That’s functional in the sense that the data of interest forms a mathematical function or curve, not in the sense that flats are functional and high heels are not.
So say you’re dealing with like a bit of handwriting, or a dinosaur footprint [x(h), y(h)], or a financial time series $(t), or a weather time series [long vector], or a bunch of electrodes all over someone’s brain [short vector], or measuring several points on an athlete’s body to see how they sync up [short vector]. That is not point data. It’s a time series, or a “space series”, or both.
- principal components analysis on the Fourier components
- landmark registration
- using derivatives or differences
- fitting splines
- smoothing and penalties for over-smoothing
The problem you’re always trying to solve is the “big p, small n problem”. Lots of causes (p) and not enough data (n) to resolve them precisely.
You can see all of their examples, with code, at http://www.springerlink.com/content/978-0-387-95414-1.