Fitting optimal piecewise linear functions using genetic algorithms

Constructing a model for data in R² is a common problem in many scientific fields, including pattern recognition, computer vision, and applied mathematics. Often little is known about the process which generated the data or its statistical properties. For example, in fitting a piecewise linear model, the number of pieces, as well as the knot locations, may be unknown. Hence, the method used to build the statistical model should have few assumptions, yet, still provide a model that is optimal in some sense. Such methods can be designed through the use of genetic algorithms. We examine the use of genetic algorithms to fit piecewise linear functions to data in R². The number of pieces, the location of the knots, and the underlying distribution of the data are assumed to be unknown. We discuss existing methods which attempt to solve this problem and introduce a new method which employs genetic algorithms to optimize the number and location of the pieces. Experimental results are presented which demonstrate the performance of our method and compare it to the performance of several existing methods, We conclude that our method represents a valuable tool for fitting both robust and nonrobust piecewise linear functions