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.

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.

The constellation of science and technology that is now considered a unit (Geographic Information Science and Technology – GIS&T) has emerged from many source disciplines through many divergent and convergent pasts in different times and places. This narrative limits itself to the perspective of the English-speaking community, leaving other regions for a separate chapter As in the case of many technical developments in the second half of the twentieth century, academic institutions played a key (though far from exclusive) role in innovation and risk-taking. In a number of locations, academic innovators tried out new technology for handling geographic information, beginning as early as the 1960s. Three institutions (University of Washington, Laboratory for Computer Graphics – Harvard University, and Experimental Cartography Unit – Royal College of Art (UK)) deserve particular treatment as examples of the early innovation process. Their innovations may look crude by current standards, but they laid some groundwork for later developments. Academic institutions played a key role in innovation over the past decades, but the positioning of that role has shifted as first government, then commercial sectors have taken the lead in certain aspects of GIS&T. Current pressures on the academic sector may act to reduce this role.

Epistemology is the lens through which we view reality. Different epistemologies interpret the earth and patterns on its surface differently. In effect, epistemology is a belief system about the nature of reality that, in turn, structures our interpretation of the world. Common epistemologies in GIScience include (but are not limited by) positivism and realism. However, many researchers are in effect pragmatists in that they choose the filter that best supports their work and a priori hypotheses. Different epistemologies – or ways of knowing and studying geography – result in different ontologies or classification systems. By understanding the role of epistemology, we can better understand different ways of representing the same phenomena.