A method for optimizing missing value filling based on unlabeled data

Abstract

The application discloses a method for optimizing missing value filling based on unlabeled data, which comprises the following steps: step 1, data set preparation; step 2, generating a data set containing missing values; step 3, basic filling; step 4, deep mining of effective information of massive unlabeled data; and step 5, forming a table according to the calculation in step 4, and observing the change of filling precision of each basic filling method after the unlabeled data is used for auxiliary optimization of filling values. The method realizes accurate filling of missing values, reduces the dependence on labeled data, improves the accuracy and generalization ability of the filling result, is suitable for different types of data sets and different missing mechanisms, reduces the data preprocessing cost, and improves the training effect of a machine learning model.

Description

Technical Field

[0001] This invention belongs to the field of data preprocessing technology, such as machine learning and deep learning. Specifically, it relates to a method for optimizing missing value imputation based on unlabeled data. It is particularly suitable for machine learning applications where labeled data is scarce and unlabeled data is abundant. It can be widely applied in data mining, artificial intelligence, big data analysis and other related fields to accurately preprocess datasets containing missing values, improve data quality, and provide reliable data support for subsequent model training, prediction and decision-making. It solves the technical pain points of existing imputation methods, such as high dependence on labeled data and low utilization of unlabeled data. Background Technology

[0002] In machine learning, big data analytics, and artificial intelligence applications, data is the core foundation for model training and decision analysis. Missing values ​​are prevalent in various datasets, primarily caused by sensor malfunctions leading to abnormal data acquisition, data transmission interruptions, omissions in manual recording, and missing attributes of the samples themselves. The presence of missing values ​​directly prevents machine learning models from processing the data, wasting data resources and compromising data integrity and distribution. This severely impacts model training effectiveness, convergence speed, and final predictive performance, becoming a key bottleneck restricting data preprocessing quality and downstream task accuracy.

[0003] To address the aforementioned missing value problem, various missing value imputation methods have been proposed in the prior art, which can be categorized into the following four types:

[0004] 1. Deletion method: This method cleans up data quickly by directly deleting samples or features containing missing values. However, its drawbacks are obvious. It will lead to the loss of a large amount of effective information and destroy the distribution characteristics of the original data, causing data bias. Especially in scenarios with a small total number of samples or a high proportion of missing values, it will seriously affect the generalization ability of the subsequent model.

[0005] 2. Statistical imputation: Using statistical measures such as mean, median, and mode to imput missing values ​​is simple and efficient. However, this method only utilizes a single statistical characteristic of the data and completely ignores the inherent correlation between different features and the data distribution pattern. The imputation results often deviate significantly from the real data and are prone to introducing false information.

[0006] 3. Model imputation: Missing values ​​are imputed using models such as K-Nearest Neighbors (KNN), Matrix Factorization (MF), Generative Adversarial Networks (GAIN), and Iterative Regression (MICE). Compared with the previous two methods, the imputation accuracy is improved. However, these methods still have limitations. They only rely on the data distribution of the target dataset itself for learning and imputation, and fail to mine useful information from external data.

[0007] 4. Integrated Filling: By combining the advantages of multiple filling models, the filling results are output comprehensively, which improves the filling defects of a single model to a certain extent. However, this method is still limited to the internal information of labeled datasets and has not broken through the limitations of existing filling ideas.

[0008] In summary, existing missing value imputation methods all have significant technical shortcomings, with the core issues concentrated in the following four aspects: First, all existing methods only utilize the information of the target dataset (i.e., labeled data) itself for imputation operations, failing to effectively mine and utilize the rich distributional knowledge and structural information contained in external unlabeled data, resulting in a waste of unlabeled data resources; Second, the imputation results can only reflect the local features of the training data (labeled data). When the amount of training data is limited, the data quality is low, or the data distribution is uneven, the learning effect of the imputation model is limited, thus making it difficult to improve the imputation accuracy; Third, in real-world application scenarios, unlabeled data (such as unlabeled raw collected data) is abundant and easily accessible, but existing technologies have failed to use it as an effective knowledge source to optimize the quality of missing value imputation, failing to fully leverage the application value of unlabeled data.

