranes and live cells. By leveraging environmentally sensitive fluorophores, multi-modal single molecule localisation microscopy, and advanced analysis methods, we achieve nanometre scale mapping of membrane properties and assess changes in response to external perturbation with methyl-β-cyclodextrin. This integrated methodology represents an integrated toolset for investigating marked point pattern data at nanometre spatial scales.

Machine Learning Classification of Spatial Patterns of Malignant Cells Reveals Implications in Prognosis and Tumor Microenvironment Composition in Lymphoma

Introduction to this special issue on Geostatistics and Geospatial Techniques in Remote Sensing

An increasing number of database management systems are expanding their functionality to work with various types of spatial data. This is true for both relational and NoSQL data models. The article describes the main features of those data models for which the functions of storing and processing spatial data are implemented. A comparative analysis of the performance of typical spatial queries for database management systems based on various data models, including multi-model ones, is carried out. The dataset on which the comparison is performed is presented in the form of three blocks of OpenStreetMap vector data for the territory of the Novosibirsk region. Based on the results of the study, recommendations are made on the use of certain data models, depending on the available data and the tasks to be solved.

Cox processes are natural models for point process phenomena that are environmentally driven, but much less natural for phenomena driven primarily by interactions amongst the points. The class of log-Gaussian Cox processes (LGCPs) has an elegant simplicity, and one of its attractive features is the tractability of the multivariate normal distribution carries over, to some extent, to the associated Cox process. In the statistical analysis of spatial point patterns, it is often assumed isotropy because of a simpler interpretation and ease of analysis. However, there are many cases in which the spatial structure depends on the direction. In this paper, we introduce new families of anisotropic spatial LGCPs that are useful to model spatial anisotropic point patterns that exhibit a degree of clustering. We propose classes of families consisting of elliptical and non-elliptical models. The former can be reduced to isotropic forms after some rotations, while the latter family goes beyond this property. We derive analytical forms for the covariance of the associated random field, and some second-order characteristics. A moment-based estimation procedure is followed to make inference on the parameters that control the degree of anisotropy. The estimation procedure is evaluated through a simulation study under a variety of scenarios and various degrees of anisotropy. Our methodology is illustrated on two real datasets of earthquakes in South America and the Mediterranean Europe.

Temporal and spatial variability of stream waters in Wales, the Welsh borders and part of the West Midlands, UK — 1. Major ion concentrations

The statistical analysis of spatial data is usually done under Gaussian assumption for the underlying random field model. When this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. One of the crucial problems in this setting is specifying the block sizes. In this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the variance of sample mean for spatial lattice data, using minimization of asymptotic mean square error of the estimator. Further, an empirical method has been proposed to determine the optimal block size. Also the optimality of the empirical estimate of block size has been considered numerically in a simulation study.

A method for recording and playing back spatial sound data associated with an object in a scene of a virtual environment from the perspective of a character controlled by a user. Different types of spatial sound data can be encoded for different types of objects, e.g., fast moving, directional, slow moving and stationary objects. Based on at least the position, distance, and direction of the object in regard to the character, at least two channels of an audio file can be recorded with spatial sound data for subsequent playback in the virtual environment.

As the “third pole” of the world, the Qinghai-Tibet Plateau (QTP) is extremely ecologically sensitive and fragile while facing increasing human activities and overgrazing. In this study, livestock data from the statistical yearbook were transformed to 1 km grazing intensity raster data by integrating the net primary productivity (NPP) data for 1990, 1995, 2000, 2005, 2010 and 2015. Further, the human activity intensity (HAI) data at 1 km resolution were evaluated by the entropy weight method, which applied eight types of spatial data, including grazing intensity, Night-Time Light, population density, Gross Domestic Product (GDP) density, the ratio of cultivated land, distance to road, distance to town, and the slope of the Normalized Difference Vegetation Index (NDVI). Also, the five-year interval human activity intensity data from 1990 to 2015 were made on the QTP. By preparing the historical spatial datasets of grazing intensity and human activity intensity, our study will help to explore the influence of human disturbance on the alpine ecosystems on the QTP and provide effective support for decision-making of government aiming at regional ecosystem management and sustainable development.

In the Qinghai-Tibet Plateau (QTP); where the ecological system is fragile and sensitive; the increasing human activities have led to a series of ecological and environmental issues and social controversies and aroused much attention in the recent years; especially the construction and operation of the Qinghai-Tibet Railway. The preparation of spatial dataset of human activity intensity is critical to analyze the impact of human activities on the alpine ecosystem of the QTP. Furthermore; it is also very important for regulating human activities and regional sustainable development. In this paper; the human footprint index method was conducted to evaluate the intensity of human activity on QTP; which using six types of spatial data as agents of human activities; including population density; land use; grazing density; night lighting; railway and road. The spatial datasets of human activity intensity were prepared in 1990; 1995; 2000; 2005; 2010 and 2015.