Discovering Key Sub-Trajectories to Explain Traffic Prediction

. 2022 Dec 23;23(1):130. doi: 10.3390/s23010130

Algorithm 2 Trajectory Shapley maximum coverage

Input:
The Trajectory Shapley set M calculated by Algorithm 1,
Trajectories set

P = {T_{1}, \dots, T_{| N |}}

in t time slot,
Submodular distance threshold

ω

.
Output:

O = {N

sub-trajectories}

1:
Initialize the trajectories Shapley subsets $S = \{ϕ (T_{i}) ∣ ϕ (T_{i}) \neq 0 \land ϕ (T_{i}) \in M\}$
2:
Initialize the trajectories subsets $K = \{T_{i} ∣ T_{i} \in P \land ϕ (T_{i}) \in M\}$
3:
Initialize segment set $R = {\emptyset}$ , segment Shapley set $S = {\emptyset}$ , segment distance matrix D
4:
for all trajectory $T_{i}$ in $P$ do
5:
Run approximate trajectory partitioning algorithm for $T_{i}$
6:
Add segment set Q to R
7:
for all segment $L_{i}$ in Q do
8:
Rerun Algorithm 1 for $L_{i}$ , adding $ϕ (L_{i})$ to S
9:
end for
10:
end for
11:
for all segment $L_{i}$ in Q do
12:
for all segment $L_{j}$ in Q do
13:
Calculate $d_{L_{i}} (L_{i}, L_{j})$ and $d_{L_{j}} (L_{i}, L_{j})$ using Equation (9).
14:
Set $D (L_{i}, L_{j}) = d_{L_{i}} (L_{i}, L_{j})$ and $D (L_{j}, L_{i}) = d_{L_{j}} (L_{i}, L_{j})$
15:
end for
16:
end for
17:
Set $D = \{1 ∣ D (i, j) \leq ω\}$ and $D = \{0 ∣ D (i, j) > ω\}$
18:
Run greedy max cover algorithm and find N common patterns.
19:
return O