Problem statement

Given an input dataset X consisting of n instances and p attributes, where p = q + r, such that q represents the class attribute and r represents the non-class attributes. The dataset is divided into two subsets:

• X_c: The subset of X with complete attribute values:(1)where x_i contains no missing values, and k is the number of possible class labels.
• X_m: The subset of X with missing values in non-class attributes:(2)where some features in x_i are missing.

The objective is to impute missing values in X_m using an adaptive SVR model optimized by GA and then classify the imputed dataset using DT. Let X_c′ be the subset of X_c with no class attributes, and X_m′ be the subset of X_m with no class attributes. Let be the imputation function that predicts missing values in X_m′, where the strategy is selected adaptively based on missingness level and the SVR configuration is optimized using GA.

The imputation function f is dynamically selected based on the missingness percentage ():

(3)

where and are predefined thresholds that classify missingness as low (<10%), moderate (10–25%), and high (>25%). We set the thresholds = 10% and by adapting cut-offs that are widely used in empirical studies on missing-data patterns [27]. Although these works are not healthcare-specific, an exploratory analysis of the missing-value percentages in our datasets showed that these thresholds naturally partition attributes into low (<10%), moderate (10–25%), and high (>25%) missingness groups. Consequently, and serve as reasonable operating points for defining the three adaptive imputation regimes used in this work. Missingness below 10% is often considered negligible and suitable for simple imputation methods like SVR. If the missingness is between 10–25%, then missing values start affecting model stability, which requires more robust techniques such as Iterative SVR. Beyond 25% of missingness, imputation becomes increasingly error-prone, and combining global modeling with local refinements (e.g., KNN-SVR) helps maintain data fidelity. The set of imputed missing values is defined as:

(4)

where, f(x_i) represents the predicted values obtained from the GA-optimized SVR (SGA) model. The dataset after imputation is:

(5)

Here X′ contains the complete dataset with imputed missing values. A decision tree classifier T is trained on X′, and the predicted class label for an instance x_i is:

(6)

Optimization objective

The objective is to find suitable hyperparameter configurations for the SVR model and the decision tree T that maximize classification accuracy while ensuring that SVR-imputed values remain within an acceptable error margin:

(7)

where is the user-defined prediction error threshold ensuring imputed values remain within an acceptable deviation from actual values, denotes the Euclidean norm to measure imputation accuracy, and is a predefined tolerance value selected within the range [0.001, 0.1] based on empirical validation, ensuring a balance between imputation precision and model generalization. In this work, is selected from the interval [0.001, 0.1] based on preliminary experiments that examined the trade-off between imputation precision and model stability. Once chosen, this value remains fixed throughout the optimization process. is the indicator function that returns 1 if the condition is true, and 0 otherwise. The objective function aims to minimize the classification error rate, while ensuring high-quality imputation from the SVR model.

Since hyperparameter optimization can increase the risk of overfitting, preventive measures are introduced in the evaluation procedure. Hyperparameter settings are assessed using 5-fold cross-validation on the training data, and generalization performance is reported on a separate held-out test set. Residual risks of overfitting and their implications for external validity are further discussed in the Threat to Validity section.

Architecture of the SGA-DT framework

The proposed SGA-DT framework presents an adaptive and intelligent solution for handling missing values in non-class attributes while ensuring reliable classification. The framework operates in two distinct yet integrated phases: (1) Missing value imputation using GA-optimized SVR, and (2) Classification using DT. By dynamically selecting the imputation strategy based on the level of missingness and optimizing SVR parameters using GA, the SGA-DT framework tries to enhance both the quality of imputed data and the overall predictive performance. Fig 1 illustrates the schematic diagram of the proposed SGA-DT framework. The choice to integrate GA and DT into the SGA-DT framework is motivated by their complementary roles in optimization and interpretability. Since the quality of SVR-based imputation depends strongly on the choice of kernel and hyperparameters, GA is employed to perform joint, data-driven optimization of these parameters, enabling the SVR model to adapt to heterogeneous missingness patterns and attribute distributions. Moreover, as SVR is not inherently interpretable, Decision Tree classifier is incorporated after imputation to provide transparent, rule-based predictions, which is essential for healthcare decision-making. Thus, GA ensures optimal and stable imputations, while DT ensures interpretability and clinically meaningful classification outcomes.

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Fig 1. Proposed SGA-DT framework.

