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A Statistically Rigorous Multi-classifier Benchmark for Crop Recommendation: K-fold Selection Criterion, Friedman-nemenyi Testing and Optuna TPE Optimisation

A
Ali Asghar Khavari1
S
Shuchita Upadhyaya1
P
Pardeep Kumar1
M
Monika Poriye1,*
1Department of Computer Science and Applications, Kurukshetra University, Kurukshetra-136 119, Haryana, India.

ABSTRACT

Background: Crop recommendation is one of the most critical challenges in precision agriculture, requiring accurate predictions and rigorous evaluation for reliable decisions. However, previous research has employed ad hoc model selection, lack of statistical validation and limited interpretability, thereby limiting reproducibility and scientific credibility.

Methods: A statistically rigorous multi-classifier benchmarking framework for crop recommendation is developed. A publicly available dataset was refined to 33,000 agronomically relevant samples from 57,000, covering 33 crop classes and seven features. A novel K-fold selection criterion optimising predictive accuracy, stability and diversity selected K=7. Friedman testing (χ2=59.23, p=1.89×10-9) with Nemenyi post-hoc analysis confirmed statistical significance of inter-model differences.

Result: Random Forest was selected as the top-ranked method through a transparent multi-criteria framework. Optuna TPE (50 trials) yielded CV F1=96.63%, Test F1=97.06%, AUC=0.9996 and generalisation gap=0.47%. Humidity and rainfall are consistently dominant predictors in both MDI and SHAP, while potassium has elevated SHAP importance, reinforcing its agronomic relevance. The frame work enhances reliability, transparency and interpretability for data-driven agricultural decision-making.

INTRODUCTION

Crop selection is one of the most critical decisions in precision agriculture, directly affecting yield, resource utilisation and soil sustainability-particularly for smallholder farmers in agro-climatically diverse regions such as India (Kayastha et al., 2024). Machine learning (ML) has emerged as a powerful paradigm for crop recommendation, with tree-based ensemble methods consistently achieving high predictive performance on structured agricultural datasets (Mohan et al., 2023).
       
However, existing crop recommendation studies share three key methodological limitations: (i) ad hoc model selection based on point estimates without comprehensive cross-algorithm comparison; (ii) absence of formal statistical validation to confirm that observed performance differences are significant rather than due to chance; and (iii) limited interpretability, with few studies providing feature-level explanations essential for agronomic decision-making.
       
To address these limitations, this paper proposes a statistically rigorous and reproducible benchmarking framework integrating multi-classifier evaluation, a novel K-fold selection criterion, Friedman-Nemenyi statistical testing and dual-layer feature importance analysis within a unified pipeline.
 
Recent developments in crop recommendation
 
Recent crop recommendation studies using supervised ML have achieved high predictive accuracy on soil and climatic datasets. Prity et al., (2024) identified Random Forest as best-performing (99.31% accuracy) and Shastri et al., (2025) used Gradient Boosting (99.27%) with SHAP interpretability. Bhimanpallewar and Narasingarao (2022) developed an ML-based crop suitability decision support system, while Samundeeswari and Srinivasan (2021) applied decision tree algorithms on NPK and pH data for crop yield prediction in Tamil Nadu. However, most studies rely on single-metric evaluation and lack formal statistical hypothesis testing, casting doubt on the reproducibility and generalisability of reported results.

From a broader ML perspective, tree-based ensemble methods-including XGBoost (Chen and Guestrin, 2016), LightGBM (Ke et al., 2017) and CatBoost (Prokhorenkova et al., 2018) -consistently outperform deep learning on medium-sized tabular agricultural datasets (Shwartz-Ziv and Armon, 2022; Kalmani et al., 2025), while transformer-based architectures such as TabNet (Arik and Pfister, 2021) show no consistent advantage. Despite this, rigorous benchmarking protocols remain underutilised. Demšar (2006) proposed the Friedman-Nemenyi framework for statistically sound multi-classifier comparison, yet it remains largely absent from agricultural ML research.
       
Interpretability via SHAP (Lundberg and Lee, 2017) has been widely adopted in agricultural AI (Shams et al., 2024; Shastri et al., 2025), but is typically applied as a post-hoc addition rather than integrated into the evaluation pipeline. Similarly, Optuna TPE (Akiba et al., 2019) enables efficient hyperparameter optimisation, while Probst et al., (2019) showed that Random Forest is relatively robust to hyperparameter settings.
 
Key contributions
 
The following key novelties are introduced to address these limitations:
1. A novel K-fold selection criterion that jointly optimises predictive performance, stability and prediction diversity entropy, eliminating arbitrary fold selection.
2. Integration of formal friedman-nemenyi statistical testing to establish the significance of inter-model performance differences.
3. Dual-layer interpretability (MDI + SHAP) embedded within the evaluation pipeline rather than treated as a post-hoc addition.

MATERIALS AND METHODS

The present study was conducted at the Department of Computer Science and Applications, Kurukshetra University, Kurukshetra, Haryana, India. The research was carried out during the period 2025–2026. The end-to-end benchmark pipeline is illustrated in Fig 1.

Fig 1: Pipeline architecture.


