Machine Learning and Feature Selection for soil spectroscopy. An evaluation of Random Forest wrappers to predict soil organic matter, clay, and carbonates

Heliyon 10 (2024) e30228 Available online 25 April 2024 2405-8440/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Research article Machine Learning and Feature Selection for soil spectroscopy. An evaluation of Random Forest wrappers to predict soil organic matter, clay, and carbonates Francisco M. Canero a , * , Victor Rodriguez-Galiano a , David Aragones b a Department of Physical Geography and Regional Geographic Analysis, Universidad de Sevilla, 41004, Seville, Spain b Remote Sensing and Geographic Information Systems Lab (LAST-EBD), Do˜ nana Biological Station, C.S.I.C., 41092, Seville, Spain ARTICLE INFO Keywords: Random forest Sequential flotant selection Sequential flotant forward selection Partial least squares regression Wrapper methods Sierra de las nieves ABSTRACT Soil spectroscopy estimates soil properties using the absorption features in soil spectra. However, modelling soil properties with soil spectroscopy is challenging due to the high dimensionality of spectral data. Feature Selection wrapper methods are promising approaches to reduce the dimensionality but are barely used in soil spectroscopy. The aim of this study is to evaluate the performance of two feature selection wrapper methods, Sequential Forward Selection (SFS) and Sequential Flotant Forward Selection (SFFS) built using the Random Forest (RF) algorithm, for dimensionality reduction of spectral data and predictive modelling of modelling soil organic matter (SOM), clay and carbonates. The reflectance of 100 soil samples, acquired from Sierra de las Nieves (Spain), was measured under laboratory conditions using ASD FieldSpec Pro JR. Four different datasets were obtained after applying two spectral preprocessing methods to raw spectra: raw spectra, Continuum Removal (CR), Multiplicative Scatter Correction (MSC), and a socalled “Global” dataset composed of raw, CR and MSC features. The performance of RF models built with feature selection methods was compared to that of Partial Least Squares Regression (PLSR) and RF (alone). RF models built with SFS and SFFS outperformed PLSR and RF alone models: The best RF models with feature selection had a respective ratio of performance to interquartile distance of 1.93, 0.38 and 2.56. PLSR models had an accuracy of 1.41, 0.29 and 1.81 for SOM, carbonates, and clay, respectively. RF alone had a respective performance of 1.29, 0.29 and 1.81. The application of feature selection wrapper methods reduced the number of features to less than 1 % of the starting features. Features were selected across all spectra for SOM and clay, and around 900 nm, 1900 nm, and 2350 nm for carbonates. However, feature selection highlighted features around 1100 nm in SOM modelling, as well as other features around 2200 nm, which is considered a main absorption feature of clay. The application of feature selection with Random Forest was very important in improving modelling accuracy, reducing the redundant features and avoiding the curse of dimensionality or Hughes effect. Thus, this research showed an alternative to dimensionality reduction approaches that have been applied to date to model soil properties with spectroscopy and paves the way for further scientific investigation based on feature selection methods and machine learning. * Corresponding author. E-mail address: [email protected] (F.M. Canero). Contents lists available at ScienceDirect Heliyon journal homepage: www.cell.com/heliyon https://doi.org/10.1016/j.heliyon.2024.e30228 Received 5 October 2023; Received in revised form 19 April 2024; Accepted 22 April 2024 Heliyon 10 (2024) e30228 2 1. Introduction Spectroscopy deals with the absorption, emission and reflection of electromagnetic radiation by atoms and molecules [1]. Soil spectroscopy allows the estimation of spectrally active properties of soil [2,3] by studying the absorption features derived from their chemical composition and structure [4–6]. Some examples of spectrally active soil properties include minerals (clays, iron and carbonates), soil organic matter (SOM), moisture content and hygroscopic water [7]. Each soil property responds to different regions of the visible and near-infrared spectrum (vis-NIR-SWIR, i.e., 400–2500 nm). Clays and carbonates have their main absorption features around 2200 nm and 2350 nm, respectively [8,9], due to vibration overtones and combination modes of functional groups presents