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Missing value imputation using adaptive SVR

Before missing values can be imputed, the dataset D must be processed and refined to ensure a robust imputation strategy. Let the dataset D be defined as:

(8)

where, represents the feature vector of instance i, y_i denotes the corresponding class label, and p is the total number of attributes in the dataset. Among these, r denotes non-class attributes and q denote class attributes, so that p = r + q describes the attribute partition used in the subsequent imputation procedure. To facilitate imputation, the dataset D containing missing values is taken. A new dataset D_c is constructed by retaining only the complete (non-missing) attributes, ensuring that reliable data is available for imputation. To facilitate the imputation process, a non-class attribute C_i with missing values is selected, which becomes the target column for imputation.

Although columns with no missing values are initially selected to form D_c, this step does not eliminate informative attributes permanently. Instead, it isolates complete attributes to establish a stable reference space for correlation analysis and model training. Using incomplete columns during imputation can introduce bias and noise because the learning algorithm would rely on partially observed data with inconsistent variance. Therefore, D_c provides a clean basis for estimating correlations and fitting the SVR model, which subsequently imputes the removed (incomplete) columns one by one. This approach preserves all original attributes in the final dataset while ensuring each imputation is guided by statistically reliable predictors rather than partially missing ones. The dataset is then analyzed to compute the correlation between C_i and other features in D_c. Features with correlation values are removed to prevent irrelevant attributes from degrading SVR imputation quality [28].

(9)

where, represents the Pearson correlation coefficient [29]. To effectively train the SVR model, the dataset is split into two subsets: Training set, containing instances where C_i has no missing values, and Testing set, which contains instances where C_i has missing values and will be used for imputation. This ensures that SVR learns from complete instances before predicting missing values. SVR is applied to predict the missing values of C_i based on the observed values in D_c. The imputation process varies based on the level of missingness.

The missingness percentage of the selected attribute C_i is assessed to determine the appropriate imputation strategy. The missing value percentage in the datasets is determined by calculating the proportion of instances that contain at least one missing attribute. This metric provides an accurate representation of the extent of missing data by considering instances that are partially incomplete, rather than just the total number of missing entries. This adaptive strategy ensures that attributes with varying degrees of missingness are handled optimally. Based on the missingness percentage, the following strategies are applied:

• Low Missingness: In this case, the percentage of missing values is ≤10%. When the missing data is minimal, the patterns and relationships in the available dataset remain largely intact. Hence, standard SVR imputation is directly applied to estimate missing values based on the correlation of the target attribute with other fully observed attributes. This ensures a reliable imputation without introducing additional computational complexity.(10)where, C_i represents the missing non-class attribute to be imputed, f(X_c) is the SVR prediction function that estimates C_i based on the observed attributes in the dataset X_c, and is the residual error term, capturing small deviations due to noise in the data.
• Medium Missingness: In this case, the percentage of missing values lies between 10% and 25%. In such cases, a single pass of imputation may not be sufficient, as missing values might still affect model predictions. To improve accuracy, an iterative SVR imputation strategy is employed, where the initially imputed values are used as inputs for subsequent refinements. The process continues over multiple iterations until the imputed values converge to stable estimates, minimizing the impact of missing data.(11)where, represents the imputed value at iteration t, and is the updated imputed value at the next iteration. The function uses both observed attributes X_c and the previous estimate of C_i to refine the imputation. The residual error term accounts for any small variations in prediction.
• High Missingness: When more than 25% of the values are missing, relying solely on SVR imputation may lead to unreliable predictions due to the lack of sufficient training data. In such cases, a two-stage hybrid imputation approach is applied:
  1. Initial KNN imputation: At first, KNN imputation is applied to provide a rough but structurally consistent estimate of missing values based on instance similarity. The imputed value is computed as the mean of the k nearest neighbors:(12)where is the initial imputed value for instance i, and C_i,j denotes the imputed value for attribute C_j of instance i, obtained from its k nearest neighbors. After identifying the k nearest neighbors with observed values for attribute C_j, the imputed value for C_i,j is computed from this neighborhood. For numerical attributes, C_i,j is set to the mean of the k neighbors’ values in column j, whereas for categorical attributes, the most frequent category (majority vote) among the k neighbors is used. This ensures that the imputation criterion respects the data type while reflecting the local structure around instance i.
  2. Refinement using SVR: After the initial KNN imputation provides rough estimates of the missing values, SVR is applied as a second-stage refinement step. At this point, the dataset, now structurally complete, enables SVR to be effectively trained. By learning from the approximate but complete input space, SVR captures complex, non-linear relationships that KNN alone cannot model. This refinement process adjusts the initial estimates to better align with the underlying data distribution, resulting in more accurate and reliable imputations, especially under high missingness conditions.

