SPOP: Time Series Compression with Quadratic Splines

Time series compression is an important topic, enabling long signals to be represented in a small number of parameters while denoising. Change-point detection methods offer a relevant framework for tackling this task. In this paper, we propose a new algorithm to approximate time series as piecewise quadratic functions with continuity constraints. We propose a dynamic programming recursion to compute the optimal solution to this problem and an approximation algorithm with quadratic complexity that locally discretizes the spaces of admissible values at change points and initial first derivatives. We validate its performance on signals from a real data set and on synthetic signals.