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.

$\dpi{300} \bg_white f: \{ \rm{space} \} \to \{\rm{another\ space} \}$

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.

Techniques include:

• 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.

hi-res