Detecting a Torus in a data cloud

[FallenApple]

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.

 

[jim mcnamara]

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.

 

[WWGD]

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]

In the meantime, best I can think is that this is from Persistent Homology and, more generally, from Topological Data Analysis.

In this case it would be better placed in the computing forum, isn't it?

 

[WWGD]

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.

 

[Nidum]

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 .

 

[WWGD]

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.

 

[fresh_42]

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.