Fitting optimal piecewise linear functions using genetic algorithms

Constructing a model for data in R-2 is a common problem in many scientific fields, including pattern recognition, computer vision, and applied mathem atics. Often little is known about the process which generated the data or its statistical properties. For example, in fitting a piecewise linear mode l, the number of pieces, as well as the knot locations, may be unknown. Hen ce, the method used to build the statistical model should have few assumpti ons, yet, still provide a model that is optimal in some sense. Such methods can be designed through the use of genetic algorithms. In this paper, we e xamine the use of genetic algorithms to fit piecewise linear functions to d ata in R-2. The number of pieces, the location of the knots, and the underl ying distribution of the data are assumed to be unknown. We discuss existin g methods which attempt to solve this problem and introduce a new method wh ich employs genetic algorithms to optimize the number and location of the p ieces. Experimental results are presented which demonstrate the performance of our method and compare it to the performance of several existing method s. We conclude that our method represents a valuable tool for fitting both robust and nonrobust piecewise linear functions.