In existing imputation studies, missingness levels are often categorized using broad empirical ranges, with values below roughly 5–10% considered low, 10–30% as moderate, and higher percentages as high. These ranges are used only to define experimental regimes rather than to dictate how individual imputation algorithms operate. Following this general practice, the present work selects and as specific cut-offs within these commonly used ranges to define low, medium, and high missingness regimes for our adaptive SGA-DT strategy.

SVR optimization for improved imputation

To enhance the accuracy of missing value imputation, the SVR model requires careful tuning of its hyperparameters. In this work, GA is employed to optimize the key hyperparameters of SVR, ensuring that the imputed values closely align with the true data distribution. The crucial hyperparameters optimized using GA include:

• Kernel Function (K(x, x′)): It determines how input features are transformed into a higher-dimensional space for better regression accuracy.
• Regularization Parameter (C): It controls the trade-off between model complexity and training error [30].
• Epsilon-insensitive Loss (): It defines the margin of tolerance for regression predictions.
• Kernel Parameter (): It regulates the influence of training instances in the feature space.
• Polynomial Degree (d): This parameter is specific to the polynomial kernel. It defines the flexibility and complexity of the regression surface.

By optimizing these parameters, the proposed model ensures that the SVR model generalizes well to different datasets, leading to robust missing value imputation.

Genetic algorithm for hyperparameter optimization:.

To enhance the accuracy of missing value imputation, the SVR model is configured with the most suitable kernel and carefully tuned hyperparameters. In the proposed model, GA is employed to simultaneously select the optimal SVR kernel type such as Linear, RBF, or Polynomial and optimize its associated hyperparameters. These include the regularization parameter C, the epsilon-insensitive margin , and kernel-specific parameters such as the kernel coefficient (for RBF and Polynomial kernels) and the polynomial degree d (for the Polynomial kernel). This kernel-aware optimization strategy allows the SVR model to effectively capture the underlying data patterns, leading to robust and accurate imputation results. The detailed configuration of hyperparameters and genetic operators used in the proposed GA-based optimization is summarized in Table 3.

1. Initialize population: A population of candidate SVR configurations is randomly generated. Each configuration includes the kernel type and its associated hyperparameters:(16)
   Each individual in the population is encoded as a chromosome that includes:
   Here, kernel_i is a categorical gene representing the SVR kernel type (Linear, RBF, or Polynomial), C_i is the regularization parameter sampled from a logarithmic scale, is the kernel coefficient (used in RBF and Polynomial kernels), is the epsilon-insensitive margin, and d_i is the polynomial degree (used only for the Polynomial kernel). This representation enables the GA to simultaneously explore both kernel selection and kernel-aware hyperparameter optimization.
2. Evaluate fitness: Each chromosome in the population encodes a candidate SVR configuration, including the kernel type and its associated hyperparameters. During fitness evaluation, only the parameters relevant to the selected kernel are used to train the SVR model. The trained SVR model is used to impute missing values, and the quality of imputation is assessed using the MSE between the actual and predicted values of the non-class attribute:(17)
   Here, C_i is the actual observed value and is the value predicted by the SVR model. MSE serves as the fitness function in GA, guiding the selection of candidate solutions that produce more accurate imputations.
3. Selection: In this work, tournament selection method is applied to choose high-quality individuals from the current population. A small subset of chromosomes is randomly selected, and their fitness values (based on MSE) are compared. The chromosome with the lowest MSE indicating the best imputation performance, is chosen as a parent for the next generation. This process is repeated to build a mating pool for crossover and reproduction.
4. Crossover: Selected parents undergo crossover to produce offspring that inherit traits from both parents. In the proposed work, chromosomes encode both kernel type and associated SVR hyperparameters. A combination of uniform and blended crossover is used:
   • Kernel type: Categorical gene (Linear, RBF, Polynomial) — inherited using uniform crossover, i.e., randomly chosen from either parent.
   • Continuous Parameters: The real-valued parameters C, , and are combined using blended crossover:
   • Polynomial Degree: As it is integer-valued, it is handled using randomized averaging or rounding:
   • Here, is a blending factor randomly chosen for each crossover event. This hybrid strategy allows for effective mixing of parent traits while respecting the nature of each gene (categorical, continuous, or discrete).
5. Mutation: To maintain genetic diversity and avoid premature convergence, mutation is applied by introducing small random changes to one or more genes in the chromosome. The mutation strategy is tailored to the type of gene:
   • Kernel Type (categorical): With a low probability, the kernel type is randomly switched to one of the other available options (Linear, RBF, Polynomial).
   • Continuous Parameters (): A small noise term is added to each parameter to introduce variability and help explore new regions of the search space:(18)where , and is sampled from a uniform or Gaussian distribution.
   • Degree: For Polynomial kernel, the degree is adjusted by a small integer:(19)
     The mutated degree is clipped to remain within a valid predefined range (e.g., 2–5).

