Another tool which might be useful to you is the Linear Directional Mean tool which "Identifies the mean direction, length, and geographic center for a set of lines."
It will not identify the clusters of lines, however. You may have to select these out manually first.
In your example, I see three major clusters of lines - top, middle, and bottom (with an outlier above the top cluster. If the start points are near the coast and the end points are near the middle of the raster, I don't know how you could programmatically select the lines in the cluster by distance.
The reason for this is because there are lines in the top and middle cluster which have endpoints which are closer than the two furthest lines in the middle cluster.
To identify clusters, you may need to look at the start points and endpoints of the lines. If the start points are close together, this may identify the cluster. You may want to look at the Spatial Statistics toolbox to help you identify these areas.
Both the Linear Directional Mean and Spatial Statistics toolbox are available for all license levels of ArcGIS.