Function which measures "error"

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    Error Function
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Discussion Overview

The discussion revolves around the properties of a function measuring "error," specifically a non-symmetric error function denoted as e(x,y). Participants explore the implications of its non-normative characteristics in the context of comparing positions and orientations of a drill.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant introduces a non-symmetric error function e(x,y) and questions its suitability as a measure of error.
  • Another participant suggests that the appropriateness of the function depends on the intended application, noting that boundedness does not necessarily require norm properties.
  • A different participant expresses concern about the measure's effectiveness given its non-symmetry, seeking clarification on what constitutes a "good" measure.
  • Further clarification reveals that x and y represent elements of SE(3), related to the positions and orientations of a drill.
  • One participant proposes that asymmetry in the error measure may be acceptable, citing practical examples where certain errors (e.g., "drill too low") could be significantly worse than others (e.g., "drill too high").

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the non-symmetric error function is a good measure, with differing opinions on the implications of its properties and the context of its application.

Contextual Notes

The discussion highlights the need for clarity on the definitions of "good" in the context of error measurement and the specific applications being considered.

hunt_mat
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I have an error, denoted [itex]e(x,y)[/itex] for example. It's not a norm and it isn't symmetric, that is to say: [itex]e(x,y)\neq e(y,x)[/itex].

My question is simply this: With such properties, is the choice of such a function a good one?
 
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I suppose that depends on what you want to do with it.
If your goal is to show that the error is bounded, then you should not need the properties of norms and symmetry, although those properties can simplify your proof.
 
I'm not worried about showing it's bounded but if it's a good measure of error with it being non-symmetric.
 
What defines "good"? What do you want to do with this number?
Also, what are x and y?
 
Okay, I am trying to compare two different positions and orientations of a drill. The x and y are elements of SE(3).
 
Something like expected and real position? Then I don't see anything wrong with an asymmetry - as an example, "drill too low" could be much worse/better than "drill too high".
 

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