Disclaimer: I'm mainland European, we tend to use the , to separate digits
from the whole numbers.
Clustering is quite a common approach to aggregate coordinates that are
relatively close together. The problem lies in the choice of algorithm to use.
This choice is highly dependent on the space in which the coordinates are laid
out. Quite often you can just use basic Euclidean distance which, for a
2-dimensional space, simply takes the square root of the sum of the squared
subtraction of the respective coordinates of each point. So if you have a
point p with coordinates (33, 52) and a point q with coordinates (82, 19),
the distance between p and q would be:
>>> import math
>>> math.sqrt(pow(33 - 82, 2) + pow(52 - 19, 2))
59.076221950967721
And based on that distance you can start to cluster points together that are
all roughly the same distance from a certain point, say 59,1. The fun part
of this is that this distance is the radius of a circle. So if you would plot
every possible coordinate at that distance you will see a circle emerge.
In looking at clustering algorithms I also encountered something called
Manhattan distance, but this algorithm only makes sense if you are working in
a grid with roughly equidistant lengths to the other coordinates in this
space. Normally the shortest distance from A to B would be a straight line, as
the Euclidean distance shows. However, if the movement from coordinate to
coordinate is restricted to straight lines, say the grid layout of a lot of
North American cities, then Euclidean distance cannot apply. This is the same
problem a taxi faces when trying to find the shortest distance to drive from A
to B and as such the algorithm is also known as the taxicab distance or
geometry. It takes the sum of the absolute value of the subtraction of the
respective coordinates of each point. So if you take point p and q again, the
distance would in this case be:
>>> abs(33 - 82) + abs(52 - 19)
82
Now, if you would plot all possible coordinates with that distance you will
see a circle emerge again. However, keep in mind that a circle is nothing more
than a set of points with a fixed distance (the radius). In this case our
geometry uses a differently defined distance. If you would plot this out with
a finer and finer grid the circle shape that emerges is a square rotated 45°
so that it rests on its point.