in clay and carbonates chemical structure. SOM and iron minerals could be primarily assessed with visible spectrum due to electron transition in atoms [10]. Moisture content leads to reduced reflectivity throughout the spectrum [11,12], with a greater impact on their relative absorption features, around 1400 and 1900 nm, and throughout the shortwave infrared spectrum [13]. A step of paramount importance in spectroscopic analysis prior to modelling is the application of spectral preprocessing (or pretreatment) methods [14]. These methods transform the spectral signal reducing the irrelevant information and improving model robustness [15]. Spectral preprocessing methods are also used to linearize the often non-linear relationship between spectral data and soil properties [16]. Furthermore, spectral preprocessing enhances absorption features and reduce the physical effects and noise in spectroscopy measurements [17]. Different spectral preprocessing methods are Continuum Removal [18], Multiplicative Scatter Correction [19], first derivative of spectra or Standard Normal Variate [20]. Predictive modelling of soil properties using spectroscopy has been performed using different linear modelling algorithms such as Multiple Linear Regression or Partial Least Squares Regression [21,22]. More recently, soil properties modelling with spectral data has benefited from the development of machine learning (ML) algorithms [23,24]. ML is a subfield of artificial intelligence inspired in biological learning [25]. ML groups together a series of algorithms for predictive modelling based on pattern recognition, such as Random Forest (RF) [25], Gradient Boosting (GB) [26] or Support Vector Machine (SVM) [27]. Different ML algorithms have been used in soil spectroscopy, including RF [28–30], SVM [31,32], GB [33], a comparison of different ML algorithms [34,35] and even the use of Deep Learning algorithms [36,37] such as Convolutional Neural Networks [38]. ML algorithms have a series of advantages compared to linear algorithms, including the ability to establish non-linear relationships among data and no assumption of normality for predictor features [39], which could have a positive impact, i.e. greater ML accuracy compared to linear algorithms in complex feature spaces [40]. Modelling soil properties using spectroscopy is challenging as spectral data are high-dimensional. Modern spectrometers have a spectral sampling near to 1 nm, resulting in more than two thousand features (i.e. wavelengths) in vis-NIR-SWIR range. However, as absorption features are located in specific parts of spectrum, most features are non-informative, which might explain the decrease in the accuracy of models if the overall spectrum is used [41]. This phenomenon is known as Hughes effect or “dimensionality curse” [42, 43], which can be addressed through ML procedures. Two main approaches have been used to deal with Hughes effect in ML, feature extraction and feature selection [44]. Feature extraction reduces the number of features prior to modelling by creating new features from existing ones. Feature extraction is embedded in some modelling algorithms such as Principal Component Regression and PLSR, therefore its use has been common in spectroscopy studies. The main issue related to feature extraction is that non-informative features are not eliminated and thus are projected in the extracted features [45]. Feature selection is a process related to predictive modelling that selects a subset of original features with the aim of reducing the dimensionality of a dataset according to a specific criterion [46]. Selecting the optimal subset involves avoiding the Hughes effect, therefore improving modelling accuracy. Moreover, the optimal subset might be related with underlying physical processes that explain modelling results [47]. Feature Selection brings together three different methods: filters, embedded and wrapper [48]. Filters methods are independent from ML algorithms [49]. Embedded methods perform the selection during the training process, and are included into specific ML algorithms [50]. Wrapper methods combine a given predictive modelling method with a feature-search strategy, selecting the optimal subset based on a given criterion [50]. This latter method is considered of better performance than filter and embedded methods [51,52]. The use of different feature selection methods has been reported in soil spectroscopy: mutual information based filters [41,53], embedded feature selection methods built with PLSR, such as