M.S. (Master of Science)
Department of Industrial and Systems Engineering
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 experiments show that cubic $L^1$ spline fits with optimized knots can better approximate data and preserve shapes. The cubic $L^1$ spline fits with optimized knots show good potential when applied in change point detection.
Xie, Manfei, "Knot Optimization For Univariate Cubic L^1 Spline Fits with Application in Change Point Detection" (2019). Graduate Research Theses & Dissertations. 7793.
Northern Illinois University
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