Table 1.

Movement similarity measures and their characteristics.

Similarity measure	Movement parameter	Purpose	Primary/ Derived	Topological/ Quantitativ	Complexity
Allen’s temporal logic	Time instance, time interval	des, beh	P	T	–
Temporal distance	Time instance, time interval, spatiotemporal position	des, beh	P	Q	L
Relational operators	Duration, distance, range, heading, shape, speed, acceleration, change of direction	des, beh	D	T	L
Quantitative difference	Duration, distance, range, heading, shape, speed, acceleration, change of direction	des, beh	D	Q	L
9-intersection	Spatial position, path	des, beh	P	T	–
Euclidean distance	Spatial position, path, spatiotemporal position, trajectory	clust, sim,	P	Q	M
Minkowski distance (e.g. Manhattan distance)	Spatial and spatiotemporal position	des	P	Q	L
Distance along curved surface	Spatial and spatiotemporal position	des	P	Q	L
Network distance	Spatial and spatiotemporal position	des	P	Q	M
Relative direction	Spatial and spatiotemporal position	des	P	–	L
Cardinal directions	Spatial and spatiotemporal position	des	P	Q	L
REMO	Heading	beh	D	Q	–
Common source and destination	Path	clust	P	Q	L
Common route	Path	clust, beh	P	Q	M
Haussdorff	Path	clust, out	P	Q	H
k points	Path	clust	P	Q	L–M
OWD	Path	sim	P	Q	L
LIP	Path	clust	P	Q	L
PCA	Path	clust	P	Q	L
Combined angular distance perpendicular distance and parallel distance	Line	sim	P	Q	L
Directional similarity	Heading	sim	D	Q	L
Head–body–tail relations	Line, (sub-)trajectory	des	P	T	–
DTW	Trajectory, shape	clust	P, D	Q	M
Squared Euclidean	Shape	sim	D	Q	M
Double cross calculus	Spatiotemporal position	des	P	T	–
QTC	Spatiotemporal position, speed, acceleration	des, beh	P, D	T	–
k-nearest neighbor	Spatiotemporal position	sim	P	Q	–
LCSS	Path, trajectory	clust, sim	P	Q	M
Time steps	Trajectory	clust	P	Q	L–M
Common route and dynamics	Trajectory	clust, beh	P	Q	H
Fréchet	Trajectory	clust	P	Q	H
EDR	Path, trajectory	sim, clust	P	Q	M
Lifeline distance	Trajectory	clust	P	Q	–
HMM	Spatiotemporal position, trajectory	out	P	Q	H
STLIP	Trajectory	clust	P	Q	L
Speed-pattern based similarity	Speed	clust	D	Q	L
NWED	Speed, acceleration	sim, clust	D	Q	M

Note: Purpose: sim = similarity search, clust = clustering, beh = behavior analysis, des = description, out = outlier detection; Primary/Derived: P = primary, D = derived; Topological/Quantitative: T = topological, Q = quantitative; Complexity: L = low, M = medium, H = high.