Abstract. The number of samples used in the calibration data set affects the quality of the generated predictive models using visible, near and shortwave infrared (VIS–NIR–SWIR) spectroscopy for soil attributes. Recently, the convolutional neural network (CNN) has been regarded as a highly accurate model for predicting soil properties on a large database. However, it has not yet been ascertained how large the sample size should be for CNN model to be effective. This paper investigates the effect of the training sample size on the accuracy of deep learning and machine learning models. It aims at providing an estimate of how many calibration samples are needed to improve the model performance of soil properties predictions with CNN as compared to conventional machine learning models. In addition, this paper also looks at a way to interpret the CNN models, which are commonly labelled as a black box. It is hypothesised that the performance of machine learning models will increase with an increasing number of training samples, but it will plateau when it reaches a certain number, while the performance of CNN will keep improving. The performances of two machine learning models (partial least squares regression – PLSR; Cubist) are compared against the CNN model. A VIS–NIR–SWIR spectra library from Brazil, containing 4251 unique sites with averages of two to three samples per depth (a total of 12 044 samples), was divided into calibration (3188 sites) and validation (1063 sites) sets. A subset of the calibration data set was then created to represent a smaller calibration data set ranging from 125, 300, 500, 1000, 1500, 2000, 2500 and 2700 unique sites, which is equivalent to a sample size of approximately 350, 840, 1400, 2800, 4200, 5600, 7000 and 7650. All three models (PLSR, Cubist and CNN) were generated for each sample size of the unique sites for the prediction of five different soil properties, i.e. cation exchange capacity, organic carbon, sand, silt and clay content. These calibration subset sampling processes and modelling were repeated 10 times to provide a better representation of the model performances. Learning curves showed that the accuracy increased with an increasing number of training samples. At a lower number of samples (< 1000), PLSR and Cubist performed better than CNN. The performance of CNN outweighed the PLSR and Cubist model at a sample size of 1500 and 1800, respectively. It can be recommended that deep learning is most efficient for spectra modelling for sample sizes above 2000. The accuracy of the PLSR and Cubist model seems to reach a plateau above sample sizes of 4200 and 5000, respectively, while the accuracy of CNN has not plateaued. A sensitivity analysis of the CNN model demonstrated its ability to determine important wavelengths region that affected the predictions of various soil attributes.
The effect of sample size on different machine learning models for groundwater potential mapping in mountain bedrock aquifers