Variable Importance in Projection [54,55], feature selection wrapper methods built with PLSR, such as Competitive Adaptive Reweighted Sampling [34,56,57]; and genetic algorithms [58,59]. Moreover, recent studies have benchmarked different Features Selection methods [37,60], stating that the best Feature Selection methods depends on the dataset and modelling algorithm used. This study provides a novel insight into the use of two feature selection wrapper methods, Sequential Forward Selection (SFS) and Sequential Flotant Forward Selection (SFFS) within the framework of soil modelling using vis-NIR-SWIR reflectance. Both methods are sequential forward search algorithms that select features one by one by adding features starting from an empty subset using a greedy procedure [61]. Forward search strategies are particularly computationally advantageous and robust against overfitting [62]. SFS and SFFS methods have not been used in soil vis-NIR-SWIR spectroscopy, although similar sequential Feature Selection methods have achieved good results [60]. Harefa and Zhou [63] did use four ML algorithms built with SFS using laser-induced breakdown spectroscopy to predict soil classes, with a better performance of models built with SFS. This study also examines the usefulness of combining different datasets (raw and preprocessed spectra) in a unique dataset. Raw and preprocessed spectra are usually modelled separately, as this may lead to a dramatic increase in the dataset’s dimensionality. Therefore, the objective of his study is three-fold, where two of the objectives are modelling-related, and the latter one is related to dimensionality reduction. The first objective is assessing the performance of Sequential Forward Selection and Sequential Flotant Forward Selection methods built with Random Forest compared to RF alone (using an embedded Feature Selection method) and PLSR (with its own Feature Extraction method for F.M. Canero et al. Heliyon 10 (2024) e30228 3 dimensionality reduction) for soil organic matter (SOM), clay and carbonates predictive modelling. The second objective was comparing the modelling performance of four different datasets, including a raw dataset, Continuum Removal dataset, Multiplicative Scatter Correction dataset, and a global dataset which combines raw, CR and MSC datasets. The third objective was evaluating the application of SFS and SFFS methods to reduce the high dimensionality of spectra data and identify key features in the modelling process. 2. Materials and methods 2.1. Study area The area selected for this study is located in Sierra de las Nieves national park in Malaga, Spain (Fig. 1). The park has an area of approximately 229.79 km 2 , with elevations ranging between 127 and 1917 m (summit of La Torrecilla). The main types of soils are leptosols, eutric cambisols, calcaric cambisols and chromic luvisols [64]. The landcover found in the study area is quite varied: there are forested areas, with species of the genus Abies, Pinus and Quercus [65]; scrublands; grasslands; bare soil and croplands. The lithological substrate is divided into two major sections: peridotite and carbonate rock [66]. These lithologies have a paramount importance in soil formation: cambisols are primarily associated with carbonate lithologies, and luvisols are associated with peridotites. The study area’s climate is distinctly Mediterranean (Csa, under the K¨ oppen-Geiger climate classification), with a dry summer period and abundant precipitation from September to May (mean annual rainfall of 954 mm) [67]. 2.2. Data 2.2.1. Soil sampling A total of 100 topsoil samples were taken between 12 and 20 October 2019. Spatial sampling was designed based on the Third Spanish National Forest Inventory (Tercer Inventario Forestal Nacional de Espa˜ na) [68], a systematic spatial sampling with a 1-km grid distance. Points were selected if they met two conditions: i) located at least 250 m away from roadways, ii) slope of less than 30 % based on the Digital Elevation Model of the National Geographic Institute of Spain (Modelo Digital de Elevaciones del Instituto Geogr´ afico Nacional de Espa˜ na) at a resolution of 5 m. In the field, the exact location of the point was selected, depending on accessibility, in a location within a 100-m buffer of the point. Sampling intensity was also increased in areas with greater soil variability. Soil samples were taken at a depth of 0–10 cm. Fig. 1. Map showing the location of Sierra de las Nieves national park. CRS: WGS84. False colour composition of a Sentinel-2 image from October 2019 (near infrared, red and green bands). