Pattern Discovery from Power Spectra: An Overview and Report on Recent Developments

Dynamics of Learning Seminar

Santa Fe Institute

March 2004


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.

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