Good features of paths for machine learning

Question

I'm looking into ML problems (mostly density estimation and anomaly detection) with paths made up of coordinates (GPS). Other than the coordinates themselves and deltas (changes between adjacent coordinate points) and polar coordinates what are some other good features? What features make intuitive attributes like straightness, curvy-ness, smoothness, and loopy-ness explicit?

Answer 1

For straightness/curviness you may want to calculate an approximate first derivative of the curve, for smoothness the second and higher derivatives. If by loopiness you mean the tendency to return to places several times, you could for instance count how many segments intersect each other.