# 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.