https://code.usgs.gov/lcmap/research/Harmonic-Adaptive-Penalty-Operator-HAPO-
HAPO introduced a new penalty function to minimize unnecessary fluctuations in the harmonic regression model, reducing the over-fitting issue in time series (https://doi.org/10.1016/j.isprsjprs.2022.01.006).
Zhou, Q., Zhu, Z., Xian, G. and Li, C., 2022. A novel regression method for harmonic analysis of time series. ISPRS Journal of Photogrammetry and Remote Sensing, 185, pp.48-61.
The figure demonstrates the different regression models derived from the four methods for a Landsat NIR surface reflectance time series with a large gap between March and August, in which HAPO is the only method that is not impacted by this data gap (∼ 4 months) (HAPO: Harmonic Adaptive Penalty Operator; LASSO: least absolute shrinkage and selection operator; OLS: ordinary least squares; and Ridge: Ridge regression). The observation data are acquired from Landsat Analysis Ready Data (ARD) products (https://earthexplorer.usgs.gov/). The location is grassland near Montgomery, Alabama, USA (Latitude: 32.408041°, Longitude −86.272600°).
It's highly recommended to do all your development & testing in anaconda virtual environment.
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python3-dev
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python-virtualenv
Required modules
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numpy>=1.18.1
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scikit-learn>=0.22.1
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scipy>=1.4.1
Please run the test.py to get the following plot
