Geostatistical Analysis

Geostatistical techniques involve the application of statistical methods to spatially distributed data in order to analyze and model the spatial variability of phenomena. These methods utilize the principles of both statistics and geography to explore patterns, trends, and relationships within spatial datasets.


Spatial autocorrelation examines the presence of spatial patterns and relationships, determining whether nearby locations tend to have similar or dissimilar values. Additionally, spatial interpolation methods, such as inverse distance weighting or spline interpolation, are employed to estimate values at unsampled locations based on the values of surrounding sampled points.


Key geostatistical techniques include kriging, variogram analysis, spatial autocorrelation, and spatial interpolation (ordinary, simple, universal, indicator, probability, disjunctive, and empirical Bayesian), 


Generating a continuous surface used to represent a particular attribute is a key capability required in most geographic information system (GIS) applications.  


Having explored the data, you can then create a variety of output map types using many variants of kriging and cokriging algorithms and associated tools (for example, data transformation, declustering, and detrending).


These techniques find applications in diverse fields such as environmental science, radiation leaking from a nuclear power plant, an oil spill, or elevation heights, geology, agriculture, and urban planning, providing valuable insights into spatial patterns and assisting in decision-making processes related to resource management, risk assessment, and environmental monitoring.


​Heatmap

Volttus Geospatial offers the possibility of visualizing a heatmap using certain point layers to determine hot zones or areas with a high concentration of features.

A heatmap is a two-dimensional representation of data in which various values are represented by colors. A simple heatmap provides an immediate visual summary of information across two axes, allowing users to quickly grasp the most important or relevant data points.

This method is helpful because it can provide an efficient and comprehensive overview of a topic at-a-glance. Unlike charts or tables, which have to be interpreted or studied to be understood, heatmaps are direct data visualization tools that are more self-explanatory and easy to read.

An interactive map is shown with a heatmap over the weather stations in Canada using the Kernel density estimate (KDE) which can be represented in the form of 2D density graphs or density plots.

Spatial Clustering

Spatial clustering refers to the identification and grouping of spatially proximate data points or regions that exhibit similar characteristics or patterns. This technique plays a crucial role in spatial data analysis and pattern recognition, aiming to uncover inherent structures and relationships within geographic datasets.


One commonly used method for spatial clustering is the K-means clustering algorithm, which partitions the spatial domain into distinct clusters based on the similarity of data points. Another approach is DBSCAN (Density-Based Spatial Clustering of Applications with Noise), which identifies clusters based on density and is particularly effective in detecting clusters of arbitrary shapes.


Spatial clustering finds applications in various fields, including geography, ecology, epidemiology, and urban planning. It assists in revealing spatial trends, identifying hotspots, and understanding the distribution of phenomena across geographical space. By grouping spatial entities with similar characteristics, spatial clustering facilitates insights into regional patterns and supports decision-making processes in areas such as resource allocation, urban development, and environmental management


SPATIAL INTERPOLATIONS

​Inverse distance weighting(IDW) 

Inverse Distance Weighting (IDW) is a spatial interpolation technique commonly used in geographic information systems (GIS) and spatial analysis. It operates on the principle that values at unmeasured locations can be estimated based on the proximity and influence of surrounding measured locations. IDW assumes that closer points have a more significant impact on the estimation than those farther away.


The method assigns weights to neighboring data points inversely proportional to their distance from the target location. This means that closer points have higher weights, reflecting their stronger influence on the interpolated value.

IDW is versatile and widely used in environmental modeling, terrain analysis, and other spatial applications. However, it has some limitations, such as sensitivity to outliers and a tendency to oversmooth surfaces. Despite these considerations, IDW remains a valuable tool for spatial interpolation, providing a straightforward and intuitive approach to estimate values at unsampled locations within a spatial dataset.

The interactive map shows the temperature interpolation of Canadian weather stations using the IDW method.


Kriging

​Krigingis an advanced geostatistical procedure that follows the theory of regional change. It considers spatial variation to be statistically consistent across the surface of the region.

The basic principle of Kriging interpolation is to assume that the spatial variation of an attribute is neither completely random nor completely determined but is codetermined by spatial autocorrelation factors, offsets, and random error.

Kriging is considered to be the best unbiased linear interpolation method. 

The interactive map shows the temperature interpolation of Canadian weather stations using the Kriging method

Nearest Neighbor spatial Interpolation

The k-nearest neighbors algorithm (k-NN), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values.

In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It is used for classification and regression. In both cases, the input consists of the k closest training examples in a data set. The output depends on whether k-NN is used for classification or regression.

   

In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small).

Both for classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that the nearer neighbors contribute more to the average than the more distant ones. For example, a common weighting scheme consists in giving each neighbor a weight of 1/d, where d is the distance to the neighbor.

The interactive map shows the temperature interpolation of Canadian weather stations using the k-NN method