Adaptive spline fitting with particle swarm optimization
This work addresses a specific bottleneck in spline fitting for data analysis, offering an incremental improvement over existing methods.
The paper tackled the problem of optimal knot placement in spline fitting, which is a high-dimensional and non-convex optimization challenge, by using particle swarm optimization (PSO) with regularization to mitigate overfitting, resulting in significantly improved performance on noisy data.
In fitting data with a spline, finding the optimal placement of knots can significantly improve the quality of the fit. However, the challenging high-dimensional and non-convex optimization problem associated with completely free knot placement has been a major roadblock in using this approach. We present a method that uses particle swarm optimization (PSO) combined with model selection to address this challenge. The problem of overfitting due to knot clustering that accompanies free knot placement is mitigated in this method by explicit regularization, resulting in a significantly improved performance on highly noisy data. The principal design choices available in the method are delineated and a statistically rigorous study of their effect on performance is carried out using simulated data and a wide variety of benchmark functions. Our results demonstrate that PSO-based free knot placement leads to a viable and flexible adaptive spline fitting approach that allows the fitting of both smooth and non-smooth functions.