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How to find distance between 2 points when dimensions are all of different nature?

Artificial Intelligence Asked by Manish Kausik Hari Baskar on January 23, 2021

I have a dataset with four features:

  • the x coordinate
  • the y coordinate
  • the velocity magnitude
  • angle

Now, I want to measure the distance between two points in the dataset, taking into account the facts that the angle dimension is toroidal, and taking into account the difference in nature of the dimensions (2 of them are distances, one of them is velocity magnitude, and the other an angle).

What kind of distance function would suit this need?

If I have to go for an $L^p$ norm, can I determine which value of $p$ would be apt by some means?

Also, if you are aware, please, let me know how such problems have been solved in various applications.

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