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-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
  • Describe the relationships between kernels and classical spatial interaction approaches, such as surfaces of potential
  • Outline the likely effects on analysis results of variations in the kernel function used and the bandwidth adopted
  • Explain why and how density estimation transforms point data into a field representation
  • Explain why, in some cases, an adaptive bandwidth might be employed
  • Create density maps from point datasets using kernels and density estimation techniques using standard software
  • Differentiate between kernel density estimation and spatial interpolation
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 methods
  • Describe the relationship between the semi-variogram and kriging
  • Explain why it is important to have a good model of the semi-variogram in kriging
  • Explain the concept of the kriging variance, and describe some of its shortcomings
  • Explain how block-kriging and its variants can be used to combine data sets with different spatial resolution (support)
  • Compare and contrast block-kriging with areal interpolation using proportional area weighting and dasymetric mapping
  • Outline the basic kriging equations in their matrix formulation
  • Conduct a spatial interpolation process using kriging from data description to final error map
  • Explain why kriging is more suitable as an interpolation method in some applications than others
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
  • Describe the effect of non-stationarity on local indices of spatial association
  • Decompose Moran’s I and Geary’s c into local measures of spatial association
  • Compute the Gi and Gi* statistics
  • Explain how geographically weighted regression provides a local measure of spatial association
  • Explain how a weights matrix can be used to convert any classical statistic into a local measure of spatial association
  • Compare and contrast global and local statistics and their uses
AM-46 - Location-allocation modeling
  • Describe the structure of origin-destination matrices
  • Explain Weber’s locational triangle
  • Assess the outcome of location-allocation models using other spatial analysis techniques
  • Compare and contrast covering, dispersion, and p-median models
  • Locate, using location-allocation software, service facilities that meet given sets of constraints
  • Explain the concepts of demand and service
AM-06 - Map algebra
  • Explain the categories of map algebra operations (i.e., local, focal, zonal, and global functions)
  • Explain why georegistration is a precondition to map algebra
  • Differentiate between map algebra and matrix algebra using real examples
  • Perform a map algebra calculation using command line, form-based, and flow charting user interfaces
  • Describe a real modeling situation in which map algebra would be used (e.g., site selection, climate classification, least-cost path)
  • Describe how map algebra performs mathematical functions on raster grids
AM-45 - Mathematical modeling
  • Explain how optimization models can be used to generate models of alternate options for presentation to decision makers
  • Explain, using the concept of combinatorial complexity, why some location problems are very hard to solve
  • Compare and contrast the concepts of discrete location problems and continuous location problems
  • Explain the concept of solution space
  • Explain the principles of operations research modeling and location modeling