Fitting Piecewise Linear Functions Using Particle Swarm Optimization

The problem of determining a piecewise linear model for 2-dimensional data is commonly encountered by researchers in countless fields of scientific study. Examples of the problem or challenge are that of 2-dimensional digital curves, reliability, and applied mathematics. Nevertheless, in solving the problem, researchers are typically constrained by the lack of prior knowledge of the shape of the curve. Therefore, fitting a piecewise linear curve into a given set of data points is a useful technique. Moreover, any 2-dimensional continuous curve can be approximated arbitrarily by a piecewise linear function. In fitting a piecewise linear model, the number of segments and knot locations may be unknown. Several techniques can be employed, such as genetic algorithms as well as the least square error function, but not all techniques can guarantee convergence to a near optimal. In this paper, a method which employs the particle swarm optimization as the primary model fitting tool is introduced. The aim is to approximate a curve by optimizing the number of segments as well as their knot locations with fixed initial and final points. The experimental results which reveal the performance of the proposed algorithm are also presented.