 
Dataset
 
The benchmark uses publicly available crop recommendation data from the Mendeley Data Repository (Thangatamilan, 2025), comprising 33,000 samples across 33 crop classes and seven features: soil nitrogen (N, kg/ha), phosphorus (P, kg/ha), potassium (K, kg/ha), soil pH, mean monthly temperature (°C), relative humidity (%) and mean monthly rainfall (mm/month). The dataset is perfectly class-balanced (1,000 samples per class). Summary statistics and exploratory analysis are in Table 1 and Fig 2.

Fig 2: EDA: (a) class distribution, (b) feature violin plots, (c) Pearson correlation heatmap.



Table 1: Summary statistics of the benchmark dataset (33,000 samples; 33 crops; 7 features).


       
The original dataset comprised 57 crop classes with 1,000 samples each. Filtering was applied in two stages: (i) crops specific to South Indian tropical climates-such as Tamil Nadu minor millets, vegetables and tropical tubers-were removed as they are not cultivated under North Indian semi-arid conditions; and (ii) crops incompatible with North Indian alkaline soil (pH 7.1-8.7) were excluded based on published tolerance ranges. This removed 24 crop classes, yielding a perfectly balanced benchmark of 33,000 samples across 33 classes. Full preprocessing code: https://github.com/AliAsgharKhavari/kurukshetra-crop-recommendation.
 
Data preprocessing
 
Agronomic range clipping was applied to remove biologically impossible values without removing any data points. Feature scaling was omitted as eight of ten classifiers are tree-based and invariant to monotonic transformations. Labels were integer-encoded via scikit-learn LabelEncoder (Pedregosa et al., 2011).
 
Train-test split
 
Stratified random 80/20 partitioning yielded 26,400 training samples (800 per class) and 6,600 test samples (200 per class). The test set was locked and excluded from K selection, model training and hyperparameter optimisation, ensuring zero data leakage.
 
K-fold selection criterion
 
The number of cross-validation folds K was selected systematically from six candidates: K ∈ {3, 5, 7, 10, 15, 20} using the following author-proposed composite criterion:
 
                             Score (K) = Mean F1(K) - 2 × Std F1 (K) + 0.5 × H(K)                   ...(1)  
  
Where,
Mean F1(K)= The mean weighted F1-score across K folds.
Std F1(K)= The fold-level standard deviation.
H(K)= The prediction-diversity entropy.
 
                                                                  H(K) = -∑k [Pk × log2 (Pk)]                ...(2)    
                                    
Where,
pk= The fraction of fold-level predictions assigned to class k (Shannon, 1948).
       
The three terms simultaneously optimise: (i) classification performance, (ii) fold-level stability and (iii) prediction diversity. The coefficient of 2 applied to Std F1(K) is grounded in the bias-variance decomposition framework, prioritising estimation stability over marginal accuracy gains. The entropy coefficient of 0.5 is intentionally modest as prediction diversity is a secondary stabilising criterion. Robustness analysis across penalty coefficients of 1.5, 2 and 3 confirmed that all three variants selected K=7, validating that the result is not an artefact of coefficient choice. Full sensitivity results are in Table 2.

Table 2: K-fold sensitivity analysis (Random forest; 26,400 training samples).


 
Ten-classifier benchmark
 
Ten classifiers spanning the major supervised learning paradigms were evaluated under identical experimental conditions (random_state=42, n_jobs=1, class_ weight= ’balanced’ where applicable) using scikit-learn 1.4.2 (Pedregosa et al., 2011), with XGBoost, LightGBM and CatBoost implemented via their respective Python libraries. No preprocessing beyond Section 3.2 was applied, ensuring performance differences reflect inherent algorithmic characteristics. Table 3 lists all classifiers.

Table 3: Classifiers included in the benchmark.


 
Evaluation metrics and model selection
 
For each model, the following metrics were computed: (i) 7-fold CV weighted F1 (CV F1); (ii) CV fold-level standard deviation (CV Std); (iii) test weighted F1 (Test F1); (iv) test accuracy; (v) weighted one-vs-rest AUC; (vi) CV-Test Gap = |CV F1-Test F1|; (vii) prediction diversity entropy H. Models with Gap > 5% were deemed potentially overfit. Standard metric equations are provided in Table 4.

Table 4: Performance metrics used to evaluate classifiers.


       
The top models were ranked by the following composite selection score:
 
                 Selection score = CV F1 - 2 × CV Std - 1 × Gap + 0.5 × H                    ...(3) 
 
Where,
CV F1= The mean cross-validation weighted F1-score,
CV Std= The fold-level standard deviation,
Gap= |CV F1 - Test F1|= The generalisation gap.
H= The prediction-diversity entropy.
       
Random forest achieved the highest composite score (98.236), confirming its selection as the optimal classifier.
       
For the multi-class setting (33 crop classes), the weighted F1-score is:

                                               
Where,
ni= The number of true instances of class i.
N= The total number of test instances.
F1i= The F1-score for class i.
 
Friedman-nemenyi statistical testing
 
Friedman test
 
A 7×10 matrix of fold-level F1 scores was formed and the Friedman non-parametric test (Friedman, 1937) was used to check if there were statistically significant differences between the ten classifiers. The assumption of paired observations (Demšar, 2006) is satisfied by cross-validation folds.

   
Where,
N= 7 (cross-validation folds).
k= 10 (classifiers).
R̄j= The average rank of classifier j across all folds.
 
Nemenyi post-hoc test
 
Following rejection of the null hypothesis, the Nemenyi post-hoc test (Nemenyi, 1963) was applied following Demšar (2006), with critical difference:

  
Where,
qα= 2.939 at α = 0.05 for k=10 and N=7.
       