[0009] Therefore, in view of the technical problems of existing missing value imputation methods, such as insufficient information utilization, limited imputation accuracy, and ineffective utilization of unlabeled data, there is a need for a missing value imputation method that can break through the existing limitations, fully explore the value of unlabeled data, combine a small amount of labeled data, achieve accurate imputation, and adapt to downstream tasks, so as to solve the above-mentioned technical bottlenecks and meet the actual needs of machine learning data preprocessing. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of existing missing value imputation methods and provide a missing value imputation method based on unlabeled data optimization. This method fully explores the potential features and correlation information of unlabeled data and combines them with labeled data to achieve accurate imputation of missing values, reduce dependence on labeled data, improve the accuracy and generalization ability of the imputation results, and adapt to different types of datasets and different missing mechanisms. It also reduces data preprocessing costs and improves the training effect of machine learning models.

[0011] The technical solution to achieve the objective of this invention is:

[0012] A missing value imputation method based on unlabeled data optimization includes the following steps:

[0013] Step 1: Dataset Preparation: Prepare a complete and unmissing dataset D, where D contains n samples, each denoted as . ,in Indicates the first There are 10 samples, each containing multiple features. and a label , Indicates the first in the sample One feature;

[0014] Step 2: Generate a dataset with missing values: For the complete and unmissing dataset D, apply the MCAR missing values ​​mechanism (i.e., completely random missing values) to generate missing values ​​proportionally across all data features (generating missing values ​​only for the feature data in D, not for the labels). Generate missing values), with the missing value ratio configured to 0.15-0.35, to obtain the dataset D_mcar containing missing values;

[0015] Step 3: Basic Imputation: Perform basic imputation on the dataset D_mcar with missing values ​​using any of the imputation methods from statistical learning (Mean, KNNI), machine learning (RRSI, MFI, MICE, XGBI), and deep learning (GAIN, MLPI). Assume the first step is... Sample The Features It is missing. After filling it using the above filling method, The value is After filling in all missing values, the basic imputed result D_mcar_imputed is obtained.

[0016] Step 4: In-depth mining of effective information from massive unlabeled data: For each sample with missing values ​​in the dataset D_mcar, k similar samples are selected from the Internet using the KNN method for matching. Distance-based weights are assigned to each of the k similar samples, and weighted products are performed to obtain multiple auxiliary imputation results. After integrating and verifying the sample integrity, the samples are reconstructed to obtain the complete auxiliary imputation dataset D_auxiliary_imputed. Then, a linear fusion function is used to fuse and optimize the basic and auxiliary imputation values ​​at the same positions in the two matrices D_mcar_imputed and D_auxiliary_imputed, and the values ​​are returned to their original positions to obtain the final imputation dataset D_final_imputed. The basic imputation result D_mcar_imputed obtained in Step 3 is compared with the complete and missing-free dataset D from Step 1 using the AMAE evaluation criterion. The final imputed dataset D_final_imputed is then evaluated using the AMAE evaluation criteria along with the complete and missing data set D from step 1. Then calculate ;

[0017] Step 5: Calculate the result obtained in Step 4. Create a table and observe the changes in filling accuracy of each basic filling method after using unlabeled data to assist in optimizing the filling values. If more than 3 / 4 of the filling methods in step 3 can achieve an improvement in filling accuracy, it can prove that this method of optimizing filling values ​​with unlabeled data is effective and practical.