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) F.M. Canero et al. Heliyon 10 (2024) e30228 4 Three soil properties were selected as target features: SOM, carbonates content and clay content (measured in percentage). The SOM percentage was determined using loss-on-ignition calcination method, measured as the percentage of weight loss of soil before and after burning away its organic matter (as per UNE-EN 13039:2012, “Soil improvers and growing media - Determination of organic matter content and ash”). The percentage of carbonates was extracted using the Bernard calcimeter method [69,70], which consisted of quantifying the percentage of CO 2 released when the sample was treated with hydrochloric acid. The percentage of clay was taken alongside the other two textural fractions, silt, and sand. Textural fractions were determined using the hydrometer method, also termed densimeter or Bouyoucos method [71]. A total of 100 measurements were taken for SOM and carbonates, and 99 measurements were taken for clay due to an error that occurred when measuring the textural fractions in one sample. 2.2.2. Spectroscopic measurements Spectroscopic measurements were carried out using an ASD FieldSpec Pro JR spectrometer (Analytical Spectral Devices Inc., Boulder, CO, USA). This spectrometer can detect electromagnetic energy across three spectral ranges: the first is in the visible and near infrared range (VNIR, 350–1000 nm), and the latter two are in the shortwave infrared range (SWIR1, 1000–1800 nm) and (SWIR2, 1800–2500 nm). The sensor has a spectral resolution of 3 nm (@ 0.7 μ m) and 30 nm (@ 1.4 μ m, 2.1 μ m), resampled to 1 nm. 250 g of the soil samples were placed into 10-cm Petri dishes. The light source was directed at an angle of incidence of 75◦from the horizontal plane at a distance of 60 cm from the soil sample. Radiance was converted to reflectance using a Spectralon™ white reflectance panel with a reflectivity close to 100 %, and reflectance was recalibrated after every ten soil samples. Ten reflectivity samples were taken for each soil sample and the average was calculated using ViewSpecPro software. The ends of each spectrum (350–399 nm and 2451–2500 nm) were removed due to the noise generated by the spectroradiometer [72]. A total of 2051 predictor features (i.e. wavelength measurements) per spectrum were obtained for each sample. Spectroscopic measurements were taken before the samples were dried out and sieved so that spectral data would resemble data measured under natural conditions via remote sensing or field spectroscopy. Fig. 2. a Median (solid line), minimum and maximum (dashed lines) and p25 and p75 values (dotted lines) by wavelength for raw (top), continuum removal-processed (centre) and multiplicative scatter correction-processed (bottom) spectra. Fig. 2b. Spectra of the minimum, 25th percentile, average, 75th percentile and maximum sample value for SOM (above), carbonates (center) and clay (below). The intensity of the colour refers to position: the whitest spectra is the minimum, while the blackest one is the maximum. Solid line is the average, dotted line refers to 25th and 75th percentiles, and dashed lines refers to minimum and maximum. F.M. Canero et al. Heliyon 10 (2024) e30228 5 2.3. Methods 2.3.1. Spectral preprocessing Two spectral preprocessing methods were used: Continuum Removal (CR) and Multiplicative Scatter Correction (MSC). CR normalises spectra in order to have a common baseline to compare individual absorption features [18] and it also enhances absorption features independent of observation scales and conditions [73]. MSC is a process that corrects the noise generated by physical conditions when measuring reflectance, reducing the internal variability of predictor features [14]. CR and MSC were applied using R [74] with the prospectr 0.2 and pls 2.7–3 packages [75]. Fig. 2a shows the median, maximum, minimum, and 25th and 75th percentile values by wavelength for three datasets: raw spectra, CR spectra and MSC spectra. Some negative values were found around 400–600 nm for MSC spectra, derived from the reference spectrum used in this study, the average spectra. Fig. 2b represents the spectra of the median, minimum, maximum 25th and 75th percentiles samples for each soil property. A bivariate correlations analysis was performed between each soil property and each wavelength (i.e. predictor feature), differentiating between datasets. A fourth dataset, “Global”, was generated by combining the three individual datasets (raw, CR and MSC) containing 6153 predictor features (2051 features per dataset). 