Spatial clustering of points within a given line

On Fri, 11 Sep 2009 03:48:29 -0700 (PDT) Julius Tesoro
<jutesoro at yahoo.com> asked about "Spatial clustering of points within a
given line", saying:

I have a dilemma, Considering I have a number of points and a line
(shapefile). How do I compute for the shortest distance between a line
and a point? Also how do you identify which points aggregate near the
line like in spatial clustering?

Thanks.

Notes by Professor B.K.P.Horn of MIT
(http://dspace.mit.edu/bitstream/handle/1721.1/41068/AI_WP_034.pdf)
are appropriate here.  I've used these in a little illustrative exercise
(
http://my.opera.com/ekzept/blog/2009/09/14/clustering-of-points-for-given-lines).
Given you know where lines are, associating involves classifying a point
based upon the (signed) perpendicular distance to each of the candidate
lines. For two, it looks something like:
http://bilge.pyrate.mailbolt.com/blogBeginningNewtonmas2008/20090913ClassifyPointsBySignedDistance005.png

I provided R code at the blog post.  No doubt more formality is
possible.

 -- Jan Galkowski.