Rank 1 indicates the best-performing classifier. Results are shown in Fig 3.

Fig 3: (a) Friedman rank plot (RF rank=1.000). (b) Nemenyi p-value heatmap.


 
Confusion matrix and learning curves
 
The confusion matrix (Fig 5) shows per-class predictions as fractions of true-class samples. Learning curves (Fig 6) used 5-fold CV across 10%-100% of training data.
 
Hyperparameter optimisation (50-trial optuna TPE)
 
The selected random forest was optimised using optuna TPE (Akiba et al., 2019) with median pruner warm-start pruning over 50 trials (Bischl et al., 2023), searching: n_estimators ∈ [100, 600], max_depth ∈ [5, 35], min_samples_split ∈ [2, 12], min_samples_leaf ∈ [1, 6], max_features ∈ {sqrt, log2, None}. Optimal hyperparameters are in Table 5 and convergence in Fig 4.

Fig 4: Optuna TPE convergence (50 trials).



Table 5: Optimal hyperparameters from Optuna TPE (50 trials). Best CV F1 = 96.63% at trial 21.



Final model validation
 
The tuned random forest was trained on all 26,400 training samples and evaluated on the locked test set: CV F1 = 96.58%±0.215%, Test F1 = 97.06%, Test Acc = 97.06%, AUC = 0.9996, Gap = 0.47%. The model was retrained on the full 33,000-sample set to maximise learned representation.
 
Feature importance: MDI and SHAP
 
MDI importance was sourced from the fitted random forest tree structure (Breiman, 2001). SHAP values (Lundberg and Lee, 2017) were generated by tree explainer (Lundberg et al., 2020) on 500 stratified test samples, averaged across all 33 classes (mean|SHAP|). MDI tiers: T1 (≥ mean = 0.1429), T2 (≥ mean+1SD = 0.2145), T3 (≥ Pareto 80th percentile = 0.1084). Results are in Table 8 and Fig 7-8.
 
Computational environment
 
All experiments were implemented in python 3.10 using scikit-learn 1.4.2, XGBoost 2.0.3, LightGBM 4.1.0, CatBoost 1.2.2, SHAP 0.44.0 and Optuna 3.5.0 on Google Colaboratory (NVIDIA T4 GPU, 16 GB VRAM, 12.7 GB RAM). Total execution time was approximately 3.8 hours, of which Optuna optimisation accounted for 2.5 hours.

RESULTS AND DISCUSSION

Multi-classifier benchmark performance
 
Table 6 presents all ten classifier results. Every model achieved CV-test gap ≤5%, confirming absence of pathological overfitting. Random Forest achieved the best performance with CV F1 = 96.55% and Test F1 = 96.93%, AUC = 0.9995 and Gap = 0.38%. The 95% confidence interval (CV F1±1.96 × CV Std/√K) = 96.55%±0.178%, confirming the 0.37 percentage point advantage over gradient boosting (96.18%) is statistically reliable and not attributable to fold-level sampling variation. Gradient boosting, light GBM (96.14%) and XGBoost (96.11%) formed a closely competing high-performance group, while KNN (87.92%) and Logistic Regression (85.81%) performed substantially worse, confirming that instance-based and linear models are unsuitable for this dataset. Fold-level variability is reported in Table 6.

Table 6: Complete 7-fold CV benchmark results for all 10 classifiers (26,400 training samples).


       
The confusion matrix (Fig 5) confirms high per-class accuracy across all 33 crop classes, while learning curves (Fig 6) show convergence at approximately 70% of training data with a generalisation gap of 3.43%.

Fig 5: Normalised confusion matrix-held-out test set (6,600 samples; 33 classes).



Fig 6: Random forest learning curves (5-fold CV; 10%-100% of 26,400 training samples).


 
Statistical significance analysis
 
Friedman-nemenyi statistical analysis
 
The Friedman test yielded χ2=59.23 (p=1.89×10-9, df=9), strongly rejecting the null hypothesis of equal classifier performance and confirming that observed differences are not due to chance.
       
Nemenyi post-hoc analysis (CD=3.428) identified three distinct performance clusters. The top cluster random forest (rank 1.000), gradient boosting (3.000), LightGBM (3.143) and XGBoost (3.571)-was statistically equivalent (all Nemenyi p≥0.838). An intermediate group comprised CatBoost, extra trees, decision tree and naive bayes, while KNN and logistic regression formed an inferior cluster with significant performance degradation relative to the top models (p<0.03). Pairwise results are in Fig 3.
       
Random forest was selected as optimal through the composite selection criterion, confirming its suitability for agricultural deployment under data variability.
 
Model selection justification
 
Random forest achieved the highest composite selection score (98.236), supported by the lowest CV variability (CV Std=0.240), near-minimal generalisation gap (0.38%) and best Friedman rank (1.000), confirming its selection as the optimal classifier. This represents a departure from equating the best model solely with highest accuracy, emphasising stability and generalisation as equally critical criteria.
       
Although Prity et al., (2024) and Shastri et al., (2025) report higher accuracies (99.31% and 99.27%), these studies use fewer output classes and lack formal statistical validation. A comparative summary of these approaches and the proposed method is presented in Table 7. The proposed approach achieves test F1=97.06% on a more challenging 33-class problem with rigorous statistical testing and multi-criteria selection, making the findings more robust and scientifically grounded.

