2.1. RFECV-PRF Algorithm

Recursive feature elimination (RFE) is commonly used in feature selection tasks. It works by recursively removing the least important features, followed by training and evaluating the model on the remaining features, until the desired number of features is achieved or a performance criterion is met ²⁶.

The RFECV method selects a key subset of features by recursively eliminating those with minimal contribution to the model, and uses cross-validation to assess performance at different feature set sizes in order to determine the optimal subset size. The core steps include recursive ranking of feature importance, stepwise removal, and cross-validation to select the feature set with the highest average performance. PRF generates multiple decision trees in parallel during each feature subset iteration, utilizing a parallel computing framework to simultaneously train and validate the model on each fold of cross-validation data. This approach maintains the RFECV’s recursive elimination mechanism while reducing the computational complexity of feature importance evaluation and model validation from linear to logarithmic scale. The basic process of PRF-enhanced RFECV is as follows:

1. (1)

   Training the model and calculating the root mean square error: For the current feature subset \(S_k\), we train a random forest model using cross-validation and compute the root mean square error (RMSE) to evaluate the model’s performance:

   \begin{equation} \label{eq:1} \textrm{RMSE}\left(S_k\right)=\sqrt{\dfrac{1}{n}\sum_{i=1}^n \left(y_i -\hat{y}\left(S_k\right)\right)^2}. \end{equation}

   In this context, \(S_k\) represents the feature subset in the \(k\)-th round of RFE, \(y_i\) denotes the true values, and \(\hat{y}\,(S_k)\) refers to the predicted values obtained using the feature subset \(S_k\).

2. (2)

   Feature elimination: In each iteration, the feature with the smallest contribution is removed based on the model’s feature importance value \(I_j\). The feature importance \(I_j\) can be computed using the formula for the cumulative impurity reduction in the random forest:

   \begin{equation} \label{eq:2} I_j=\sum_{t=1}^T \sum_{s\in S(j,t)} \Delta I(s,t). \end{equation}

   Then, the feature with the smallest \(I_j\) value is removed.

3. (3)

   As the RFE progresses, the number of features is gradually reduced, and the RMSE of the model is calculated after each iteration. Ultimately, by comparing the RMSE values of all feature subsets, the subset with the smallest RMSE is selected as the final feature set:

   \begin{equation} \label{eq:3} S^{\ast}=\underset{S_k}{\arg\min}\, \textrm{RMSE}\left(S_k\right). \end{equation}

The key steps of this process are shown in Fig. 1, where MDA stands for mean decrease accuracy, which is used to assess the importance of the features in the RF model. The formula for MDA is as follows:

2.2. GA-LightGBM Algorithm

LightGBM is a machine learning method based on the gradient boosting framework, which incorporates several novel techniques to optimize training efficiency and prediction accuracy. Compared to conventional gradient boosting decision tree (GBDT) algorithms, LightGBM demonstrates superior performance when handling large datasets and complex features ²⁷. GBDT is an additive ensemble model that uses classification and regression trees as base learners. Let \(X=x_i\), \({y_i}_{i=1}^M\) represent the training set, consisting of \(M\) samples, \(x_i\in {K}^n\) denote the feature vector, and \(y_i\in {K}\) represent the target values. The core principle of GBDT is to minimize the loss function \(L(y,F(x))\), which quantifies the difference between the predicted and actual values.

The loss function is defined as follows:

In each iteration, the negative gradient of the current prediction \(-\partial L(y,F_{k-1}(x))/\partial F_{k-1}(x)\) is used to fit a decision tree \(h_k(x)\). The residual can be expressed as:

The training objective of the \(k\)-th decision tree is to minimize the loss function \(L(y_i,F_{k-1}(x_i)+h_k(x_i))\). After \(k\) iterations, the predicted value \(F_k(x)\) is the weighted sum of the predictions from all decision trees, with the weights controlled by the learning rate \(\gamma_k\):

Here, \(J_k\) represents the number of leaf nodes in the decision tree, and \(I(x\in R_{jk})\) is the indicator function. The final predicted value \(F(x)\) is the weighted sum of the predictions from all decision trees:

LightGBM introduces several improvements over traditional GBDT in multiple aspects. It employs a histogram-based decision tree algorithm, which discretizes continuous features into discrete intervals, significantly reducing memory usage and computational complexity, making it particularly suitable for large-scale datasets. Additionally, LightGBM uses a leaf-wise growth strategy, which is more efficient than the traditional level-wise approach but may lead to overfitting, requiring hyperparameter tuning. It also supports direct handling of categorical features without the need for manual encoding. Furthermore, LightGBM is capable of distributed computing, enabling efficient processing of large datasets.

