I am trying to find a way to automatically find the appropriate coordinate system for a physical problem.
For example, in the case of a simple pendulum, polar coordinates are the most appropriate ones. I have the data for the x,y cartesian coordinates of the pendulum at various times. I would like to be able to jump from this to the angular data at a given time.
I feel that this is a form of dimensionality reduction. Could we use auto-encoders for this or are methods such as ISOMAP or CDA more appropriate?
I feel that PCA would not work well for this problem as I need to perform a non-linear dimensionality reduction.