2.3.2. Modelling algorithms PLSR is a two-step parametric regression algorithm combining a Feature Extraction method that first extracts latent features from the predictor, and then applies a multivariate linear regression using the latent features [75]. The feature extraction of PLSR performs an iteration using different projections of the predictor dataset to extract the scores and aims to optimise covariance between the extracted scores in feature extraction and the target feature. Targeting the covariance between predictor features and the target feature to improve predictive accuracy differentiates PLSR feature extraction from Principal Component Analysis [76]. PLSR is used for regression problems in disciplines where only a small number of observations are available with a higher dimensionality [77]. PLSR may be more effective than multiple linear regression and other parametric algorithms when a greater number of features are available compared to the number of observations. These datasets may also present multicollinearity [78] or a linear combination could exist between two features, which would make it impossible to use multiple linear regression and other linear algorithms for modelling. The PLSR algorithm was applied in R using the pls 2.7–3 package [79] with the following parameters: plskernel method, a maximum of 10 latent features and a 10-fold cross validation. The one-sigma algorithm was used to select the optimum number of latent features [79]. Variance Importance in Projection (VIP) scores [77] were used to assess feature importance in PLSR modelling. Fig. 2. (continued). F.M. Canero et al. Heliyon 10 (2024) e30228 6 Random Forest (RF) is a machine learning algorithm based on a decision tree ensemble [25,40]. RF is based on a bagging process (or bootstrapping aggregation): each individual tree of the ensemble is grown with different training data subsets that use a random selection of features and observations from the original dataset [42]. The terminal nodes of each individual tree in the RF have an associated simple regression model that applies to that node only. RF computes the output value by averaging the resulting value for all trees (as observed in Fig. 3). The subset composed of unused samples is called “out-of-bag” (OOB), which can be used by individual trees for evaluation purposes. By averaging the individual error of each tree, RF can compute an unbiased and internal estimation of the generalisation error [80]. The advantages of RF with regards to individual decision trees are largely a result of the bagging process [81], that is, its ability to handle complex data structures [82] and its relatively simple hyperparameter tuning process, only requiring two hyperparameters to be tuned: the number of trees (ntree) and the number of selected random features per tree (mtry). The strategy for hyperparameter optimisation in RF was carried out in two steps due to the application of feature selection. The hyperparameter ntree was optimised in a range of 100–2000 trees, at an interval of 100 trees. The second step consisted of applying the feature selection algorithms using the ntree number selected in the previous step for each soil property and dataset combination. 2.3.3. Feature selection Two feature selection wrapper methods were selected, Sequential Forward Selection (SFS) and Sequential Flotant Forward Selection (SFFS). Feature selection wrapper algorithms select a relevant feature subset, evaluating prediction within a modelling algorithm [48]. The process can be outlined in three steps: i) establish an evaluation metric to serve as a feature selection criterion (i.e. Root Mean Square Error (RMSE)), ii) select a search algorithm to choose the order in which feature subsets are evaluated, and iii) train the model. There are several different search algorithms, such as an exhaustive search, genetic algorithms, random search, or sequential search, with the latter being the method used in this study. Sequential searching is defined by the iterative nature of the algorithm [83] and can be run in several ways. Sequential Forward Selection method starts with a set without features, and progressively adds features until an improvement in the accuracy of the models is no longer observed or until a specific number of features is reached. SFFS method works similarly to SFS, but when a subset is defined, a sequential backward selection is applied until the best subset of features is obtained, and SFS will begin again in the event this does not occur. A sequential search was chosen over other search algorithms because there was a better trade-off between performance and computational cost [50], selecting local optimum instead of global optimum. The alpha parameter (search detection threshold) was set at 0.001. RMSE was used as optimisation criteria, and the combination with the lowest RMSE was selected. Both steps were run in R using the mlr 2.17.1 package [84]. 