(6) Dimensionality Reduction
Dimensionality Reduction is a technique that allows one to map multidimensional data to a Key-Value model or to other non-multidimensional models.
Traditional geographic information systems use some variation of a Quadtree or R-Tree for indexes. These structures need to be updated in-place and are expensive to manipulate when data volumes are large. An alternative approach is to traverse the 2D structure and flatten it into a plain list of entries. One well known example of this technique is a Geohash. A Geohash uses a Z-like scan to fill 2D space and each move is encoded as 0 or 1 depending on direction. Bits for longitude and latitude moves are interleaved as well as moves. The encoding process is illustrated in the figure below, where black and red bits stand for longitude and latitude, respectively: