Analytics and Modeling

This knowledge area embodies a variety of data driven analytics, geocomputational methods, simulation and model driven approaches designed to study complex spatial-temporal problems, develop insights into characteristics of geospatial data sets, create and test geospatial process models, and construct knowledge of the behavior of geographically-explicit and dynamic processes and their patterns.

Topics in this Knowledge Area are listed thematically below. Existing topics are in regular font and linked directly to their original entries (published in 2006; these contain only Learning Objectives). Entries that have been updated and expanded are in bold. Forthcoming, future topics are italicized. 

 

Methodological Context Surface & Field Analyses Space-Time Analysis & Modeling
Geospatial Analysis & Model Building Modeling Surfaces Time Geography
Changing Context of GIScience Gridding, Interpolation, and Contouring Capturing Spatio-Temporal Dynamics in Computational Modeling 
Building Blocks Inverse Distance Weighting GIS-Based Computational Modeling
Overlay & Combination Operations Radial Basis & Spline Functions Computational Movement Analysis
Areal Interpolation Polynomial Functions Volumes and Space-Time Volumes
Aggregation of Spatial Entities Kriging Interpolation  
Classification & Clustering LiDAR Point Cloud Analysis Geocomputational Methods & Models
Boundaries & Zone Membership Intervisibility, Line-of-Sight, and Viewsheds Cellular Automata
Spatial Queries Digital Elevation Models & Terrain Metrics Agent-based Modeling
Buffers TIN-based Models and Terrain Metrics Simulation Modeling
Grid Operations & Map Algebra Watersheds & Drainage Artificial Neural Networks
Data Exploration & Spatial Statistics 3D Parametric Surfaces Genetic Algorithms & Evolutionary Computing 
Spatial Statistics Network & Location Analysis Big Data & Geospatial Analysis
Spatial Sampling for Spatial Analysis Intro to Network & Location Analysis Problems & with Large Spatial Databases
Exploratory Spatial Data Analysis (ESDA) Location & Service Area Problems Pattern Recognition & Matching
Point Pattern Analysis Network Route & Tour Problems Artificial Intelligence Approaches
Kernels & Density Estimation Modelling Accessibility Intro to Spatial Data Mining
Spatial Interaction Location-allocation Modeling Rule Learning for Spatial Data Mining
Cartographic Modeling The Classic Transportation Problem Machine Learning Approaches
Multi-criteria Evaluation   CyberGIS and Cyberinfrastructure
Grid-based Statistics and Metrics   Analysis of Errors & Uncertainty
Landscape Metrics   Error-based Uncertainty
Hot-spot and Cluster Analysis   Conceptual Models of Error & Uncertainty
Global Measures of Spatial Association   Spatial Data Uncertainty
Local Indicators of Spatial Autocorrelation   Problems of Scale & Zoning
Simple Regression & Trend Surface Analysis   Thematic Accuracy & Assessment
Geographically Weighted Regression   Stochastic Simulation & Monte Carlo Methods
Spatial Autoregressive & Bayesian Methods   Mathematical Models of Uncertainty
Spatial Filtering Models   Fuzzy Aggregation Operators

 

AM-22 - Global Measures of Spatial Association

Spatial association broadly describes how the locations and values of samples or observations vary across space. Similarity in both the attribute values and locations of observations can be assessed using measures of spatial association based upon the first law of geography. In this entry, we focus on the measures of spatial autocorrelation that assess the degree of similarity between attribute values of nearby observations across the entire study region. These global measures assess spatial relationships with the combination of spatial proximity as captured in the spatial weights matrix and the attribute similarity as captured by variable covariance (i.e. Moran’s I) or squared difference (i.e. Geary’s C). For categorical data, the join count statistic provides a global measure of spatial association. Two visualization approaches for spatial autocorrelation measures include Moran scatterplots and variograms (also known as semi-variograms).

AM-56 - Impacts of transformations
  • Compare and contrast the impacts of different conversion approaches, including the effect on spatial components
  • Create a flowchart showing the sequence of transformations on a data set (e.g., geometric and radiometric correction and mosaicking of remotely sensed data)
  • Prioritize a set of algorithms designed to perform transformations based on the need to maintain data integrity (e.g., converting a digital elevation model into a TIN)
AM-16 - Interpolation methods
  • Identify the spatial concepts that are assumed in different interpolation algorithms
  • Compare and contrast interpolation by inverse distance weighting, bi-cubic spline fitting, and kriging
  • Differentiate between trend surface analysis and deterministic spatial interpolation
  • Explain why different interpolation algorithms produce different results and suggest ways by which these can be evaluated in the context of a specific problem
  • Design an algorithm that interpolates irregular point elevation data onto a regular grid
  • Outline algorithms to produce repeatable contour-type lines from point datasets using proximity polygons, spatial averages, or inverse distance weighting
  • Implement a trend surface analysis using either the supplied function in a GIS or a regression function from any standard statistical package
  • Describe how surfaces can be interpolated using splines
  • Explain how the elevation values in a digital elevation model (DEM) are derived by interpolation from irregular arrays of spot elevations
  • Discuss the pitfalls of using secondary data that has been generated using interpolations (e.g., Level 1 USGS DEMs)
  • Estimate a value between two known values using linear interpolation (e.g., spot elevations, population between census years)
AM-17 - Intervisibility
  • Define “intervisibility”
  • Outline an algorithm to determine the viewshed (area visible) from specific locations on surfaces specified by DEMs
  • Perform siting analyses using specified visibility, slope, and other surface related constraints
  • Explain the sources and impact of errors that affect intervisibility analyses
AM-08 - Kernels and Density Estimation

