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 linked directly to either their original (2006) or revised entries; forthcoming, future topics are italicized. 


Basic Spatial Operations Advanced Spatial Analysis Surface Analysis
Buffers Identifying & designing analytical procedures Calculating surface derivatives
Overlay Point pattern analysis Interpolation methods
Neighborhoods Cluster analysis Intervisibility
Map algebra Exploratory data analysis (EDA) Cost surfaces
  Analyzing multi-dimensional attributes  
Spatial Modeling Multi-criteria evaluation Network Analysis
Cartographic modeling Weighting schemes Least-cost (shortest) path analysis 
Components of models Spatial interaction Flow modeling
Coupling scientific models with GIS The spatial weights matrix The Classic Transportation Problem
Mathematical models Spatial interaction Other classic network problems
Spatial process models Space-scale algorithms Modeling Accessibility
Using models to represent info & processes    
Workflow analysis and design Space-Time Analytics & Modeling Data Mining
  Computational movement analysis Data mining approaches
Data Manipulation Time geography Knowledge discovery
Approaches to point, line, area generalization   Pattern recognition
Coordinate transformations Spatial Statistics Geospatial data classification
Data conversion Global measures of spatial association Multi-layer feed-forward neural networks
Impacts of transformations Local measures of spatial association Rule learning
Raster resampling Spatial sampling for statistical analysis  
Vector-to-raster and raster-to-vector conversions Stochastic processes Spatial Simulation
  Outliers Simulation modeling
Analysis of Errors and Uncertainty  Bayesian methods Cellular Automata
Problems of currency, source, and scale Principles of semi-variogram construction Simulated annealing
Theory of error propagation Semi-variogram modeling Agent-based models
Propagation of error in geospatial modeling Kriging methods Adaptive agents
Fuzzy aggregation operators Principles of spatial econometrics Microsimulation & calibration of agent activities
  Spatial autoregressive models  
  Spatial filtering Spatial Optimization
  Kernels and density estimation Location-allocation modeling
  Spatial expansion & Geographically weighted regression Greedy heuristics
  Spatial distribution Interchange heuristics
  Mathematical models of uncertainty Genetic algorithms
  Non-linearity relationships and non-Gaussian distributions  
  Interchange with probability  


AM-38 - Pattern recognition
  • Differentiate among machine learning, data mining, and pattern recognition
  • Explain the principles of pattern recognition
  • Apply a simple spatial mean filter to an image as a means of recognizing patterns
  • Construct an edge-recognition filter
  • Design a simple spatial mean filter
  • Explain the outcome of an artificial intelligence analysis (e.g., edge recognition), including a discussion of what the human did not see that the computer identified and vice versa
AM-07 - Point pattern analysis
  • List the conditions that make point pattern analysis a suitable process
  • Identify the various ways point patterns may be described
  • Identify various types of K-function analysis
  • Describe how Independent Random Process/Chi-Squared Result (IRP/CSR) may be used to make statistical statements about point patterns
  • Outline measures of pattern based on first and second order properties such as the mean center and standard distance, quadrat counts, nearest neighbor distance, and the more modern G, F, and K functions
  • Outline the basis of classic critiques of spatial statistical analysis in the context of point pattern analysis
  • Explain how distance-based methods of point pattern measurement can be derived from a distance matrix
  • Explain how proximity polygons (e.g., Thiessen polygons) may be used to describe point patterns
  • Explain how the K function provides a scale-dependent measure of dispersion
  • Compute measures of overall dispersion and clustering of point datasets using nearest neighbor distance statistics
AM-27 - Principles of semi-variogram construction
  • Identify and define the parameters of a semi-variogram (range, sill, nugget)
  • Demonstrate how semi-variograms react to spatial nonstationarity
  • Construct a semi-variogram and illustrate with a semi-variogram cloud
  • Describe the relationships between semi-variograms and correlograms, and Moran’s indices of spatial association
AM-31 - Principles of spatial econometrics
  • Explain how spatial dependence and spatial heterogeneity violate the Gauss-Markov assumptions of regression used in traditional econometrics
  • Demonstrate how the spatial weights matrix is fundamental in spatial econometrics models
  • Demonstrate why spatial autocorrelation among regression residuals can be an indication that spatial variables have been omitted from the models
  • Demonstrate how spatially lagged, trend surface, or dummy spatial variables can be used to create the spatial component variables missing in a standard regression analysis
  • Describe the general types of spatial econometric models
AM-87 - Problems of currency, source, and scale
  • Describe the problem of conflation associated with aggregation of data collected at different times, from different sources, and to different scales and accuracy requirements
  • Explain how geostatistical techniques might be used to address such problems
AM-85 - Propagation of error in geospatial modeling
  • Compare and contrast error propagation techniques (e.g., Taylor, Monte Carlo)
  • Explain how some operations can exacerbate error while others dampen it (e.g., mean filter)
AM-60 - Raster resampling
  • Evaluate methods used by contemporary GIS software to resample raster data on-the-fly during display
  • Select appropriate interpolation techniques to resample particular types of values in raster data (e.g., nominal using nearest neighbor)
  • Resample multiple raster data sets to a single resolution to enable overlay
  • Resample raster data sets (e.g., terrain, satellite imagery) to a resolution appropriate for a map of a particular scale
  • Discuss the consequences of increasing and decreasing resolution
AM-68 - Rule learning
  • Describe how a neural network may use training rules to learn from input data
AM-28 - Semi-variogram modeling
  • List the possible sources of error in a selected and fitted model of an experimental semi-variogram
  • Describe the conditions under which each of the commonly used semi-variograms models would be most appropriate
  • Explain the necessity of defining a semi-variogram model for geographic data
  • Apply the method of weighted least squares and maximum likelihood to fit semi-variogram models to datasets
  • Describe some commonly used semi-variogram models
AM-76 - Simulated annealing
  • Outline the rationale for and usefulness of simulated annealing