Table 7: Comparative analysis of crop recommendation methods.


 
Hyperparameter optimisation analysis
 
Optuna TPE identified the optimal configuration at trial 21 (n_estimators=348, max_depth=31, min_samples_ split=12, min_samples_leaf=2, max_features=log2), yielding a marginal gain of +0.08 percentage points in CV F1 (96.55% to 96.63%), reinforcing the well-established hyperparameter robustness of Random Forest on tabular datasets (Probst et al., 2019).
       
The flat convergence surface (Fig 4) confirms the default configuration is near pareto-optimal- performance is governed more by dataset quality than hyperparameter tuning, yielding diminishing returns from extensive search.

Final validated performance: CV F1=96.58% ± 0.215%, Test F1=97.06%, AUC=0.9996, Gap=0.47%, confirming strong predictive power, generalisation ability and low overfitting risk with minimal tuning effort.
 
Feature importance and interpretability
 
MDI and SHAP analysis (Table 8; Fig 7-8) provide dual-layer interpretation of model decisions. Humidity ranked 1st in both MDI (0.2573) and SHAP (0.02337), with rainfall ranked 2nd by MDI and 3rd by SHAP. Nitrogen and temperature showed moderate importance, while pH and phosphorus ranked lowest in both methods.

Table 8: MDI and SHAP feature importance with tier classification (tuned random forest). T1=MDI≥0.1429; T2=MDI≥0.2145; T3=MDI≥0.1084. SHAP via tree explainer on 500 test samples (Lundberg et al., 2020).



Fig 7: Feature importance (tuned RF).



Fig 8: SHAP interpretability (Tree explainer; 500 samples; 33 classes).


       
A notable discrepancy was observed for potassium (K): ranked 5th by MDI (0.1084) but 2nd by SHAP (0.02172). This is consistent with known MDI bias for high-cardinality continuous features (Strobl et al., 2007) -impurity-based measures underestimate features that influence predictions through magnitude rather than split frequency. SHAP captures this correctly, revealing potassium as a key discriminative feature for crops with similar climatic profiles (e.g. similar temperature and humidity), an important agronomic insight not visible through MDI alone.
       
The dual MDI+SHAP framework enhances transparency and provides direct practical guidance for fertiliser management and crop planning in precision agriculture.
 
Ablation perspective, framework validation and practical implications
 
An ablation analysis confirms that each framework component serves a distinct purpose: removing the entropy term reduces prediction diversity; removing the stability component increases fold-to-fold variance; removing the generalisation gap penalty increases overfitting risk. Framework strength emerges from their combined balance rather than any individual measure.
       
The proposed framework is practically deployable. The tuned random forest model generates a single prediction in under one millisecond, making it suitable for lightweight mobile or web-based decision-support applications. Soil input values (N, P, K, pH) can be obtained from low-cost portable soil testing kits, while meteorological inputs (temperature, humidity, rainfall) are accessible via public weather data services such as NASA POWER and OpenWeatherMap, enabling operation without specialist infrastructure in resource-constrained agricultural environments.

CONCLUSION

This study presented a statistically rigorous and reproducible crop recommendation benchmarking framework addressing key limitations of prior work-ad hoc model selection, lack of statistical validation and limited interpretability. A novel K-fold selection criterion, ten-classifier evaluation and formal friedman-nemenyi testing established that random forest is the optimal classifier, confirmed by the lowest CV standard deviation (0.240%), near-minimal generalisation gap (0.38%) and best Friedman rank (1.000). Final validated performance: Test F1=97.06%, AUC=0.9996.
       
Dual-layer interpretability (MDI and SHAP) confirmed humidity and rainfall as dominant predictors, while revealing potassium as a critically underestimated feature for crop differentiation -an agronomic insight invisible through MDI alone. Ablation analysis confirmed that each framework component is necessary, with strength arising from the synergy of performance, stability and interpretability measures.
       
The framework is robust, reproducible and practically deployable, offering a solid basis for decision-support systems in precision agriculture for crop planning, resource optimisation and sustainable farming. A key limitation is evaluation on a single dataset; validation on additional independent datasets from diverse agro-climatic zones remains important future research.

ACKNOWLEDGEMENT

No funding was received for this research. The authors thank the Department of Computer Science and Applications, Kurukshetra University, Kurukshetra, Haryana, India, for institutional support. The dataset was made publicly available through the Mendeley Data repository.
 
Disclaimers
 
The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided, but do not accept any liability for any direct or indirect losses resulting from the use of this content.
 
Data and code availability
 
All code, trained models and outputs are available at: https://github. com/AliAsgharKhavari/kurukshetra-crop-recommendation. Dataset: Mendeley Data Repository, https://data. mendeley.com/datasets/vynxnppr7j/1.
 
Credit author contributions
 
Ali Asghar Khavari: Conceptualisation, Methodology, Software, Formal Analysis, Writing-Original Draft. Shuchita Upadhyaya: Supervision, Validation, Writing-Review and Editing. Pardeep Kumar: Resources, Investigation, Writing-Review and Editing. Monika Poriye: Data Curation, Visualisation, Writing-Review and Editing.

CONFLICT OF INTEREST

The authors have no conflict of interest to declare with regard to the publication of this article.

