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-O...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | article |
| Language: | EN |
| Published: |
IEEE
2021
|
| Subjects: | |
| Online Access: | https://doaj.org/article/05e4a3fc584e4cc1a738e960034db8c4 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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 <inline-formula> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula>-penalized least-square regression. While the least-squares regression ensures fitting fidelity, the <inline-formula> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula> 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. |
|---|