Detecting a Torus in a data cloud

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    Cloud Data Torus
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Discussion Overview

The discussion revolves around a proposed method for detecting a torus shape within a data cloud using a graph-based approach. Participants explore the feasibility of this method in both practical and topological contexts, questioning its effectiveness in distinguishing between different shapes, such as a coffee mug and a doughnut.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests a method of uniformly distributing points in a data cloud and creating edges based on a metric value to identify denser regions, questioning its practical and topological effectiveness.
  • Several participants express confusion regarding the clarity of the original question, requesting a more precise problem statement to facilitate better answers.
  • There is a mention of Persistent Homology and Topological Data Analysis as relevant concepts, though the connection to the original method remains unclear.
  • Another participant draws a parallel between the proposed method and established fields like image enhancement and recognition, suggesting that similar mathematical theories and computational methods may apply.
  • One participant indicates that the thread may be misplaced in the current forum, suggesting it would be better suited for a computing forum.
  • A later reply suggests that the proposed method resembles a Monte Carlo method for pattern recognition, though uncertainty remains about the exact relationship.
  • One participant ultimately closes the thread due to the lack of clarity in the original post, indicating that speculation without a clear question is unproductive.

Areas of Agreement / Disagreement

Participants generally agree that the original question lacks clarity and that a more precise formulation is necessary. Multiple competing views regarding the applicability of the proposed method and its relation to other fields remain unresolved.

Contextual Notes

The discussion highlights limitations in the original problem statement, with participants noting the need for clearer definitions and a more focused inquiry to facilitate productive dialogue.

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.
 
WWGD said:
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?
 
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.
 

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