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    A Statistically Rigorous Multi-classifier Benchmark for Crop Recommendation: K-fold Selection Criterion, Friedman-nemenyi Testing and Optuna TPE Optimisation

    A
    Ali Asghar Khavari1
    S
    Shuchita Upadhyaya1
    P
    Pardeep Kumar1
    M
    Monika Poriye1,*
    1Department of Computer Science and Applications, Kurukshetra University, Kurukshetra-136 119, Haryana, India.

    ABSTRACT

    Background: Crop recommendation is one of the most critical challenges in precision agriculture, requiring accurate predictions and rigorous evaluation for reliable decisions. However, previous research has employed ad hoc model selection, lack of statistical validation and limited interpretability, thereby limiting reproducibility and scientific credibility.

    Methods: A statistically rigorous multi-classifier benchmarking framework for crop recommendation is developed. A publicly available dataset was refined to 33,000 agronomically relevant samples from 57,000, covering 33 crop classes and seven features. A novel K-fold selection criterion optimising predictive accuracy, stability and diversity selected K=7. Friedman testing (χ2=59.23, p=1.89×10-9) with Nemenyi post-hoc analysis confirmed statistical significance of inter-model differences.

    Result: Random Forest was selected as the top-ranked method through a transparent multi-criteria framework. Optuna TPE (50 trials) yielded CV F1=96.63%, Test F1=97.06%, AUC=0.9996 and generalisation gap=0.47%. Humidity and rainfall are consistently dominant predictors in both MDI and SHAP, while potassium has elevated SHAP importance, reinforcing its agronomic relevance. The frame work enhances reliability, transparency and interpretability for data-driven agricultural decision-making.

    INTRODUCTION

    Crop selection is one of the most critical decisions in precision agriculture, directly affecting yield, resource utilisation and soil sustainability-particularly for smallholder farmers in agro-climatically diverse regions such as India (Kayastha et al., 2024). Machine learning (ML) has emerged as a powerful paradigm for crop recommendation, with tree-based ensemble methods consistently achieving high predictive performance on structured agricultural datasets (Mohan et al., 2023).
           
    However, existing crop recommendation studies share three key methodological limitations: (i) ad hoc model selection based on point estimates without comprehensive cross-algorithm comparison; (ii) absence of formal statistical validation to confirm that observed performance differences are significant rather than due to chance; and (iii) limited interpretability, with few studies providing feature-level explanations essential for agronomic decision-making.
           
    To address these limitations, this paper proposes a statistically rigorous and reproducible benchmarking framework integrating multi-classifier evaluation, a novel K-fold selection criterion, Friedman-Nemenyi statistical testing and dual-layer feature importance analysis within a unified pipeline.
     
    Recent developments in crop recommendation
     
    Recent crop recommendation studies using supervised ML have achieved high predictive accuracy on soil and climatic datasets. Prity et al., (2024) identified Random Forest as best-performing (99.31% accuracy) and Shastri et al., (2025) used Gradient Boosting (99.27%) with SHAP interpretability. Bhimanpallewar and Narasingarao (2022) developed an ML-based crop suitability decision support system, while Samundeeswari and Srinivasan (2021) applied decision tree algorithms on NPK and pH data for crop yield prediction in Tamil Nadu. However, most studies rely on single-metric evaluation and lack formal statistical hypothesis testing, casting doubt on the reproducibility and generalisability of reported results.

    From a broader ML perspective, tree-based ensemble methods-including XGBoost (Chen and Guestrin, 2016), LightGBM (Ke et al., 2017) and CatBoost (Prokhorenkova et al., 2018) -consistently outperform deep learning on medium-sized tabular agricultural datasets (Shwartz-Ziv and Armon, 2022; Kalmani et al., 2025), while transformer-based architectures such as TabNet (Arik and Pfister, 2021) show no consistent advantage. Despite this, rigorous benchmarking protocols remain underutilised. Demšar (2006) proposed the Friedman-Nemenyi framework for statistically sound multi-classifier comparison, yet it remains largely absent from agricultural ML research.
           
    Interpretability via SHAP (Lundberg and Lee, 2017) has been widely adopted in agricultural AI (Shams et al., 2024; Shastri et al., 2025), but is typically applied as a post-hoc addition rather than integrated into the evaluation pipeline. Similarly, Optuna TPE (Akiba et al., 2019) enables efficient hyperparameter optimisation, while Probst et al., (2019) showed that Random Forest is relatively robust to hyperparameter settings.
     
    Key contributions
     
    The following key novelties are introduced to address these limitations:
    1. A novel K-fold selection criterion that jointly optimises predictive performance, stability and prediction diversity entropy, eliminating arbitrary fold selection.
    2. Integration of formal friedman-nemenyi statistical testing to establish the significance of inter-model performance differences.
    3. Dual-layer interpretability (MDI + SHAP) embedded within the evaluation pipeline rather than treated as a post-hoc addition.

    MATERIALS AND METHODS

    The present study was conducted at the Department of Computer Science and Applications, Kurukshetra University, Kurukshetra, Haryana, India. The research was carried out during the period 2025–2026. The end-to-end benchmark pipeline is illustrated in Fig 1.

    Fig 1: Pipeline architecture.


     
    Dataset
     
    The benchmark uses publicly available crop recommendation data from the Mendeley Data Repository (Thangatamilan, 2025), comprising 33,000 samples across 33 crop classes and seven features: soil nitrogen (N, kg/ha), phosphorus (P, kg/ha), potassium (K, kg/ha), soil pH, mean monthly temperature (°C), relative humidity (%) and mean monthly rainfall (mm/month). The dataset is perfectly class-balanced (1,000 samples per class). Summary statistics and exploratory analysis are in Table 1 and Fig 2.

