## basic analytical methods

##### 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-10 - Spatial Interaction

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.

##### AM-09 - Classification and Clustering

Classification and clustering are often confused with each other, or used interchangeably. Clustering and classification are distinguished by whether the number and type of classes are known beforehand (classification), or if they are learned from the data (clustering). The overarching goal of classification and clustering is to place observations into groups that share similar characteristics while maximizing the separation of the groups that are dissimilar to each other. Clusters are found in environmental and social applications, and classification is a common way of organizing information. Both are used in many areas of GIS including spatial cluster detection, remote sensing classification, cartography, and spatial analysis. Cartographic classification methods present a simplified way to examine some classification and clustering methods, and these will be explored in more depth with example applications.

##### 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-07 - Point Pattern Analysis

Point pattern analysis (PPA) focuses on the analysis, modeling, visualization, and interpretation of point data. With the increasing availability of big geo-data, such as mobile phone records and social media check-ins, more and more individual-level point data are generated daily. PPA provides an effective approach to analyzing the distribution of such data. This entry provides an overview of commonly used methods in PPA, as well as demonstrates the utility of these methods for scientific investigation based on a classic case study: the 1854 cholera outbreaks in London.

##### 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-10 - Spatial Interaction

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.

##### AM-09 - Classification and Clustering

Classification and clustering are often confused with each other, or used interchangeably. Clustering and classification are distinguished by whether the number and type of classes are known beforehand (classification), or if they are learned from the data (clustering). The overarching goal of classification and clustering is to place observations into groups that share similar characteristics while maximizing the separation of the groups that are dissimilar to each other. Clusters are found in environmental and social applications, and classification is a common way of organizing information. Both are used in many areas of GIS including spatial cluster detection, remote sensing classification, cartography, and spatial analysis. Cartographic classification methods present a simplified way to examine some classification and clustering methods, and these will be explored in more depth with example applications.

##### 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-07 - Point Pattern Analysis

Point pattern analysis (PPA) focuses on the analysis, modeling, visualization, and interpretation of point data. With the increasing availability of big geo-data, such as mobile phone records and social media check-ins, more and more individual-level point data are generated daily. PPA provides an effective approach to analyzing the distribution of such data. This entry provides an overview of commonly used methods in PPA, as well as demonstrates the utility of these methods for scientific investigation based on a classic case study: the 1854 cholera outbreaks in London.