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Analysing spectroscopy data using two-step group penalized partial least squares regression

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Abstract

A statistical challenge to analyse hyperspectral data is the multicollinearity between spectral bands. Partial least squares (PLS) has been extensively used as a dimensionality reduction technique through constructing lower dimensional latent variables from the spectral bands that correlate with the response variables. However, it does not take into account the grouping structure of the full spectrum where spectral subsets may exhibit distinct relationships with the response variables. We propose a two-step group penalized PLS regression approach by performing a PLS regression on each group of predictors identified from a clustering approach in the first step. In the second step, a group penalty is imposed on the latent components to select the group with the highest predictive power. Our proposed method demonstrated a superior prediction performance, higher R-squared value and faster computation time over other PLS variations when applied to simulations and a real-world observational data set. Interpretations of the model performance are illustrated using the real-world data example of leaf spectra to indirectly quantify leaf traits. The method is implemented in an R package called “groupPLS”, which is accessible from github.com/jialiwang1211/groupPLS.

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Acknowledgements

The authors would like to thank Dr. Klara L Verbyla and Dr. Alexander B Zwart for their insightful discussions and comments. Dr. William Woodgate is supported by an Australian Research Council DECRA Fellowship (DE190101182). The OzFlux and SuperSite network is supported by the National Collaborative Infrastructure Strategy (NCRIS) through the Terrestrial Ecosystem Research Network (TERN).

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Authors and Affiliations

  1. Research School of Finance, Acturial Studies and Statistics, College of Business and Economics, The Australia National University, Canberra, ACT, Australia

    Le Chang

  2. Data61, Commonwealth Scientific and Industrial Research Organisation, Canberra, ACT, Australia

    Jiali Wang

  3. Land and Water, Commonwealth Scientific and Industrial Research Organisation, Canberra, ACT, Australia

    William Woodgate

  4. School of Earth and Environmental Sciences, The University of Queensland, Brisbane, QLD, Australia

    William Woodgate

Authors
  1. Le Chang
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  2. Jiali Wang
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  3. William Woodgate
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Corresponding author

Correspondence to Jiali Wang.

Additional information

Communicated by Pierre Dutilleul.

Appendix

Appendix

Fig. 8
figure 8

Root mean squared prediction error (RMSPE) for predicting Carotene (\(\mu g~cm^{-2}\)), Chlorophyll (\(\mu g~cm^{-2}\)), EPS and Weight (g) by the six methods in the eucalypt data set

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Fig. 9
figure 9

R-squared value (\(R^2\)) for Carotene (\(\mu g~cm^{-2}\)), Chlorophyll (\(\mu g~cm^{-2}\)), EPS and Weight (g) by the six methods in the eucalypt data set

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Table 3 The averages and standard deviations (in brackets) of the root mean squared prediction error (RMSPE) for Carotene (\(\mu g~cm^{-2}\)), Chlorophyll (\(\mu g~cm^{-2}\)), EPS and Weight (g) by the six methods in the eucalypt data set
Full size table
Table 4 The averages and standard deviations (in brackets) of R-squared value (\(R^2\)) for Carotene (\(\mu g~cm^{-2}\)), Chlorophyll (\(\mu g~cm^{-2}\)), EPS and Weight (g) by the six methods in the eucalypt data set
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Chang, L., Wang, J. & Woodgate, W. Analysing spectroscopy data using two-step group penalized partial least squares regression. Environ Ecol Stat 28, 445–467 (2021). https://doi.org/10.1007/s10651-021-00496-2

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  • DOI: https://doi.org/10.1007/s10651-021-00496-2

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