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. 

 

Conceptual Frameworks for Spatial Analysis & Modeling Data Exploration & Spatial Statistics Network & Location Analysis
Basic Primitives Spatial Sampling for Spatial Analysis Intro to Network & Location Analysis
Spatial Relationships Exploratory Spatial Data Analysis (ESDA) Network Route & Tour Problems
Neighborhoods Kernels & Density Estimation Location & Service Area Problems
First & Second Laws of Geography Spatial Interaction Modelling Accessibility
Spatial Statistics Cartographic Modeling Location-allocation Modeling
Methodological Context Multi-criteria Evaluation The Classic Transportation Problem
Spatial Analysis as a Process Spatial Process Models Space-Time Analysis & Modeling
Geospatial Analysis & Model Building Grid-based Statistics and Metrics Time Geography
Changing Context of GIScience Landscape Metrics Capturing Spatio-Temporal Dynamics in Computational Modeling 
Data Manipulation DEM and Terrain Metrics GIS-Based Computational Modeling
Point, Line, and Area Generalization Point Pattern Analysis Computational Movement Analysis
Coordinate transformations Hot-spot and Cluster Analysis Accounting for Errors in Space-Time Modeling
Data conversion Global Measures of Spatial Association Geocomputational Methods & Models
Impacts of transformations Local Measures of Spatial Association Cellular Automata
Raster resampling Simple Regression & Trend Surface Analysis Agent-based Modeling
Vector-to-raster and raster-to-vector conversions Geographically Weighted Regression Simulation Modeling
Generalization & Aggregation Spatial Autoregressive & Bayesian Methods Simulation & Modeling Systems for Agent-based Modeling
Transaction Management Spatial Filtering Models Artificial Neural Networks
Building Blocks   Genetic Algorithms & Evolutionary Computing 
Spatial & Spatiotemporal Data Models Surface & Field Analysis Big Data & Geospatial Analysis
Length & Area Operations Modeling Surfaces Problems & with Large Spatial Databases
Polyline & Polygon Operations Surface Geometry Pattern Recognition & Matching
Overlay & Combination Operations Intervisibility Artificial Intelligence Approaches
Areal Interpolation Watersheds & Drainage Data Mining Approaches
Classification & Clustering Gridding, Interpolation, and Contouring Rule Learning for Spatial Data Mining
Boundaries & Zone Membership Deterministic Interpolation Models Machine Learning Approaches
Tesselations & Triangulations Inverse Distance Weighting CyberGIS
Spatial Queries Radial Basis & Spline Functions Analysis of Errors & Uncertainty
Distance Operations Triangulation Problems of Currency, Source, and Scale
Buffers Polynomial Functions Problems of Scale & Zoning
Directional Operations Core Concepts in Geostatistics Theory of Error Propagation
Grid Operations & Map Algebra Kriging Interpolation Propagation of Error in Geospatial Modeling
    Fuzzy Aggregation Operators
    Mathematical Models of Uncertainty

 

AM-77 - Genetic Algorithms and Evolutionary Computing

Genetic algorithms (GAs) are a family of search methods that have been shown to be effective in finding optimal or near-optimal solutions to a wide range of optimization problems. A GA maintains a population of solutions to the problem being solved and uses crossover, mutation, and selection operations to iteratively modify them. As the population evolves across generations, better solutions are created and inferior ones are selectively discarded. GAs usually run for a fixed number of iterations (generations) or until further improvements do not obtain. This contribution discusses the fundamental principles of genetic algorithms and uses Python code to illustrate how GAs can be developed for both numerical and spatial optimization problems. Computational experiments are used to demonstrate the effectiveness of GAs and to illustrate some nuances in GA design.

AM-81 - GIS-Based Computational Modeling

GIS-based computational models are explored. While models vary immensely across disciplines and specialties, the focus is on models that simulate and forecast geographical systems and processes in time and space. The degree and means of integration of the many different models with GIS are covered, and the critical phases of modeling: design, implementation, calibration, sensitivity analysis, validation and error analysis are introduced. The use of models in simulations, an important purpose for implementing models within or outside of GIS, is discussed and the context of scenario-based planning explained. To conclude, a survey of model types is presented, with their application methods and some examples, and the goals of modeling are discussed.

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
  • 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 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.

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