hammad93
commented
10 months ago The differences in distance is on a cartesian plane for things like mean squared error but it should be in a spherical coordinate plane. This more accurately describes the error in real distance.
https://mathworld.wolfram.com/CircularSegment.html
If we take the arithmetic difference between the two coordinates, it will produce the length in the diagram a or chord length but we are trying to get the arc length, s
We might need to find another way to implement our error functions like Mean Squared Error or Mean Average Percent Error such that it is taking the arc length since this more accurate models the position and distance a tropical storm travels.
When understanding something like mean squared error as a loss for the neurons in a machine learning model, the formula wants to calculate the difference between two values. When these two values represent geographic locations like latitude and longitude, arithmetic subtraction is not an accurate estimate of the distance. We have to incorporate the Great Circle calculations with a projection like WGS84 to get a better estimate of the distance.
Because the neural network optimizes based on this loss, a custom loss function that is similar to mean squared error but incorporates the error of geographic coordinates utilizing the Great Circle formula will likely do better on validating steps that also utilize the Great Circle formula.