Algorithm 1. The Improved Center Clustering Algorithm

1: Input: k //the number of clusters

2:     $\xi$ //the threshold value

3:      $l_i,i=1,\dots ,m$ //the label of every trajectory

4: Output: the cluster results

5: /*Abnormal trajectories detection*/

6:  (a) IF ${\xi }_i\ge \xi$

7:    then $l_i=0$, the trajectory perhaps is abnormal.

8:     /*Identifying abnormal trajectories*/

9:     if SOG = 0, or $SOG>2V_{average}$, or $COG[(t_i-t_{i+1})>2\min ]>{30}^{\circ }$

10:     // $V_{average}=({\displaystyle \sum _{i=1}^{C_m^2}{V}_i})/C_m^2$, $V_i,i=1,\dots ,m$ denotes the speed of every vessel.

11:     // $t_i-t_{i+1}$ means the time difference.

12:      then delete the abnormal trajectories.

13:     else

14:     modify $l_i=1$.

15:     end

16:  (b) ELSE

17:    then $l_i=1$, normal trajectories, enter the next step.

18:    end

19: /*The clustering center automatic selection algorithm*/

20: for k = 2 to m do

21:  (a) IF k = 2

22:    then the two trajectories corresponding to the maximum distance are taken as the clustering centers.

23:   end

24:  (b) ELSE

25:    find the top k maximum distance

26:    if the top k maximum distance are the distance among k trajectories,

27:      then the k trajectories are taken as the clustering centers.

28:    end

29:      if the top k distance are formed by the [k + 1, 2k] trajectories,

30:      then choose the k trajectories which are repeated most often as the cluster centers.

31:     end

32:   end

33: /*Cluster analysis and trajectory pattern mining*/

34: (a) The trajectories are grouped into k clusters

35:   // Trajectory clustering according to the known k centers.

36: (b) Cluster analysis

37:   // Find the custom routes and make safety routes.