Distinguishing extensive and intensive properties for meaningful geocomputation and mapping

Abstract

A most fundamental and far-reaching trait of geographic information is the distinction between extensive and intensive properties. In common understanding, originating in Physics and Chemistry, extensive properties increase with the size of their supporting objects, while intensive properties are independent of this size. It has long been recognized that the decision whether analytical and cartographic measures can be meaningfully applied depends on whether an attribute is considered intensive or extensive. For example, the choice of a map type as well as the application of basic geocomputational operations, such as spatial intersections, aggregations or algebraic operations such as sums and weighted averages, strongly depend on this semantic distinction. So far, however, the distinction can only be drawn in the head of an analyst. We still lack practical ways of automation for composing GIS workflows and to scale up mapping and geocomputation over many data sources, e.g. in statistical portals. In this article, we test a machine-learning model that is capable of labeling extensive/ intensive region attributes with high accuracy based on simple characteristics extractable from geodata files. Furthermore, we propose an ontology pattern that captures central applicability constraints for automating data conversion and mapping using Semantic Web technology.

Quantifying the scale effect in geospatial big data using semi-variograms

“…Geospatial big data, such as social media check-in data and taxi origin-destination data, are extensive and additive [28], meaning that the most common way to aggregate the data is using a simple sum operation. This aggregation process inevitably introduces an increasing intra-unit variation and a larger nugget variance ( c 0 ) at a coarser scale.…”

“…This aggregation process inevitably introduces an increasing intra-unit variation and a larger nugget variance ( c 0 ) at a coarser scale. One solution to compare indicators at different scales is to make extensive data intensive [28] (e.g., convert population to population density). Another solution is to use a normalized and scale-free indicator.…”

“…In this case, it is necessary to look into the variances of points within each cell (i.e., the intra-unit variance) to understand how much information was lost during aggregation. In addition, the cell values in remote sensing imagery are mostly intensive data (e.g., NDVI), meaning that the cell values are normalized and cannot be added up, whereas point-based big geo-data are extensive so the aggregated cell values can be added up [28]. The mathematical operations are different for these two types of data, therefore, the statistical measures for intensive remote sensing data cannot be directly applied to extensive spatial data.…”

Geo-analytical question-answering with GIS

“…to catchments and service areas. Similar to levels of measurement and other semantic types (Chrisman 2002;Scheider and Huisjes 2019;Scheider and Tomko 2016), core concepts work as constraints to spatial analysis (Sinton 1978).…”

“…As these examples illustrate, there are plenty of reasons to assume that core concepts of spatial information, together with levels of measurement (Chrisman 2002) and related semantic distinctions (Scheider and Huisjes 2019), are indispensable in order to assess how a given data source might be transformed into meaningful answers. Our task in the future is therefore to (1) settle on a definite set of semantic types which capture the diverse ways how core concepts are represented within a given geodata type and (2) to find ways to scale up the semantic annotations across various geodata sources.…”