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.
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.

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.

f: {space} \to ’ {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