A Learning Algorithm for Optimal Representation of Experimental Data

Abstract

We have developed a procedure for finding optimal representations of experimental data. Criteria for optimality vary according to context; an optimal state space representation will be one that best suits one’s stated goal for reconstruction. We consider an ∞-dimensional set of possible reconstruction coordinate systems that include time delays, derivatives, and many other possible coordinates; and any optimality criterion is specified as a real valued functional on this space. We present a method for finding the optima using a learning algorithm based upon the genetic algorithm and evolutionary programming. The learning algorithm machinery for finding optimal representations is independent of the definition of optimality, and thus provides a general tool useful in a wide variety of contexts.

Nonlinear Dynamics of Chaotic and Stochastic Systems

“…The same feature is characteristic for the method of moving averages [453]: The same feature is characteristic for the method of moving averages [453]:…”

“…A large number of methods have been developed (see the good survey in [453]) which allow one to identify a state vector. Obviously, the accuracy of derivative computation depends on the sampling step ∆t.…”

Application of nonlinear time series analysis techniques to high-frequency currency exchange data

“…Apart from the methods mentioned above, there are several other methods of reconstructing state space from the observed quantity s(t) that have appeared in the literature -for a critical review see Breeden and Packard (1994). Although the method of reconstruction can make a big difference in the quality of the resulting coordinates, it is not clear in general which method is the best.…”

On‐Line runaway detection in batch reactors using chaos theory techniques

“…There are several methods of reconstructing state space Ž . from the observed quantity Breeden and Packard, 1994 , in Ž . our case the temperature T t .…”