    Fig 2: EDA: (a) class distribution, (b) feature violin plots, (c) Pearson correlation heatmap.



    Table 1: Summary statistics of the benchmark dataset (33,000 samples; 33 crops; 7 features).


           
    The original dataset comprised 57 crop classes with 1,000 samples each. Filtering was applied in two stages: (i) crops specific to South Indian tropical climates-such as Tamil Nadu minor millets, vegetables and tropical tubers-were removed as they are not cultivated under North Indian semi-arid conditions; and (ii) crops incompatible with North Indian alkaline soil (pH 7.1-8.7) were excluded based on published tolerance ranges. This removed 24 crop classes, yielding a perfectly balanced benchmark of 33,000 samples across 33 classes. Full preprocessing code: https://github.com/AliAsgharKhavari/kurukshetra-crop-recommendation.
     
    Data preprocessing
     
    Agronomic range clipping was applied to remove biologically impossible values without removing any data points. Feature scaling was omitted as eight of ten classifiers are tree-based and invariant to monotonic transformations. Labels were integer-encoded via scikit-learn LabelEncoder (Pedregosa et al., 2011).
     
    Train-test split
     
    Stratified random 80/20 partitioning yielded 26,400 training samples (800 per class) and 6,600 test samples (200 per class). The test set was locked and excluded from K selection, model training and hyperparameter optimisation, ensuring zero data leakage.
     
    K-fold selection criterion
     
    The number of cross-validation folds K was selected systematically from six candidates: K ∈ {3, 5, 7, 10, 15, 20} using the following author-proposed composite criterion:
     
                                 Score (K) = Mean F1(K) - 2 × Std F1 (K) + 0.5 × H(K)                   ...(1)  
      
    Where,
    Mean F1(K)= The mean weighted F1-score across K folds.
    Std F1(K)= The fold-level standard deviation.
    H(K)= The prediction-diversity entropy.
     
                                                                      H(K) = -∑k [Pk × log2 (Pk)]                ...(2)    
                                        
    Where,
    pk= The fraction of fold-level predictions assigned to class k (Shannon, 1948).
           
    The three terms simultaneously optimise: (i) classification performance, (ii) fold-level stability and (iii) prediction diversity. The coefficient of 2 applied to Std F1(K) is grounded in the bias-variance decomposition framework, prioritising estimation stability over marginal accuracy gains. The entropy coefficient of 0.5 is intentionally modest as prediction diversity is a secondary stabilising criterion. Robustness analysis across penalty coefficients of 1.5, 2 and 3 confirmed that all three variants selected K=7, validating that the result is not an artefact of coefficient choice. Full sensitivity results are in Table 2.

    Table 2: K-fold sensitivity analysis (Random forest; 26,400 training samples).


     
    Ten-classifier benchmark
     
    Ten classifiers spanning the major supervised learning paradigms were evaluated under identical experimental conditions (random_state=42, n_jobs=1, class_ weight= ’balanced’ where applicable) using scikit-learn 1.4.2 (Pedregosa et al., 2011), with XGBoost, LightGBM and CatBoost implemented via their respective Python libraries. No preprocessing beyond Section 3.2 was applied, ensuring performance differences reflect inherent algorithmic characteristics. Table 3 lists all classifiers.

    Table 3: Classifiers included in the benchmark.


     
    Evaluation metrics and model selection
     
    For each model, the following metrics were computed: (i) 7-fold CV weighted F1 (CV F1); (ii) CV fold-level standard deviation (CV Std); (iii) test weighted F1 (Test F1); (iv) test accuracy; (v) weighted one-vs-rest AUC; (vi) CV-Test Gap = |CV F1-Test F1|; (vii) prediction diversity entropy H. Models with Gap > 5% were deemed potentially overfit. Standard metric equations are provided in Table 4.

    Table 4: Performance metrics used to evaluate classifiers.


           
    The top models were ranked by the following composite selection score:
     
                     Selection score = CV F1 - 2 × CV Std - 1 × Gap + 0.5 × H                    ...(3) 
     
    Where,
    CV F1= The mean cross-validation weighted F1-score,
    CV Std= The fold-level standard deviation,
    Gap= |CV F1 - Test F1|= The generalisation gap.
    H= The prediction-diversity entropy.
           
    Random forest achieved the highest composite score (98.236), confirming its selection as the optimal classifier.
           
    For the multi-class setting (33 crop classes), the weighted F1-score is:

                                                   
    Where,
    ni= The number of true instances of class i.
    N= The total number of test instances.
    F1i= The F1-score for class i.
     
    Friedman-nemenyi statistical testing
     
    Friedman test
     
    A 7×10 matrix of fold-level F1 scores was formed and the Friedman non-parametric test (Friedman, 1937) was used to check if there were statistically significant differences between the ten classifiers. The assumption of paired observations (Demšar, 2006) is satisfied by cross-validation folds.

       
    Where,
    N= 7 (cross-validation folds).
    k= 10 (classifiers).
    R̄j= The average rank of classifier j across all folds.
     
    Nemenyi post-hoc test
     
    Following rejection of the null hypothesis, the Nemenyi post-hoc test (Nemenyi, 1963) was applied following Demšar (2006), with critical difference:

      
    Where,
    qα= 2.939 at α = 0.05 for k=10 and N=7.
           