2.3.4. Model evaluation Four performance measures were used: R-squared (R 2 ), RMSE, ratio of performance to deviation (RPD) and ratio of performance to interquartile distance (RPIQ) and the following equations were used for the metrics: R2=1−RSS TSS Fig. 3. RF algorithm diagram. CART=Classification And Regression Trees. Rodriguez-Galiano, Chica-Olmo [80]. F.M. Canero et al. Heliyon 10 (2024) e30228 7 RMSE = ∑n i=1(pi−oi)2 n √ RPD =sd RMSE RPIQ =Q3−Q1 RMSE where: RSS =Residual sum of squares, TSS =Total sum of squares, n =number of observations, p i =predicted ith value, o i =observed value for the ith observation, sd =standard deviation and Q 3 and Q 1 correspond to third and first quartiles. It is worth mentioning that the possible values for R 2 range from negative infinity (worst result) to 1 (best result). An internal model validation was used due to the limited number of samples (n =100). PLSR used 10-fold cross validation. In Random Forest, RMSE was calculated by averaging the measures of error for each tree using out-of-bag data. The optimal hyperparameters and feature subset were identified as those with a lower RMSE. RPIQ was also considered to evaluate the performance of models, as RPD is correlated to R 2 [85]. 3. Results 3.1. Soil analysis and correlations with spectra The boxplots of modelled soil properties are shown in Fig. 4. SOM showed a skewed distribution, with a mean value of 12.19 %, a range of 3.9–42.18 % and a standard deviation of 7.37, with a median value of 10.14 % and values of the first and third quantile of 7.87 % and 13.96 %. Carbonate samples showed a highly skewed distribution, due to the high number of samples with no carbonate content. Mean value of carbonates was 3.99 %, median of 0.25 %, a range of 0–69.6 %, a standard deviation of 9.96 % and an interquartile range of 2.325 %. Clay samples showed a normal distribution, with an average value of 28.55 % and a median of 26 %, a range of 2–64 % and a standard deviation of 13.77 %. First and third quantile of clay were 18 and 37 %. Pearson’s correlation coefficients were −0.03 for SOM and carbonates, 0.39 for SOM and clay, and 0.27 for carbonates and clay. Fig. 5 shows bivariate correlations between each soil property and predictor features (i.e. wavelength) by dataset. Correlation analysis showed higher correlations for SOM and carbonates in their main absorption features (visible region and 2350 nm), while clay had a low correlation with its main absorption feature (around 2200 nm). Moreover, most important correlations between each soil property and spectral data had negative values. The highest correlation for SOM was found around the red visible region (600–700 nm) for all three datasets, with negative values. SOM had its higher correlation in the visible region with the CR dataset than with the MSC and raw datasets, with correlation values greater than 0.7 (being a negative correlation). SOM also showed a high and negative correlation around 2150 and 2250 nm with the CR dataset. Carbonates only had a high and negative correlation around 2350 nm (main absorption feature of carbonates) with the CR dataset. Also, relevant correlations were found around 1200–1400 nm and 1500–1800 nm with the CR dataset, and around 800–1200 nm and 1400–1900 nm with the MSC dataset. Clay had a high and negative correlations with the red visible region of the raw dataset, and around 1400 and 1900 nm with the CR dataset. A high and positive correlation between MSC and clay was found around 1600–1800 nm with the CR dataset. Fig. 4. Boxplot of modelled soil properties. F.M. Canero et al. Heliyon 10 (2024) e30228 8 3.2. Accuracy assessment of the models The results of PLSR models are shown in Table 1. SOM models outperformed clay and carbonates models according to R 2 and RDP, independently of the dataset. However, clay models were more accurate according to RPIQ. SOM-Global was the most accurate model for SOM (R 2 =0.65, RPIQ =1.41), but with similar performance of the other datasets. PLSR models for carbonates