# Can data clustering algorithms be used to find the borders of an area in 2D space ?

If we have spatial points randomly distributed in 2D space, then we clustered those points according to some parameters, say location x,y. Can we use the same clustering algorithm and apply it on finding a geographical area borders? . In another words , If a set of points with the same characteristics are clustered according to their geographical relationship , can we say that we have found the area borers that contains those points ? For example this paper

• There doesn't seem to be enough information to answer this question, because you haven't posited any connection whatsoever between the locations of these points and the geographical area in which you might consider them to enclosed. Could you provide more specifics about your actual problem? – whuber Jan 1 '17 at 18:12
• To map boundaries you would need to be able to evaluate what cluster a hypothetical new data point would belong to, i.e. you would need a classification style decision function. As noted here, clustering can be considered as classification with hidden labels. So your clustering approach may already implicitly give you a classification function. (Or you could just train a classifier on the data w/label=cluster-id.) This will give an answer, but how useful/reliable this answer is will depend on the specifics, as noted by @whuber. – GeoMatt22 Jan 1 '17 at 19:15
• @whuber Here is my idea, I have overlapped shapes , and there are points arrived randomly to this space(some maybe inside the overlapped areas and some can be out), I want to make use of those points to find the overlapped areas so that in the future I can tell if a new arrived point is inside or outside an overlapped area. – Paulo Jan 2 '17 at 1:33

Yes, people have successfully used clustering algorithms such as DBSCAN for this.

I don't have references for you, but look for image segmentation by clustering.

I don't think it is the best way to do this (in particular on images, you really should exploit the pixel grid for performance) and I really do not recommend k-means for this. But a well built generalized DBSCAN in a special implementation for your data may work well, and give you good control over the desired outcome. Generalized DBSCAN is much superior here, because you can specify both adjacency and similarity thresholds.