I've been looking into clustering algorithms, as some of my projects
will use them. It seems all of the ones I've looked at use similar
math, which leads to what I would call "cartographic" issues. I'm sure
people know of the issues (see examples below), and they are somewhat
inherent to the algorithms, particularly if performance is high
priority. However, I'm wondering if anyone knows of any other
approaches that alleviate these issues. Or more broadly, are there any
good web pages that examine and compare the pros and cons of various
approaches?

Here are some of the issues. These apply to the distance-based
algorithms -- I'm not considering grid-based ones. Mostly the issues
are the result of using marker locations for the cluster location and
the fact that markers are considered in order one-by-one. Note that
the issues do not mean that clustering doesn't work, just that the
results are not the best cartographically.

For the examples below X is the clustering distance and E is some
small epsilon distance.

Ex. #1: Different order produces different clusters
Consider the points: (1) <-- X-E --> (2) <-- X-E --> (3)
Which cluster as: (1&2) <-- 2X-2E --> (3)
Reordering to: (2) <-- X-E --> (1) <-- X-E --> (3)
Clusters as: (1&2&3)

Ex. #2: Same issue, but a less trivial case than above
Points: (1) <------ X-E ------> (2) <-- 4E --> (3) <------ X-E ------>
(4)
Clusters: (1&2) <-------- 2X+2E --------> (3&4)
Ideal(?): (1) <------ X+E ------> (2&3) <------ X+E ------> (4)

(Hopefully the formatting is okay.)


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