Investigating schema-free encoding of categorical data using prime numbers in a geospatial context

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.