HOPS: A Fast Algorithm for Segmenting Piecewise Polynomials of Arbitrary Orders

The segmentation of piecewise polynomial signals arises in a variety of scientific and engineering fields. When a signal is modeled as a piecewise polynomial, the key then becomes the detection of breakpoints followed by curve fitting and parameter estimation. This paper proposes HOPS, a fast High-Order Polynomial Segmenter, which is based on
$\ell _{0}$
-penalized least-square regression. While the least-squares regression ensures fitting fidelity, the
$\ell _{0}$
penalty takes the number of breakpoints into account. We show that dynamic programming can be applied to find the optimal solution to this problem and that a pruning strategy and matrix factorization can be utilized to accelerate the execution speed. Finally, we provide some illustrative examples, and compare the proposed method with state-of-the-art alternatives.