Abstract
Prime numbers are routinely used in a variety of applications, e.g., cryptography and hashing. A prime number can only be divided by one and the number itself. A semi-prime number is a product of two or more prime numbers (e.g., 5 × 3 = 15) and can only be formed by these numbers (e.g., 3 and 5). Exploiting this mathematical property allows schema-free encoding of geographical data in nominal or ordinal measurement scales for thematic maps. Schema-free encoding becomes increasingly important in the context of data variety. In this paper, I investigate the encoding of categorical thematic map data using prime numbers instead of a sequence of all natural numbers (1, 2, 3, 4, ..., n) as the category identifier. When prime numbers are multiplied, the result as a single value contains the information of more than one location category. I demonstrate how this encoding can be used on three use-cases, (1) a hierarchical legend for one theme (CORINE land use/land cover), (2) a combination of multiple topics in one theme (Köppen-Geiger climate classification), and (3) spatially overlapping regions (tree species distribution). Other applications in the field of geocomputation in general can also benefit from schema-free approaches with dynamic instead of handcrafted encoding of geodata.
Highlights
It is common to encode variables of geospatial data in nominal or ordinal measurement scales by mapping the category identifiers using integers from a sequence of positive natural numbers, i.e., 1, 2, 3, ..., n
I investigated the application of prime numbers as a schema-free approach for storing geospatial datasets in categorical variables, i.e., values in the nominal or ordinal measurement scale
If prime numbers are used to encode category identifiers on locations, it is always and uniquely possible to reconstruct them and their information from the semi-prime number
Summary
It is common to encode variables of geospatial data in nominal or ordinal measurement scales by mapping the category identifiers using integers from a sequence of positive natural numbers, i.e., 1, 2, 3, ..., n. Spatially overlapping regions are routinely modelled using multiple layers or bands This means, users are required to find and rely on error-prone workarounds or ignore the problems, i.e., by shifting them to another part of the workflow. It is possible and beneficial to employ schema-free encodings for storing variables in nominal and ordinal scale levels.
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