Linked to from “High Performance Spatiotemporal Trajectory Matching”
Space Weighted Similarity (SWS)
The formula to the Space Weighted Similarity is:
\[SWS(T_1,T_2)=\frac {\int _α ^β m(p_1(t),\ p_2(t))v_1(t)dt} {\int _{α_1} ^{β_1} v_1(t)dt}\]Whereas;
- $m(.,.)$ is the Point similarity function.
- $v_1(t)$ denotes the velocity of $T_1$ at time $t$.
To simplify computation the following approximation can be used: \(\int _α ^β m(p_1(t),\ p_2(t))v_1(t)dt \approx \frac {1} {2} \sum _{i=1} ^{n-1} (m_i+m_{i+1})l_i)\)
Whereas;
- $t_i$ denotes the timestamp after interpolation.
- $m_i$ dnotes the point similarity of two trajectories at timestamp $t_i$.
- $l_i$ denotes the length of line segment of $T_1$ between timestamp $t_i$ and $t_{i+1}$.
The “space weighted segment score”: $(m_i+m_{i+1})l_i$
Making sense of the meaning of $v_1(t)dt$ I am turning to dimensionality analysis; the units of which would be $m/s\cdot s$ therefore denoting the distance covered over the course of the set. This is in fact backed by the comment within the paper: “… Then divide the result by the duration or total distance of $T_a$ …” Time weighted Similarity (TWS)