Detecting a Torus in a data cloud

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FallenApple
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Would the following method work? I could uniformly distribute points into the data cloud. Of the "darts" that I threw in, create edges between all points with a metric value under a certain amount. The nodes in the resulting graph that have more neighbors would indicate greater density. I could tune the amount of darts and since the connective density would increase in a more non linear fashion for denser regions vs less dense regions, I could tell if there's a cavity or not.

Would this work in practice?

Would it work topologically? That is, I would get the same indication for a coffee mug cloud vs a doughnut? I mean, regardless of the shape, I would end up with two less dense regions.
 
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This is not my area and it seems to be confusing for other mentors, too. In an attempt to get some clarity, could you please provide a considerably more precise sample problem you are trying to solve?

My goal is to get you an answer - good clear questions get answers, fuzzy or overly general questions get more questions.
 
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jim mcnamara said:
This is not my area and it seems to be confusing for other mentors, too. In an attempt to get some clarity, could you please provide a considerably more precise sample problem you are trying to solve?

My goal is to get you an answer - good clear questions get answers, fuzzy or overly general questions get more questions.
In the meantime, best I can think is that this is from Persistent Homology and, more generally, from Topological Data Analysis.
 
fresh_42 said:
In this case it would be better placed in the computing forum, isn't it?
Yes, it seems like it would be a better fit there, tho we may make a nonclustered index and include a link to it from here if possible, I would think.
 
Is this essentially the same problem as in image enhancement and image recognition ? These subjects have been extensively researched and there is a large amount of published material available about both the mathematical theory and practical computation methods .
 
Nidum said:
Is this essentially the same problem as in image enhancement and image recognition ? These subjects have been extensively researched and there is a large amount of published material available about both the mathematical theory and practical computation methods .
Not sure, sorry, but sounds right/close. The dart thing suggests a Monte Carlo method for pattern recognition.
 
Since the OP is obviously not well formulated, such that meanwhile everyone guesses what might have been meant, I close this thread. It makes no sense to start a discussion on speculations. The more as it is not clear, if we're right.

@FallenApple If you repost this, please make sure that you're understood and place it in an appropriate forum. If it's computation, then it shouldn't be here.