Kernel density estimation is an important nonparametric technique to estimate density from point-based or line-based data. It has been widely used for various purposes, such as point or line data smoothing, risk mapping, and hot spot detection. It applies a kernel function on each observation (point or line) and spreads the observation over the kernel window. The kernel density estimate at a location will be the sum of the fractions of all observations at that location. In a GIS environment, kernel density estimation usually results in a density surface where each cell is rendered based on the kernel density estimated at the cell center. The result of kernel density estimation could vary substantially depending on the choice of kernel function or kernel bandwidth, with the latter having a greater impact. When applying a fixed kernel bandwidth over all of the observations, undersmoothing of density may occur in areas with only sparse observation while oversmoothing may be found in other areas. To solve this issue, adaptive or variable bandwidth approaches have been suggested.

AM-37 - Knowledge discovery
  • Explain how spatial data mining techniques can be used for knowledge discovery
  • Explain how a Bayesian framework can incorporate expert knowledge in order to retrieve all relevant datasets given an initial user query
  • Explain how visual data exploration can be combined with data mining techniques as a means of discovering research hypotheses in large spatial datasets
AM-29 - Kriging Interpolation

Kriging is an interpolation method that makes predictions at unsampled locations using a linear combination of observations at nearby sampled locations. The influence of each observation on the kriging prediction is based on several factors: 1) its geographical proximity to the unsampled location, 2) the spatial arrangement of all observations (i.e., data configuration, such as clustering of observations in oversampled areas), and 3) the pattern of spatial correlation of the data. The development of kriging models is meaningful only when data are spatially correlated.. Kriging has several advantages over traditional interpolation techniques, such as inverse distance weighting or nearest neighbor: 1) it provides a measure of uncertainty attached to the results (i.e., kriging variance); 2) it accounts for direction-dependent relationships (i.e., spatial anisotropy); 3) weights are assigned to observations based on the spatial correlation of data instead of assumptions made by the analyst for IDW; 4) kriging predictions are not constrained to the range of observations used for interpolation, and 5) data measured over different spatial supports can be combined and change of support, such as downscaling or upscaling, can be conducted.

AM-54 - Landscape Metrics

Landscape metrics are algorithms that quantify the spatial structure of patterns – primarily composition and configuration - within a geographic area. The term "landscape metrics" has historically referred to indices for categorical land cover maps, but with emerging datasets, tools, and software programs, the field is growing to include other types of landscape pattern analyses such as graph-based metrics, surface metrics, and three-dimensional metrics. The choice of which metrics to use requires careful consideration by the analyst, taking into account the data and application. Selecting the best metric for the problem at hand is not a trivial task given the large numbers of metrics that have been developed and software programs to implement them.

AM-40 - Least-cost (shortest) path analysis
  • Describe some variants of Dijkstra’s algorithm that are even more efficient
  • Discuss the difference of implementing Dijkstra’s algorithm in raster and vector modes
  • Demonstrate how K-shortest path algorithms can be implemented to find many efficient alternate paths across the network
  • Compute the optimum path between two points through a network with Dijkstra’s algorithm
  • Explain how a leading World Wide Web-based routing system works (e.g., MapQuest, Yahoo Maps, Google)
AM-23 - Local Measures of Spatial Association

Local measures of spatial association are statistics used to detect variations of a variable of interest across space when the spatial relationship of the variable is not constant across the study region, known as spatial non-stationarity or spatial heterogeneity. Unlike global measures that summarize the overall spatial autocorrelation of the study area in one single value, local measures of spatial association identify local clusters (observations nearby have similar attribute values) or spatial outliers (observations nearby have different attribute values). Like global measures, local indicators of spatial association (LISA), including local Moran’s I and local Geary’s C, incorporate both spatial proximity and attribute similarity. Getis-Ord Gi*, another popular local statistic, identifies spatial clusters at various significance levels, known as hot spots (unusually high values) and cold spots (unusually low values). This so-called “hot spot analysis” has been extended to examine spatiotemporal trends in data. Bivariate local Moran’s I describes the statistical relationship between one variable at a location and a spatially lagged second variable at neighboring locations, and geographically weighted regression (GWR) allows regression coefficients to vary at each observation location. Visualization of local measures of spatial association is critical, allowing researchers of various disciplines to easily identify local pockets of interest for future examination.

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