    Rank 1 indicates the best-performing classifier. Results are shown in Fig 3.

    Fig 3: (a) Friedman rank plot (RF rank=1.000). (b) Nemenyi p-value heatmap.


     
    Confusion matrix and learning curves
     
    The confusion matrix (Fig 5) shows per-class predictions as fractions of true-class samples. Learning curves (Fig 6) used 5-fold CV across 10%-100% of training data.
     
    Hyperparameter optimisation (50-trial optuna TPE)
     
    The selected random forest was optimised using optuna TPE (Akiba et al., 2019) with median pruner warm-start pruning over 50 trials (Bischl et al., 2023), searching: n_estimators ∈ [100, 600], max_depth ∈ [5, 35], min_samples_split ∈ [2, 12], min_samples_leaf ∈ [1, 6], max_features ∈ {sqrt, log2, None}. Optimal hyperparameters are in Table 5 and convergence in Fig 4.

    Fig 4: Optuna TPE convergence (50 trials).



    Table 5: Optimal hyperparameters from Optuna TPE (50 trials). Best CV F1 = 96.63% at trial 21.



    Final model validation
     
    The tuned random forest was trained on all 26,400 training samples and evaluated on the locked test set: CV F1 = 96.58%±0.215%, Test F1 = 97.06%, Test Acc = 97.06%, AUC = 0.9996, Gap = 0.47%. The model was retrained on the full 33,000-sample set to maximise learned representation.
     
    Feature importance: MDI and SHAP
     
    MDI importance was sourced from the fitted random forest tree structure (Breiman, 2001). SHAP values (Lundberg and Lee, 2017) were generated by tree explainer (Lundberg et al., 2020) on 500 stratified test samples, averaged across all 33 classes (mean|SHAP|). MDI tiers: T1 (≥ mean = 0.1429), T2 (≥ mean+1SD = 0.2145), T3 (≥ Pareto 80th percentile = 0.1084). Results are in Table 8 and Fig 7-8.
     
    Computational environment
     
    All experiments were implemented in python 3.10 using scikit-learn 1.4.2, XGBoost 2.0.3, LightGBM 4.1.0, CatBoost 1.2.2, SHAP 0.44.0 and Optuna 3.5.0 on Google Colaboratory (NVIDIA T4 GPU, 16 GB VRAM, 12.7 GB RAM). Total execution time was approximately 3.8 hours, of which Optuna optimisation accounted for 2.5 hours.

    RESULTS AND DISCUSSION

    Multi-classifier benchmark performance
     
    Table 6 presents all ten classifier results. Every model achieved CV-test gap ≤5%, confirming absence of pathological overfitting. Random Forest achieved the best performance with CV F1 = 96.55% and Test F1 = 96.93%, AUC = 0.9995 and Gap = 0.38%. The 95% confidence interval (CV F1±1.96 × CV Std/√K) = 96.55%±0.178%, confirming the 0.37 percentage point advantage over gradient boosting (96.18%) is statistically reliable and not attributable to fold-level sampling variation. Gradient boosting, light GBM (96.14%) and XGBoost (96.11%) formed a closely competing high-performance group, while KNN (87.92%) and Logistic Regression (85.81%) performed substantially worse, confirming that instance-based and linear models are unsuitable for this dataset. Fold-level variability is reported in Table 6.

    Table 6: Complete 7-fold CV benchmark results for all 10 classifiers (26,400 training samples).


           
    The confusion matrix (Fig 5) confirms high per-class accuracy across all 33 crop classes, while learning curves (Fig 6) show convergence at approximately 70% of training data with a generalisation gap of 3.43%.

    Fig 5: Normalised confusion matrix-held-out test set (6,600 samples; 33 classes).



    Fig 6: Random forest learning curves (5-fold CV; 10%-100% of 26,400 training samples).


     
    Statistical significance analysis
     
    Friedman-nemenyi statistical analysis
     
    The Friedman test yielded χ2=59.23 (p=1.89×10-9, df=9), strongly rejecting the null hypothesis of equal classifier performance and confirming that observed differences are not due to chance.
           
    Nemenyi post-hoc analysis (CD=3.428) identified three distinct performance clusters. The top cluster random forest (rank 1.000), gradient boosting (3.000), LightGBM (3.143) and XGBoost (3.571)-was statistically equivalent (all Nemenyi p≥0.838). An intermediate group comprised CatBoost, extra trees, decision tree and naive bayes, while KNN and logistic regression formed an inferior cluster with significant performance degradation relative to the top models (p<0.03). Pairwise results are in Fig 3.
           
    Random forest was selected as optimal through the composite selection criterion, confirming its suitability for agricultural deployment under data variability.
     
    Model selection justification
     
    Random forest achieved the highest composite selection score (98.236), supported by the lowest CV variability (CV Std=0.240), near-minimal generalisation gap (0.38%) and best Friedman rank (1.000), confirming its selection as the optimal classifier. This represents a departure from equating the best model solely with highest accuracy, emphasising stability and generalisation as equally critical criteria.
           
    Although Prity et al., (2024) and Shastri et al., (2025) report higher accuracies (99.31% and 99.27%), these studies use fewer output classes and lack formal statistical validation. A comparative summary of these approaches and the proposed method is presented in Table 7. The proposed approach achieves test F1=97.06% on a more challenging 33-class problem with rigorous statistical testing and multi-criteria selection, making the findings more robust and scientifically grounded.

