Pattern Discovery from Power Spectra: An Overview and Report on Recent Developments
Dynamics of Learning Seminar
Santa Fe Institute
March 2004
Abstract:
Power Spectra are common representations of data for many complex,
disordered systems. Traditional techniques of analysis have often centered
on finding auto correlation functions that are then used to characterize
the underlying dynamics responsible for the spectrum. A significant task,
though, is to build a model of the underlying dynamics that can reproduce
the spectrum as well as allow for the calculation of parameters of
physical interest. In this talk, I will review basic notions of power
spectra and auto correlation functions. I will discuss the difficulties
inherent to ``inverting" a power spectrum to find a statistical description
of the underlying dynamics. I will briefly review some past attempts at
solving this problem in the context of x-ray diffraction spectra and
discuss their shortcomings, including their limitation to block Markovian
processes and the generation of unphysical dynamics. I will finally
outline a new algorithm based on a maximum entropy principle that shows
promise in overcoming many of these difficulties.