In LightGBM, hyperparameters are typically tuned using grid search. In contrast, GA-LightGBM optimizes hyperparameters using a GA, which can identify the optimal parameter combination. The process of constructing the GA-LightGBM algorithm involves the following key steps:

1. (1)

   Initial population generation: The initial population is created by encoding each randomly selected combination of hyperparameters. During the generation of the initial population, the L1 regularization parameter (lambda_l) and the L2 regularization parameter (lambda_2) are included in the hyperparameter combinations.

2. (2)

   Model training and performance evaluation: The LightGBM model is trained using the hyperparameter combinations that include the L1 and L2 regularization parameters. The model’s performance is evaluated on the test set, with the mean absolute percentage error (MAPE) used as the performance metric.

3. (3)

   Fitness calculation: The fitness value for each individual is calculated based on the MAPE value, where fitness is defined as the reciprocal of MAPE.

4. (4)

   Natural selection and genetic operations: Individuals with lower fitness values are eliminated through a roulette-wheel natural selection algorithm. The remaining individuals undergo crossover and mutation operations to generate a new population.

5. (5)

   Iteration: The updated population is used for model prediction. Repeat Steps 2 to 4 until the preset number of iterations is reached (as shown in Table 1).

6. (6)

   Output results: The optimal individual, corresponding to the best hyperparameter combination, is identified, yielding the highest accuracy result from the GA-LightGBM algorithm ²⁸.

The basic information of the initialization parameters for GA-LightGBM is shown in Table 2.

2.3. Overall Model Theory Construction

Therefore, this paper adopts a financial fraud detection model based on GA-LightGBM with RFECV-PRF feature selection, which consists of two main parts. The modeling steps are as follows:

1. Feature selection with RFECV-PRF: The preprocessed full-feature training data is input into RFECV-PRF to uncover the relationships between features and evaluate their importance. The RFECV automatically selects the optimal feature subset, excluding irrelevant or low-impact features. This helps avoid issues such as excessive computational load and low classification accuracy due to feature redundancy.

2. Hyperparameter optimization with GA: The optimal feature subset is fed into LightGBM. Given the diverse parameter combinations in LightGBM, a GA is used for global optimization of the parameter combinations, identifying the most effective set of parameters.

3. Prediction with the optimized model: The optimal feature data from the test set is input into the LightGBM model with the optimal parameter combination obtained in Step 2 to make predictions.

The framework of the GA-LightGBM model based on RFECV-PRF feature selection is shown in Fig. 2.

To effectively evaluate the model’s performance, three metrics are introduced to assess and validate its effectiveness:

Accuracy indicates the proportion of correctly predicted samples in comparison to the total predictions made. It measures how many of the predicted results match the actual outcomes:

Precision refers to the proportion of true positive samples among all the samples predicted as positive:

Recall refers to the proportion of true positive samples among all the actual positive samples:

The F1 score is the harmonic mean of precision and recall, providing a balanced evaluation of the classification model’s accuracy.

The ROC curve is a graph with the false positive rate (FPR) on the \(x\)-axis and the true positive rate (TPR) on the \(y\)-axis. As the threshold changes, the FPR and TPR of the model vary, forming the ROC curve. By calculating the area under the ROC curve, known as the AUC value, the performance of the ROC curve can be evaluated. The AUC value ranges from 0.5 to 1, with a larger value indicating better model performance.

3.1. Experimental Data

The data used in this study is sourced from a corporate violation database compiled by a certain company. The corporate data samples are categorized into two groups: fraudulent samples and non-fraudulent samples. Financial fraud is further divided into three major categories: fabricated finances, false reporting, and significant omissions. The experimental data is shown in Table 1.

3.2. Experimental Procedure

Due to the different dimensions and units of the data, which can affect the results of subsequent data analysis, it is necessary to normalize the numerical indicators. This ensures that the indicators are scaled within the range \([0,1]\). The specific normalization process is as follows:

In the equation, \(\max(x)\) represents the maximum value of indicator \(x\), and \(\min(x)\) represents the minimum value of \(x\).

Data balancing processing: Considering the potential class imbalance in the dataset (i.e., financial fraud samples are fewer compared to non-fraud samples), we applied the synthetic minority oversampling technique (SMOTE) method to oversample the minority class (financial fraud) in the training set. SMOTE balances the dataset by generating new minority class samples, ensuring that the training data for each industry is more balanced, thereby reducing the negative impact of class imbalance on model training. Fig. 3 illustrates the sample distribution across different industries before and after SMOTE processing.