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Table 3. SVR hyperparameters and genetic algorithm configuration.

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This mutation strategy supports kernel-aware exploration and ensures that each gene evolves in a manner appropriate to its data type.

The GA proceeds through multiple generations until the minimal fitness value (i.e., the lowest MSE) is obtained, indicating that no further improvement can be achieved. After the optimization process, the SVR configuration with the lowest MSE is selected, including the best-performing kernel type (Linear, RBF, or Polynomial) and its optimized hyperparameters. This kernel-aware GA-driven search ensures that the imputation model is both accurate and well-aligned with the underlying data structure. The selected SVR model is then applied to impute the missing values. Algorithm 1 outlines the step-by-step procedure of the proposed SGA-DT framework. Initially, the adaptive imputation strategy is presented (lines 12–20), where the choice of SVR variant (standard, iterative, or KNN + SVR) taken by considering the level of missingness. The GA-based optimization of the SVR model is presented in second part from lines 21–27, which includes kernel selection and tuning of hyperparameters (C, , and d). This optimization is applied only when SVR is used, ensuring the model is well adapted to the imputation task. The subsequent steps involve imputation followed by classification using DT, and then evaluating the model performance.

Algorithm 1 GA-optimized SVR imputation followed by decision tree classification

Classification using DT

Once the missing values are imputed, the complete dataset is used to train the DT. The overall procedure for decision tree induction is illustrated in Algorithm 2, which builds the tree based on recursive partitioning of the data and selection of optimal split conditions. The algorithm begins with a training set consisting of instances and their corresponding class labels. Initially, an empty node N is created. If all instances belong to the same class, the node is labeled accordingly. In case the attribute list becomes empty, the node is labeled with the majority class, following the majority-voting rule [32]. Otherwise, the best attribute is selected for splitting based on attribute selection criteria. The subsequent steps guide the recursive splitting of data tuples based on attribute types. For discrete and binary attributes, splitting occurs based on distinct values, while for continuous attributes, midpoints between adjacent sorted values are considered. A critical component in this process is the splitting criterion, which identifies the attribute that best partitions the dataset into homogeneous subsets [33]. The partitioning continues until further splitting is not possible or meaningful, resulting in a fully induced tree [34].

Algorithm 2 Decision tree induction

In our proposed SGA-DT framework, the classification and regression trees (CART) algorithm is used for classification [35]. CART constructs binary decision trees and can handle both discrete and continuous attributes. It employs the Gini Index (GI) as a splitting criterion, which measures node impurity and helps select the attribute that best separates the data. For a dataset D, the Gini Index is computed as [36]:

(20)

where, is the ratio of number of tuples present in the dataset with respect to a particular class to the total number of tuples present in D. For a binary split with respect to an attribute ‘t’, GI can be calculated as:

(21)

where, D_i is the gini index with respect to a partition. Due to the binary split on attribute t, the reduction in impurity is computed as:

(22)

All feasible binary splits are considered for each attribute, and the split yielding the maximum impurity reduction, with minimum GI_red(t) is chosen. For continuous-valued attributes, CART evaluates all possible midpoints between adjacent values, similar to ID3 [37].

Computational complexity analysis

The overall computational complexity of the SGA-DT framework for missing value prediction and classification can be evaluated by adding up the time complexities of each step in the algorithm. The computational complexity of the proposed SGA-DT imputation and classification algorithm is primarily influenced by three phases: missing value imputation using SVR, hyperparameter optimization using GA, and classification using DT. The first phase involves computing correlations between the target attribute and other available features, which takes O(nm) time, where n is the number of features and m is the number of samples. Splitting the dataset into training and testing subsets requires O(m) time, while training the SVR model incurs a complexity of O(m³) in the worst case due to matrix operations, which can be optimized to O(m²) with efficient kernel approximations. Predicting missing values for each instance takes time, where d is the number of missing values. The second phase, hyperparameter tuning using GA, optimizes SVR parameters () by iterating over a population of candidate solutions. Each generation requires evaluating P individuals, and since each SVR training takes O(m²), the per-generation complexity is , leading to an overall GA complexity of for G generations. Finally, the decision tree classifier is trained on the imputed dataset, with a training complexity of , assuming a balanced tree structure. The classification of test instances requires operations, making the overall DT complexity . The dominant computational factor is the SVR training complexity (O(m³) in the worst case) and GA-based hyperparameter tuning (), making the algorithm computationally intensive for large datasets. However, techniques such as kernel approximations for SVR, parallel GA execution, and decision tree pruning can significantly reduce computation time. Thus, while the SGA-DT framework offers high imputation accuracy and classification performance, its computational efficiency largely depends on dataset size, the number of features, and GA parameters, making it well-suited for medium to large-scale datasets with proper optimizations.

