Engineering Commons^™

Knot Optimization For Univariate Cubic L^1 Spline Fits With Application In Change Point Detection, Manfei Xie

Graduate Research Theses & Dissertations

Cubic $L^1$ spline fits, as a type of $L^1$ approximating splines, have shown superior performance in shape preservation of geometric data with great changes. To better construct a cubic $L^1$ spline fit, the number and the location of the spline knots should be optimized rather than predetermined. This research investigates knot optimization methods for univariate cubic $L^1$ spline fits. When the number of knots is given, we design an optimization-based method to determine the best location of the knots. When the number and the location are unknown, we propose a heuristic method to find proper knot number and location. Numerical …