showed low values for R 2 (0.12–0.32) and RPIQ (0.25–0.29). The most accurate carbonates model was Carbonates-CR (R 2 =0.32, RPIQ =0.29), but with minimal differences with respect to other predictions. Clay models had similar accuracy, with the R 2 and RPIQ values for Clay-PLSR models ranging between 0.33–0.43 and 1.69–1.83, respectively. The Global clay model was the most accurate model (R 2 =0.43, RPIQ =1.83). Table 2 summarises modelling results with RF alone, RF with Sequential Forward Selection (RF-SFS) and RF with Sequential Flotant Forward Selection (RF-SFFS). The RF models with feature selection were more accurate than the RF alone models for all three soil properties. SOM models had a higher R 2 than clay and carbonates, but clay models showed higher RPIQ. SOM models had a R 2 range from 0.19 to 0.71. SOM models with RF and feature selection outperformed models with RF alone. RF-SFS models showed a RPIQ of between 1.26 and 1.93. being the Global dataset the model with the best performance (R 2 =0.7). The accuracy of RF-SFFS models Fig. 5. Pearson’s correlation coefficients between each wavelength and soil property by dataset. RAW =raw spectra, CR =continuum removal, MSC =multiplicative scatter correction. Table 1 Performance results for PLSR models. LF =latent features, RAW =raw dataset, CR =continuum removal, MSC =multiplicative scatter correction. Soil property Spectral preprocessing No. of LFs R 2 RMSE RPD RPIQ SOM RAW 7 0.53 4.97 1.48 1.22 CR 5 0.60 4.64 1.59 1.31 MSC 7 0.51 5.12 1.44 1.19 Global 8 0.65 4.3 1.71 1.41 Carbonates RAW 4 0.16 9.07 1.09 0.26 CR 8 0.32 8.14 1.22 0.29 MSC 4 0.27 8.45 1.18 0.28 Global 5 0.12 9.39 1.06 0.25 Clay RAW 3 0.33 11.23 1.23 1.69 CR 5 0.41 10.57 1.3 1.80 MSC 5 0.39 10.74 1.29 1.77 Global 4 0.43 10.37 1.33 1.83 F.M. Canero et al. Heliyon 10 (2024) e30228 9 Table 2 Performance results for Random Forest (RF), RF with Sequential Forward Selection (RF-SFS) and RF with Sequential Flotant Forward Selection (RF-SFFS). ntree =number of trees, raw =raw spectra, CR =continuum removal, MSC =multiplicative scatter correction. ntree RF RF-SFS RF-SFFS R 2 RMSE RPD RPIQ R 2 RMSE RPD RPIQ R 2 RMSE RPD RPIQ SOM raw 1300 0.28 5.42 1.36 1.12 0.35 4.82 1.52 1.26 0.15 5.14 1.43 1.18 CR 300 0.43 5.35 1.38 1.14 0.68 3.37 2.19 1.81 0.71 3.4 2.17 1.79 MSC 100 0.37 4.7 1.57 1.29 0.54 4.09 1.8 1.49 0.44 4.15 1.77 1.47 Global 400 0.19 4.96 1.48 1.23 0.7 3.15 2.33 1.93 0.34 3.47 2.12 1.75 Carbonates raw 100 −23.4 11.97 0.83 0.19 −61.3 9.49 1.05 0.24 −6.18 9.48 1.05 0.25 CR 200 −0.07 8.08 1.23 0.29 0.05 6.07 1.64 0.38 0.22 6.27 1.59 0.37 MSC 400 −3.49 9.93 1 0.23 −6.1 7.12 1.39 0.33 −7.53 6.57 1.47 0.35 Global 500 −2.2 8.81 1.12 0.26 0.48 6.42 1.55 0.36 0.13 6.34 1.57 0.37 Clay raw 600 0.09 12.26 1.13 1.55 0.31 10.84 1.27 1.75 0.04 10.86 1.27 1.75 CR 1300 0.12 11.21 1.23 1.69 0.37 9.08 1.52 2.09 0.45 9.73 1.41 1.95 MSC 1400 0.21 10.8 1.28 1.76 0.34 9.67 1.42 1.96 0.55 8.79 1.57 2.16 Global 800 0.34 10.49 1.31 1.81 0.66 7.86 1.76 2.42 0.66 7.41 1.86 2.56 F.M. Canero et al. Heliyon 10 (2024) e30228 16 presence of various minerals in clay, such as smectite and kaolinite. Other studies have selected key features in both the main absorption feature of clay and other related absorption features [24,104,111]. Coblinski, Giasson [111] used Cubist, a decision-tree-based algorithm with an embedded feature selection method, to estimate textural fractions (clay, silt, and sand) in southern Brazil. The wavelengths 1415, 2200 and 2480 nm were significant in the modelling process, with 2480 nm having greater relative importance. Wang, Qiao [104] used Successive Projection Algorithm to select key features for clay prediction, which selected 10 features, and 3 of the features (1410, 2250 and 2400 nm) could be associated with both the main absorption feature of clay and with the absorption features selected in our study. Viscarra Rossel and Behrens [24] used two feature selection methods (Variable Importance in Projection and multivariate adaptive regression splines), selecting 31 and 13 key features, respectively. Both algorithms selected features near 1395 nm (absorption feature of kaolinite), 2172, 2212 and 2228 nm (close to the main absorption feature) and 2432 nm (absorption feature of illite). Perhaps the most controversial point of feature selection may be the fact that various plausible models made of different features can be obtained with a similar level of performance. This is known in the literature as the Rashomon effect or the multiplicity of good models [25] and was