few questions on geometry angle loss about social-implicit HOT 3 CLOSED

Thanks for asking:
For the first point:
It calcs the cosine similarity between two (nodes). Each node location can be seen as a vector and we calc the the cosine angle between both. Your interpretation is correct and the figure should be updated.

So we are comparing these two angles:

For the second point:
We used relative velocity with the first point as a normalization method for the trajectories. So in a sense it is velocities.

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Thank you very much for the clarification and figure.

One last question, if V_pred and V_target are velocities, is the calculation G-distance loss at

consistent with the description in the above figure? We are not matching the intra-distance between the locations $t$ and $j$ but instead dealing with velocities.

I think for g-distance loss, the V_pred_min_ and V_target_ in line 112 should be absolute points instead of velocities. Please correct me if I'm wrong.

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We are dealing with velocities from normalization point of view but originally they are distance.
The normalization of trajectories can be done by:
1- Relative difference between steps = velocity per each step
2- Divide by a fixe large amount = keep distance
3- Difference with origin point or last point = velocity w.r.t to the origin or last point

In our case, we do the matching between intra velocities vector, but one can change it based on normalization choice. For example, if I used the abs positions it will explode the gradients. Overall, you are correct in your interpretation but I wanted to highlight the issue of normalization and it is impact on describing the intent of the loss function design.

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