Datasets

To evaluate the effectiveness of the proposed SGA-DT framework, we considered a diverse collection of datasets obtained from well-established repositories including UCI, KEEL, and Kaggle. These datasets exhibit varying levels of missingness across numerical and categorical attributes, enabling a thorough assessment of the framework under different data quality conditions. The selected datasets span multiple domains such as healthcare, environmental science, with a particular focus on healthcare datasets to demonstrate the model’s applicability in critical decision-making contexts. To ensure generalizability, we also include two synthetic datasets with controlled missing value patterns generated under the missing at random (MAR) pattern. These datasets support systematic evaluation of the model’s performance on high-dimensional and mixed type data. Table 4 summarizes the characteristics of all datasets used, including the number of instances, attribute types, and missing value distributions. The proposed SGA-DT framework was trained and evaluated independently on each dataset without any merging or joint training. Moreover, missing-value imputation and GA-based SVR optimization were performed exclusively within the training folds of each dataset under 5-fold cross-validation. As no information from test folds or external datasets is used during imputation or optimization, this design avoids data leakage and reduces the risk of overfitting associated with amalgamated training.

• Breast Cancer [38]: The Breast Cancer dataset, sourced from the Oncology Institute and accessed via KEEL, is widely used in medical data mining research. It captures demographic and pathological factors associated with breast cancer recurrence. The dataset has been frequently cited in oncology-related machine learning studies due to its real-world origin and interpretability of features.
• Mammographic [39]: It is obtained via the KEEL repository and originally collected at the Institute of Radiology, University of Erlangen-Nuremberg, supports the classification of breast mass lesions using BI-RADS features. It is primarily used to predict malignancy and is valued for its diagnostic relevance in radiology and clinical decision support applications.
• Hepatitis [40]: It is a medical dataset used for predicting patient survival. It includes laboratory test results and clinical observations. The missing values are found in numerical attributes such as bilirubin and albumin levels. This dataset is particularly useful for assessing the effectiveness of imputation in healthcare-related classification tasks.
• Air Quality [41]: It is used for predicting pollutant concentration levels in the environment based on chemical sensor readings and meteorological data. Due to its real-world application in environmental monitoring and public health, the dataset is well-suited for assessing predictive modeling techniques.
• Adult [42]: The Adult dataset, derived from the 1994 U.S. Census, is used to predict whether an individual earns more than $50K annually. It includes demographic and occupational features, with missing values occurring in categorical attributes such as work class and occupation. Proper encoding technique is used for handling these missing values effectively.
• KDD Cup 1998 [43]: It is used for binary and multi-class classification, predicting whether a donation will be made in a direct marketing campaign based on demographic and behavioral data. Due to its real-world application in customer relationship management and fundraising, the dataset is valuable for evaluating predictive modeling techniques while ensuring data confidentiality.
• Synthetic Data 1: This dataset has been generated to simulate high missingness conditions (>25%). It contains only numerical attributes, making it ideal for evaluating the robustness of imputation techniques in highly sparse data environments. The dataset ensures that the model is tested under extreme missingness scenarios.
• Synthetic Data 2: This dataset is designed to mimic real-world structured data with a mix of categorical and numerical attributes. It has moderate missing values, making it useful for assessing the imputation efficiency when handling both categorical and numerical missing data. The dataset is included to ensure a comprehensive evaluation of the proposed model.

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Table 4. Characteristics of datasets.

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Both synthetic datasets were generated programmatically to simulate controlled missingness patterns. First, fully observed records were created with the numbers of instances, feature types, and dimensionalities reported in Table 4. Then, missing values were injected using a MAR mechanism, in which the probability that an entry in attribute C_j was set to missing depended on the observed values of auxiliary attributes rather than on the unobserved value itself. The corresponding missingness probabilities were calibrated so that the overall missingness levels matched the desired targets (e.g., high missingness for Synthetic Data 1 and moderate missingness for Synthetic Data 2).

The Mammographic dataset does not contain raw mammography images; instead, it consists of structured, tabular BI-RADS based features derived from mammographic examinations. In contrast, the Breast Cancer dataset comprises clinical and pathological attributes related to disease prognosis and recurrence, rather than radiological descriptors. Thus, while both datasets address breast cancer–related prediction tasks, they differ in the clinical stage and information source they represent, radiology-derived assessment features versus patient-level clinical and pathological variables. The Adult and KDD Cup 1998 datasets contain large volumes of data, making them suitable for validating the scalability of the proposed framework. Most datasets contain mixed or numerical attributes, with a few involving only categorical features. To enable SVR-based imputation, categorical attributes with missing values are transformed using label encoding, which assigns unique integers to categorical values while preserving their distinct identities. For example, in the Adult dataset, categorical variables such as Workclass, Occupation, and Native-country are encoded before imputation.