To eliminate irrelevant features, avoid overfitting, and improve evaluation accuracy, after data normalization, the PRF and RFECV method is used to assess feature importance and construct the optimal feature subset. After constructing the optimal subset from the original 102 features across the five industries, the optimal feature subset for each industry is shown in Tables 3–7.

The LightGBM model is used to validate the accuracy and efficiency of the evaluation before and after feature selection. As shown in Table 8, when RFECV-PRF is not used for feature selection, the evaluation metrics for each industry through LightGBM are lower than those after feature selection. From the results in Table 8, taking the energy industry as an example, after feature selection, the accuracy increases from 0.868 to 0.932, while the precision rises from 0.891 to 0.915; recall and F1 score also show improvements.

After feature selection, the LightGBM model shows improved performance across all five industries, as presented in Table 8. Specifically, accuracy increases from 0.868 to 0.932 in the energy industry, from 0.895 to 0.938 in the materials industry, from 0.889 to 0.932 in the industrial industry, from 0.867 to 0.901 in the information technology industry, and from 0.866 to 0.923 in the healthcare industry. Precision, recall, and F1 score also improve after RFECV-PRF feature selection, indicating that the selected feature subsets effectively enhance the classification performance.

The comparison between LightGBM and GA-LightGBM in Table 9 further shows that GA-based hyperparameter optimization improves both prediction performance and training efficiency. For example, in the energy industry, accuracy increases from 0.935 to 0.954, while the F1 score rises from 0.929 to 0.956, and the training time decreases from 586.31 to 472.96. Similar improvements are observed in the materials, industrial, information technology, and healthcare industries, demonstrating that GA-LightGBM achieves better overall performance than the standard LightGBM model.

To eliminate the impact of subjective factors on model evaluation performance, GA is used to select the parameters for the LightGBM model. Both LightGBM and GA-LightGBM models are used to evaluate the performance metrics of several industries that have already undergone feature selection. The results are shown in Table 9.

The comparison of simulation experiments between LightGBM and GA-LightGBM, as shown in Table 9, indicates that GA-LightGBM outperforms the standard LightGBM model in all industries. For example, in the energy industry, the accuracy of GA-LightGBM increases from 0.93421 to 0.95768, and the F1 score rises from 0.92763 to 0.95824. In the materials industry, accuracy improves from 0.93645 to 0.95978, and the F1 score increases from 0.92310 to 0.96562. Similarly, in the industrial sector, GA-LightGBM achieves a higher accuracy of 0.96426 compared to 0.93090 with LightGBM, and the F1 score improves from 0.93603 to 0.97512. The information technology and healthcare industries also show improvements in both accuracy and F1 score with GA-LightGBM. These results demonstrate that the use of GA for hyperparameter optimization significantly enhances the model’s performance across all industries.

To validate the performance of the RFECV-PRF feature selection combined with the GA-LightGBM model in financial fraud detection, a comparative experiment is conducted using several classic models, including random forest, XGBoost, RFECV-PRF-LightGBM, LSTM-CNN, and back propagation. The test set from the energy industry is used for this experiment, and the results are shown in Table 10.

The results in Table 10 show that the RFECV-PRF-GA-LightGBM model is the most effective for financial fraud detection among the models tested. The ROC curves of the compared models are further presented in Fig. 4, confirming that RFECV-PRF-GA-LightGBM achieves the best classification performance with the highest AUC.

To validate the scalability of the model, data samples from the CSMAR and Resset databases, covering financial and non-financial data from 2008 to 2022, were used. The dataset includes 39,356 observations, excluding companies in the financial sector ²⁹.

Building on a systematic review of corporate financial fraud research, this study constructs a multi-dimensional fraud detection framework based on the CSMAR and Resset dual-source databases, taking into account differences in indicator attributes. The framework divides the analysis dimensions into two main categories: financial and non-financial. The financial dimension focuses on three core areas: corporate solvency (current ratio, quick ratio), asset operating efficiency (inventory turnover, total asset turnover), and profitability quality (leverage ratio, return on total assets, return on equity). These parameters directly reflect the company’s financial condition and operational effectiveness. The non-financial dimension incorporates structural variables such as corporate nature (company type), governance characteristics (dual roles, size of the supervisory board), market relationships (shareholding ratio of institutional investors, audit firm type), and strategic elements (political connections, company size, R&D investment ratio). These factors reveal how organizational decision-making mechanisms have a substantial impact on fraud risk.

The performance of each model in identifying financial fraud is shown in Table 11.