Table 4 Group GPS features extracted per time window and cow

Net distances to other cows

Mean

Median

Minimum

# cows within 2 m radius

# cows within 4 m radius

# cows within 8 m radius

# cows within 16 m radius

All mean cow coordinates

Group elongation index, φ

Variance explained by the first principal component through the mean x and y coordinates of all cows. Value lies by definition between 0.5 (when completely non-elongated, e.g., an exact circle) and 1 (when all coordinates lie on a straight line). Afterwards scaled between 0 and 1, by subtracting 0.5 and multiplying by 2.

Group area proxy

πσ²(1 − φ); where σ is the standard deviation of the first principal component values. This measure assumes that the area can be estimated by considering the group as an ellipse. When completely non-elongated the area is πσ² (where the variance σ² is a proxy for the extent of the direction of elongation) and when fully elongated the area is 0.

Directions to other cows

ρ

Length of the mean resultant vector

Periphery index

Maximum difference between consecutive directions, minus \( \frac{2\pi }{\# cows-1} \) and divided by 2π