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I'm thinking about a new project, so I don't have data yet, but I plan on collecting GIS information for houses within a state.

Usually in the U.S., these dead-end streets will have a large circle for cars to turn around in, meaning the fronts of each house on the cul-de-sac point toward the center of the circle.

In general, my question is how to locate a subset of data clustered in a circular pattern on a 2D grid. If the same technique could allow me to locate dead-ends, that would be useful, but not required.

I'll probably need to use a logistic classifier, but I'm not certain what the hypothesis should look like. If this is a well-known problem, I didn't know the keywords to do a proper Google search, so pointers in that direction would be helpful as well.

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A description of how the data looks like may be helpful in answering this question. – varty Nov 8 '11 at 5:46
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@varty That's an excellent question. If one merely collects, say, centroids of houses, the project looks hopeless. If the houses are represented as polygons there's a bit more hope, but it appears that having data representing the streets will be key, for then it's possible to distinguish housing clusters at the ends of streets from identical-looking clusters elsewhere. For an example, see topoquest.com/… . – whuber♦ Nov 8 '11 at 14:46
That's a good point @whuber. I thought I might need street data to avoid false positives. I've never worked with map data before. GPS coordinates seemed easy enough to deal with, but I'll have to study up before taking this project further. – jrhorn424 Nov 9 '11 at 20:24
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With a GIS you can identify the endpoints of culs-de-sac and compute distances from houses to those endpoints. If you also have addresses for the houses, this would give a very reliable way to select exactly the subsets you interested in. – whuber♦ Nov 9 '11 at 20:41

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The generic answer is that you can find circles (or lines, or ...) in 2D data with the Hough Transform. As @whuber notes in his commment, you may be in trouble if you're looking for circular patterns in house centroids. I think this image-processing approach is better than a statistical one. A related CV article is this one.

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Thanks @Wayne. The Wikipedia article only explains how a Hough Transform can detect lines. Parameterizing a circle should be even more intuitive. Do you know of a text that gives a thorough treatment of Hough Transforms? – jrhorn424 Nov 9 '11 at 20:21
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Sorry, I don't know of a good reference. I think that as the Wikipedia article says, you just use center and circumference instead of intercept and slope. – Wayne Nov 9 '11 at 22:43

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