Results and discussions

To assess the effectiveness of the proposed SGA-DT framework, we conducted a comparative analysis against various integrated frameworks that combine different imputation techniques (drop, mean, mode, median, KNN, LR, NN) with DT classification. These include statistical imputation models (Mean-DT, Median-DT, Mode-DT), a traditional model using row deletion (Drop-DT), and machine learning-based imputation models (KNN-DT, LR-DT, NN-DT). We have also used SVR-DT as a comparison model, where canonical SVR (without GA optimization) is used for imputation. To ensure consistency, DT is used as the classifier across all models.

The performance of all integrated frameworks was assessed using four evaluation metrics: accuracy, precision, recall, and F-measure. As shown in Table 5, the proposed SGA-DT framework consistently outperforms all other methods across most datasets. It achieves the highest accuracy on all eight datasets, with particularly strong results in Synthetic Data 1 (94.1%) and Adult (96.6%). SVR-DT, which employs canonical SVR for imputation, ranks second in most datasets, validating the impact of genetic algorithm-based optimization in SGA-DT. Among machine learning-based integrated frameworks, NN-DT and LR-DT also perform well, showing competitive accuracy and stability across datasets. Among the statistical methods, Median-DT demonstrates the best performance overall, whereas Mean-DT outperforms in a few specific cases. Drop-DT consistently records the lowest accuracy due to information loss caused by discarding incomplete rows. The proposed SGA-DT framework consistently outperforms all other frameworks, achieving the highest average accuracy (92.77%), followed by SVR-DT (90.81%) and NN-DT (89.87%). In terms of precision, SGA-DT again leads with an average of 91.39%, while SVR-DT and NN-DT follow with 89.50% and 89.10%, respectively. For recall, SGA-DT records the top value of 91.38%, compared to SVR-DT (89.09%) and NN-DT (88.52%). Similarly, SGA-DT achieves the highest F-measure (91.48%), indicating a well-balanced trade-off between precision and recall.

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Table 5. Performance results of various integrated frameworks across all the datasets.

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Fig 2 illustrates the comparative performance of all integrated frameworks in terms of accuracy across eight datasets. Drop-DT consistently records the lowest accuracy. Among statistical frameworks, Median-DT outperforms Mean-DT and Mode-DT in most cases, demonstrating its robustness against outliers. The machine learning-based frameworks significantly outperform statistical frameworks, with SGA-DT achieving the highest accuracy across all datasets. Notably, in datasets like Hepatitis, Adult, and Breast Cancer, SGA-DT achieves an accuracy exceeding 92%, highlighting the benefit of GA optimization. SVR-DT also performs consistently well, often ranking second, followed closely by NN-DT. LR-DT and KNN-DT show moderate accuracy but trail SGA-DT by a noticeable margin.

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Fig 2. Performance comparison of SGA-DT with other integrated frameworks in terms of accuracy.

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The precision-based comparison in Fig 3 highlights the superior performance of the SGA-DT framework across all datasets. It achieves the highest precision in every case, with particularly strong results in Synthetic Data 1 (92.9%), Adult (92.7%), and Synthetic Data 2 (94.5%). SVR-DT emerges as the second-best model overall, with close precision values in several datasets, for example, 91.8% in Breast Cancer and 92.5% in Adult. NN-DT also maintains good precision performance, with scores exceeding 86% across most datasets, followed by KNN-DT. Among the statistical frameworks, Median-DT exhibits relatively higher precision compared to Mean-DT and Mode-DT, although Mode-DT outperforms in certain instances. Drop-DT consistently shows the lowest precision, with particularly poor performance on the KDD Cup and Mammographic datasets, where its results fall significantly behind the other methods. The results confirm that machine learning-based imputation, particularly when enhanced with optimization (SGA-DT), preserves class relevant feature structure better than simple averaging or deletion methods, leading to fewer false positives and improved classification confidence.

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Fig 3. Performance comparison of SGA-DT with other integrated frameworks in terms of precision.

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Fig 4 highlights the effectiveness of different imputation techniques in correctly identifying positive instances. The proposed SGA-DT consistently achieves the highest recall, with 93.0% in KDD Cup, 86.7% in Air Quality, 92.0% in Breast Cancer datasets. SVR-DT ranks second in most cases, demonstrating strong performance, followed closely by NN-DT and LR-DT. KNN-DT performs reliably, especially in the Adult and Synthetic Data 1 datasets. Among the statistical frameworks, Median-DT consistently outperforms Mean-DT and Mode-DT, whereas there is a deviation in case of Mammographic dataset. Drop-DT continues to show the lowest recall across all datasets, reaffirming that simply removing missing values adversely affects model sensitivity.