    Table 7: Comparative analysis of crop recommendation methods.


     
    Hyperparameter optimisation analysis
     
    Optuna TPE identified the optimal configuration at trial 21 (n_estimators=348, max_depth=31, min_samples_ split=12, min_samples_leaf=2, max_features=log2), yielding a marginal gain of +0.08 percentage points in CV F1 (96.55% to 96.63%), reinforcing the well-established hyperparameter robustness of Random Forest on tabular datasets (Probst et al., 2019).
           
    The flat convergence surface (Fig 4) confirms the default configuration is near pareto-optimal- performance is governed more by dataset quality than hyperparameter tuning, yielding diminishing returns from extensive search.

    Final validated performance: CV F1=96.58% ± 0.215%, Test F1=97.06%, AUC=0.9996, Gap=0.47%, confirming strong predictive power, generalisation ability and low overfitting risk with minimal tuning effort.
     
    Feature importance and interpretability
     
    MDI and SHAP analysis (Table 8; Fig 7-8) provide dual-layer interpretation of model decisions. Humidity ranked 1st in both MDI (0.2573) and SHAP (0.02337), with rainfall ranked 2nd by MDI and 3rd by SHAP. Nitrogen and temperature showed moderate importance, while pH and phosphorus ranked lowest in both methods.

    Table 8: MDI and SHAP feature importance with tier classification (tuned random forest). T1=MDI≥0.1429; T2=MDI≥0.2145; T3=MDI≥0.1084. SHAP via tree explainer on 500 test samples (Lundberg et al., 2020).



    Fig 7: Feature importance (tuned RF).



    Fig 8: SHAP interpretability (Tree explainer; 500 samples; 33 classes).


           
    A notable discrepancy was observed for potassium (K): ranked 5th by MDI (0.1084) but 2nd by SHAP (0.02172). This is consistent with known MDI bias for high-cardinality continuous features (Strobl et al., 2007) -impurity-based measures underestimate features that influence predictions through magnitude rather than split frequency. SHAP captures this correctly, revealing potassium as a key discriminative feature for crops with similar climatic profiles (e.g. similar temperature and humidity), an important agronomic insight not visible through MDI alone.
           
    The dual MDI+SHAP framework enhances transparency and provides direct practical guidance for fertiliser management and crop planning in precision agriculture.
     
    Ablation perspective, framework validation and practical implications
     
    An ablation analysis confirms that each framework component serves a distinct purpose: removing the entropy term reduces prediction diversity; removing the stability component increases fold-to-fold variance; removing the generalisation gap penalty increases overfitting risk. Framework strength emerges from their combined balance rather than any individual measure.
           
    The proposed framework is practically deployable. The tuned random forest model generates a single prediction in under one millisecond, making it suitable for lightweight mobile or web-based decision-support applications. Soil input values (N, P, K, pH) can be obtained from low-cost portable soil testing kits, while meteorological inputs (temperature, humidity, rainfall) are accessible via public weather data services such as NASA POWER and OpenWeatherMap, enabling operation without specialist infrastructure in resource-constrained agricultural environments.

    CONCLUSION

    This study presented a statistically rigorous and reproducible crop recommendation benchmarking framework addressing key limitations of prior work-ad hoc model selection, lack of statistical validation and limited interpretability. A novel K-fold selection criterion, ten-classifier evaluation and formal friedman-nemenyi testing established that random forest is the optimal classifier, confirmed by the lowest CV standard deviation (0.240%), near-minimal generalisation gap (0.38%) and best Friedman rank (1.000). Final validated performance: Test F1=97.06%, AUC=0.9996.
           
    Dual-layer interpretability (MDI and SHAP) confirmed humidity and rainfall as dominant predictors, while revealing potassium as a critically underestimated feature for crop differentiation -an agronomic insight invisible through MDI alone. Ablation analysis confirmed that each framework component is necessary, with strength arising from the synergy of performance, stability and interpretability measures.
           
    The framework is robust, reproducible and practically deployable, offering a solid basis for decision-support systems in precision agriculture for crop planning, resource optimisation and sustainable farming. A key limitation is evaluation on a single dataset; validation on additional independent datasets from diverse agro-climatic zones remains important future research.

    ACKNOWLEDGEMENT

    No funding was received for this research. The authors thank the Department of Computer Science and Applications, Kurukshetra University, Kurukshetra, Haryana, India, for institutional support. The dataset was made publicly available through the Mendeley Data repository.
     
    Disclaimers
     
    The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided, but do not accept any liability for any direct or indirect losses resulting from the use of this content.
     
    Data and code availability
     
    All code, trained models and outputs are available at: https://github. com/AliAsgharKhavari/kurukshetra-crop-recommendation. Dataset: Mendeley Data Repository, https://data. mendeley.com/datasets/vynxnppr7j/1.
     
    Credit author contributions
     
    Ali Asghar Khavari: Conceptualisation, Methodology, Software, Formal Analysis, Writing-Original Draft. Shuchita Upadhyaya: Supervision, Validation, Writing-Review and Editing. Pardeep Kumar: Resources, Investigation, Writing-Review and Editing. Monika Poriye: Data Curation, Visualisation, Writing-Review and Editing.

    CONFLICT OF INTEREST

    The authors have no conflict of interest to declare with regard to the publication of this article.

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