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 Accessibility modeling
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 modeling
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-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
AM-48 - Mathematical models of uncertainty: probability and statistics
  • Devise simple ways to represent probability information in GIS
  • Describe the basic principles of randomness and probability
  • Compute descriptive statistics and geostatistics of geographic data
  • Interpret descriptive statistics and geostatistics of geographic data
  • Recognize the assumptions underlying probability and geostatistics and the situations in which they are useful analytical tools
AM-82 - Microsimulation and calibration of agent activities
  • Describe a “bottom-up” simulation from an activity-perspective with changes in the locations and/or activities the individual person (and/or vehicle) in space and time, in the activity patterns and space-time trajectories created by these activity patterns, and in the consequent emergent phenomena, such as traffic jams and land-use patterns
  • Describe how various parameters in an agent-based model can be modified to evaluate the range of behaviors possible with a model specification
  • Describe how measurements on the output of a model can be used to describe model behavior
AM-13 - Multi-criteria evaluation
  • Describe the implementation of an ordered weighting scheme in a multiple-criteria aggregation
  • Compare and contrast the terms multi-criteria evaluation, weighted linear combination, and site suitability analysis
  • Differentiate between contributing factors and constraints in a multi-criteria application
  • Explain the legacy of multi-criteria evaluation in relation to cartographic modeling
  • Determine which method to use to combine criteria (e.g., linear, multiplication)
  • Create initial weights using the analytical hierarchy process (AHP)
  • Calibrate a linear combination model by adjusting weights using a test data set
AM-66 - Multi-layer feed-forward neural networks
  • Analyze the stability of the network using multiple runs with the same training data and architecture
  • Compare and contrast classification results when the architecture of the network and initial parameters are changed
  • Differentiate between feed-forward and recurrent architectures
  • Describe the architecture and components of a feed-forward neural network
AM-05 - Neighborhoods
  • Discuss the role of Voronoi polygons as the dual graph of the Delaunay triangulation
  • Explain how Voronoi polygons can be used to define neighborhoods around a set of points
  • Outline methods that can be used to establish non-overlapping neighborhoods of similarity in raster datasets
  • Create proximity polygons (Thiessen/Voronoi polygons) in point datasets
  • Write algorithms to calculate neighborhood statistics (minimum, maximum, focal flow) using a moving window in raster datasets
  • Explain how the range of map algebra operations (local, focal, zonal, and global) relate to the concept of neighborhoods
AM-63 - Non-linearity relationships and non-Gaussian distributions
  • Understand how some machine learning methods might be more adept at modeling or representing such distributions
  • Define non-linear and non-Gaussian distributions in a geospatial data environment
  • Exemplify non-linear and non-Gaussian distributions in a geospatial data environment
AM-43 - Other classic network problems
  • Describe several classic problems to which network analysis is applied (e.g., the traveling salesman problem, the Chinese postman problem)
  • Explain why heuristic solutions are generally used to address the combinatorially complex nature of these problems and the difficulty of solving them optimally
AM-24 - Outliers
  • Explain how outliers affect the results of analyses
  • Explain how the following techniques can be used to examine outliers: tabulation, histograms, box plots, correlation analysis, scatter plots, local statistics
AM-04 - Overlay
  • Explain why the process “dissolve and merge” often follows vector overlay operations
  • Outline the possible sources of error in overlay operations
  • Compare and contrast the concept of overlay as it is implemented in raster and vector domains
  • Demonstrate how the geometric operations of intersection and overlay can be implemented in GIS
  • Demonstrate why the georegistration of datasets is critical to the success of any map overlay operation
  • Formalize the operation called map overlay using Boolean logic
  • Explain what is meant by the term “planar enforcement”
  • Exemplify applications in which overlay is useful, such as site suitability analysis