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Fig 4. Performance comparison of SGA-DT with other integrated frameworks in terms of recall.

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The F-measure comparison, illustrated in Fig 5, highlights the balance between precision and recall across different imputation strategies. SGA-DT consistently achieves the highest F-measure scores, with 91.4% in Breast Cancer, 92.3% in Adult, and 92.3% in Synthetic Data 1, confirming its effectiveness in maintaining classification reliability. SVR-DT follows closely in most cases maintaining a strong balance between precision and recall. KNN-DT also demonstrates consistent performance, achieving over 87% F-measure in most datasets and ranking among the top frameworks in several cases. Among statistical methods, Median-DT outperforms Mean-DT and Mode-DT across most datasets, suggesting greater stability in handling missing data. Drop-DT lags behind all other frameworks, with the lowest F-measure in nearly every dataset.

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Fig 5. Performance comparison of SGA-DT with other integrated frameworks in terms of F-measure.

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To make a comparative analysis of overall performance of all the integrated frameworks, box plot analysis is performed, which is shown in Fig 6. The analysis is performed based on each of the evaluation parameters by considering all the datasets. The results for each of the performance parameters are obtained by performing a five-fold cross-validation for each of the integrated frameworks on each of the considered datasets. The results are then shown in the form of a box plot. The box plot represents the maximum, minimum, average, 1/4th quartile, and 3/4th quartile values of each performance parameter.

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Fig 6. Boxplot analysis of performance metrics for SGA-DT and other integrated frameworks.

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Fig 6a presents the boxplot analysis for accuracy, while Fig 6b–6d illustrate the performance distributions for precision, recall, and F-measure, respectively. Across all four metrics, SGA-DT consistently outperforms other frameworks, achieving the highest median accuracy of approximately 92.7%, with values ranging from 89.9% to 96.6%. This narrow and elevated span reflects the robustness and reliability of the proposed model across diverse datasets. In comparison, other machine learning-based frameworks such as NN-DT and LR-DT exhibit competitive yet more variable accuracy distributions. NN-DT shows relatively high maximum accuracy but slightly lower median and wider interquartile range, indicating less consistency. LR-DT demonstrates moderate accuracy, but lower upper-bound accuracy. The KNN-DT framework performs better than LR-DT in terms of median accuracy.

Fig 6b presents the precision distribution across all integrated frameworks. SGA-DT achieves the highest and most stable precision across datasets, followed by SVR-DT. For precision, SGA-DT maintains a high median of 91.5%, with values ranging from 84.2% to 94.5%, indicating both high predictive quality and consistent performance in identifying true positives. Similarly, Fig 6b shows that SGA-DT achieves the highest median precision of 91.5%, followed by SVR-DT (86.8%) and KNN-DT (84.8%), highlighting its superior ability to minimize false positives. Among the statistical frameworks, Median-DT performs better than Mean-DT and Mode-DT, while Drop-DT records the lowest precision.

Fig 6c further illustrates that SGA-DT also maintains the highest recall (91.8%), confirming its reliability in capturing true positives. SVR-DT ranks second (88.2%), followed by NN-DT and KNN-DT, with LR-DT slightly behind. Statistical frameworks, particularly Mean-DT, show relatively consistent but lower recall values compared to the machine learning-based approaches. Fig 6d shows that SGA-DT achieves the highest F-measure (91.8%), confirming a well-balanced precision-recall trade-off. SVR-DT and KNN-DT follow with 87.5% and 84.4%, respectively. Among the statistical frameworks, Median-DT records the best F-measure, while Drop-DT consistently performs the worst across all metrics.

In addition to the experiments discussed earlier, an additional analysis was performed to evaluate how different levels of missingness affect model performance. For this purpose, missing values were introduced into the previously complete datasets using MAR mechanism, with missingness levels ranging from 10% to 50%. The resulting trends in accuracy, precision, recall, and F-measure for each missingness level are shown in Fig 7a–7d respectively. As expected, increasing missingness degrades the performance of all frameworks. However, SGA-DT consistently outperforms all other frameworks across every metric and missing value percentage. Notably, it maintains a clear advantage over SVR-DT, validating the effectiveness of genetic algorithm-based hyperparameter optimization and kernel selection. In Fig 7a, NN-DT, LR-DT, and KNN-DT display a linear drop in accuracy with increasing missing values. SVR-DT achieves better accuracy than these frameworks across most levels but is consistently outperformed by SGA-DT. SGA-DT achieves the highest accuracy at every point, demonstrating robust adaptation to incomplete data. Drop-DT shows the poorest performance, except at 50%, where it converges with Mean-DT.