especially noticeable in our case because spectroscopy data is characterised by its multicollinearity, particularly when raw spectra of less than 1 nm are used. Our results have yielded various feature combinations that enable predictive modelling of each soil property. Furthermore, small disturbances in training data, or during wrapper configuration, e.g., sequential searching strategies or the prediction algorithm, yield different feature subsets. However, this should be viewed merely as several different possibilities instead of as a disadvantage per se. This phenomenon is not exclusive to feature selection models with ML; it also occurs with other commonly used techniques in soil spectroscopy studies, such as PLSR, or even in multivariate linear regression. 5. Conclusions This study evaluated the performance of two feature selection wrapper methods, Random Forest with Sequential Forward Selection (SFS) and with Sequential Flotant Forward Selection (SFFS) for reducing dimensionality and modelling three soil properties with soil spectroscopy (SOM, clay, and carbonates). RF models with feature selection outperformed PLSR and RF alone in predicting all soil properties, thus avoiding the Hughes effect. The best RF model built with any feature selection method had a RPIQ values of 1.93 for SOM (RF–SFS–Global), 0.38 for carbonates (RF–SFS–CR) and 2.56 for clay (RF–SFFS–Global). PLSR-based models had a RPIQ of 1.41, 0.29 and 1.81, and RF alone models had a RPIQ of 1.29, 0.29 and 1.81 for SOM, carbonates, and clay, respectively. Feature selection wrapper methods were reported to be capable of handling the high dimensionality and multicollinearity of spectral data and selected less than 1 % of the original starting features. The features that were selected varied depending on the soil properties. The features selected for SOM were found throughout the spectrum, but feature selection highlighted the importance of features around 1100 nm. The main absorption feature of carbonates (2350 nm) was found to be crucial in applying feature selection to predict carbonates and was selected in models with improved accuracy. The features selected for clay were found throughout the spectrum due to several factors, such as the absorption features associated with clay (1415, 2200 and 2450 nm) as well as other absorption features that correspond to other soil properties and which clay also correlates with. However, the main absorption feature of clay (2200 nm) was only selected by one model with feature selection. This study provides new insights into soil properties modelling with spectroscopy in combination with different spectral preprocessing and feature selection methods. Combining different dataset (raw, Continuum Removal and Multiplicative Scatter Correction spectra) in a Global dataset resulted in improved accuracy for clay modelling, but not for SOM and carbonates modelling. Feature selection wrapper methods have shown a promising potential for the modelling of soil properties with spectroscopy. This opens an interesting field of research in comparing different feature selection wrapper methods (exhaustive, random search, genetic algorithm) and machine learning algorithms (Support vector machines, artificial neural networks, gradient boosting trees or convolutional neural networks) using spectroscopic data. These algorithms could be effective in reducing highly dimensional data from laboratory, airborne and spaceborne spectroscopy. Data availability statement The data used in this study can be found in 10.5281/zenodo.10222011. CRediT authorship contribution statement Francisco M. Canero: Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Victor Rodriguez-Galiano: Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. David Aragones: Writing – review & editing, Methodology, Funding acquisition, Data curation, Conceptualization. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. F.M. Canero et al. Heliyon 10 (2024) e30228 17 Acknowledgements The first author is a FPU grant holder funded by the Spanish Ministerio de Universidades (Reference FPU18/04274). The authors would like to express their gratitude for the financial support provided under projects 2914/2022, funded by the Ministerio para la Transici´ on Ecol´ ogica y el Reto Demogr´ afico, and AGRARIA (MIA.2021.M01.004), funded by the Ministerio de Asuntos Econ´ omicos y Transformaci´ on Digital (Subdirecci´ on General de Inteligencia Artificial y Tecnologías Habilitadoras Digitales). 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