Best distance measure to use to compare vectors of angles

Context

I have two sets of data that I want to compare. Each data element in both sets is a vector containing 22 angles (all between $-\pi$ and $\pi$). The angles relate to a given human pose configuration, so a pose is defined by 22 joint angles.

What I am ultimately trying to do is determine the “closeness” of the two sets of data. So for each pose (22D vector) in one set, I want to find its nearest neighbour in the other set, and create a distance plot for each of the closest pairs.

Questions

  • Can I simply use Euclidean distance?
    • To be meaningful, I assume that the distance metric would need to be defined as: $\theta = |\theta_1 – \theta_2| \quad mod \quad \pi$, where $|…|$ is absolute value and mod is modulo. Then using the resulting 22 thetas, I can perform the standard Euclidean distance calculation, $\sqrt{t_1^2 + t_2^2 + \ldots + t_{22}^2}$.
    • Is this correct?
  • Would another distance metric be more useful, such as chi-square, or Bhattacharyya, or some other metric? If so, could you please provide some insight as to why.

Answer

you can calculate the covariance matrix for each set and then calculate the Hausdorff distance between the two set using the Mahalanobis distance.

The Mahalanobis distance is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set and is scale-invariant.

Attribution
Source : Link , Question Author : Josh , Answer Author : skyde

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