Created: July 15, 2021
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Last Modified: October 15, 2025
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Time Weighted Similarity (TWS)
Linked to from “High Performance Spatiotemporal Trajectory Matching”
The formula for the Time Weighted Similarity is given as follows:
\[TWS(T_1,T_2)=\frac {\int _α ^β m(p_1(t),\ p_2(t))dt} {β_1-α_1}\]Whereas:
- $m(.,.)$ is the Point similarity function.
- $β_1-α_1$ is the duration of the trajectory
For computational purposes, the following approximation can be used;
\[\int _α ^β m(p_1(t),\ p_2(t))dt \approx \frac {1} {2} \sum _{i=1} ^{n-1} (m_i + m_{i+1})(t_{i+1}-t_i)\]Whereas;
- $t_i$ denotes the timestamp after interpolation.
- $m_i$ dnotes the point similarity of two trajectories at timestamp $t_i$.
The “time weighted segment score”: $(m_i+m_{i+1})(t_{i+1-t_i})$