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Fig 7. Effect of percentage of missing value on various performance parameters.

https://doi.org/10.1371/journal.pone.0343619.g007

Fig 7b shows that SGA-DT leads all frameworks in precision across all levels of missingness. SVR-DT performs well, ranking just below SGA-DT, which highlights the positive effect of GA optimization. At low missingness (10%), NN-DT edges slightly ahead of LR-DT, but their precision values converge at higher missing percentages. The recall analysis in Fig 7c reinforces this trend. SGA-DT achieves the highest recall values across the board, followed closely by SVR-DT. The performance gap between SGA-DT and SVR-DT grows with higher missingness, indicating that the adaptive imputation strategies in SGA-DT become more impactful as data quality decreases. Fig 7d confirms that SGA-DT maintains the highest F-measure at all missingness levels, demonstrating an effective balance between precision and recall. SVR-DT ranks second across most levels, again affirming the value of integrating GA into the imputation process. NN-DT and LR-DT perform comparably, slightly ahead of KNN-DT. At 50% missingness, all three converge, while Drop-DT consistently yields the lowest F-measure.

In addition to the quantitative evaluation, model interpretability is further explored through pruned decision trees generated from selected imputed datasets. Since generating trees for all datasets would be space-intensive, three representative datasets, each corresponding to a distinct level of missingness (low, medium, and high) are chosen to illustrate the interpretability of the SGA-DT framework. Pruned decision trees are used instead of fully grown ones, as the later often produce cluttered, overlapping structures that hinder interpretability. To enhance generalization and simplify the tree structure, cost-complexity pruning (CCP) is applied using Scikit-learn, where the (ccp_alpha parameter balances accuracy and model simplicity. Fig 8 shows the pruned decision tree for the Breast Cancer dataset (low missingness: 3.15%). Similarly, Fig 9 represents the Mammographic dataset (medium missingness: 13.61%), and Fig 10 illustrates the Hepatitis dataset (high missingness: 48.39%).

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Fig 8. Pruned decision tree generated for Breast Cancer dataset (ccp_alpha = 0.003).

https://doi.org/10.1371/journal.pone.0343619.g008

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Fig 9. Pruned decision tree generated for Mammographic dataset (ccp_alpha = 0.003).

https://doi.org/10.1371/journal.pone.0343619.g009

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Fig 10. Pruned decision tree generated for Hepatitis dataset (ccp_alpha = 0.007).

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Fig 8 illustrates the pruned decision tree generated for the Breast Cancer dataset. The tree begins with the most informative attribute, Inv-nodes, as the root node, followed by key predictors such as Tumor-size, Irradiated, and Deg-malig. The tree structure reflects clinically interpretable rules for predicting the likelihood of recurrence events. For example, patients with fewer involved nodes (Inv-nodes ≤ 0.5) and smaller tumor size are predominantly classified as no-recurrence-events. The model’s decisions align well with domain knowledge, and the pruning process (with (ccp_alpha = 0.003) effectively balances complexity and generalization by reducing overfitting while preserving interpretability. The use of Age and Irradiated attributes in lower branches further emphasizes their contribution to classification in more ambiguous cases.

Fig 9 illustrates the structure of the pruned decision tree for Mammographic dataset with ccp_alpha = 0.003. The tree was constructed to classify mammographic masses as benign or malignant based on five non-class attributes: BI-RADS assessment, Age, Shape, Margin, and Density. The pruning strategy effectively reduces model complexity while retaining critical decision boundaries. At the root node, the BI-RADS assessment emerges as the most discriminative feature, separating the dataset based on radiological severity. The left sub-tree captures benign cases through further splits on Shape and Age, achieving high purity (e.g., gini = 0.021 with 93 benign and 1 malignant case). On the right branch, malignant classifications are refined through Age-based splits, including a leaf with gini = 0.198, capturing 16 malignant and only 2 benign instances.

Similarly, Fig 10 shows the pruned decision tree generated for the Hepatitis datasets. In the Hepatitis tree (ccp_alpha = 0.007), ProTime and Bilirubin serve as the most influential features in predicting patient survival, with pure decision paths capturing clear distinctions between live and die classes. These decision trees not only contribute to accurate classification but also enhance the interpretability of the proposed SGA-DT framework, offering transparent, rule-based reasoning behind each prediction, thereby aligning with the adaptive and interpretable learning objectives of the framework.