[0018] The specific steps in step 4 of using a linear fusion function to optimize the basic and auxiliary padding values ​​at the same positions in the two matrices using D_mcar_imputed and D_auxiliary_imputed are as follows:

[0019] 4.1 Distance Calculation: For samples containing missing values ​​in the dataset D_mcar ,calculate The Euclidean distance values ​​between the samples and all samples in the massive unlabeled data on the Internet are calculated based solely on the samples. Calculate all observable features;

[0020] 4.2 Nearest Neighbor Selection: For samples containing missing values Select the k samples with the smallest Euclidean distance values ​​from all the Euclidean distance values ​​calculated in step 4.1 to form a set. ,in For the sample The distance set corresponding to the j-th nearest neighbor sample is , in For the sample With the j-th nearest neighbor sample The Euclidean distance value;

[0021] 4.3 Distance-weighted calculation: For samples Missing values ​​in ,exist nearest neighbor set In the middle, let set ,in For sample set Medium Euclidean distance value Calculate the reciprocal of the product. The formula is as follows:

[0022] in To prevent small constants with zero denominators ;

[0023] sample Missing values auxiliary fill value The formula is as follows:

[0024]

[0025] 4.4 Fill Value Adjustment: Adjust the base fill value With auxiliary fill value Perform linear optimization adjustments to obtain the final optimized fill value:

[0026]

[0027] in To optimize and adjust parameters, used to control the degree of introduction of unlabeled data information; when When =0, the basic padding value is retained. When the value is 1, it is filled with unlabeled data.

[0028] The advantages or beneficial effects of this technical solution are as follows:

[0029] 1. Improved filling accuracy: By introducing knowledge of the distribution of unlabeled data, the optimized filling values ​​better match the actual data distribution.

[0030] 2. Value mining of unlabeled data: It makes full use of the large amount of real-world data resources that are difficult to label, transforming them into knowledge sources without the need for additional manual labeling costs, which is in line with the semi-supervised learning concept.

[0031] 3. Method universality and compatibility: This technical solution, as a post-optimization layer, does not change the core logic of the original algorithm and has plug-and-play characteristics.

[0032] 4. Parameter Adaptation: The optimal adjustment strength λ is automatically selected through the validation set, avoiding manual parameter tuning and ensuring that the method can be stably effective under different datasets and missing rates.

[0033] 5. Strong robustness: Through distance weighting mechanism and multiple backoff strategy, it has good robustness to noisy data and extreme missing data, and can still retain the original filling value information when the quality of the neighborhood is poor. Attached Figure Description

[0034] Figure 1 Flowchart for an embodiment;

[0035] Figure 2 This is a flowchart illustrating steps 3 and 4 in the embodiment. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this is not intended to limit the scope of the invention.

[0037] Example:

[0038] The technical solution in this embodiment is implemented using the Python programming language, and the hardware environment is as follows:

[0039] CPU: 11th Gen Intel(R) Core(TM) i5-11400F @ 2.60GHz 2.59 GHz

[0040] GPU: NVIDIA RTX 3060 (12GB VRAM)

[0041] Memory: 32GB

[0042] Storage: 1TB SSD

[0043] The software environment is as follows:

[0044] Python 3.13.7

[0045] PyTorch 1.13.1

[0046] Scikit-learn 1.8

[0047] XGBoost 3.1.1

[0048] Pandas 2.3.3

[0049] NumPy 2.4.0

[0050] Matplotlib 3.10.6

[0051] Torch 2.8.0.

[0052] Reference Figure 1 A missing value imputation method based on unlabeled data optimization includes the following steps:

[0053] Step 1: Data Preparation and Data Splitting:

[0054] This example uses 10 datasets from the UCI website for demonstration. As shown in Table 1:

[0055] Table 1

[0056]

[0057] Where Dataset Name is the dataset name, and Instances is the total number of samples in the dataset (denoted as Instances). For later use (Instead), Features is the number of features in a sample (denoted as ). For later use replace).

[0058] Taking the Yeast dataset as an example, the dataset is split into dataset D and unlabeled dataset D_unlabel in a 1:1 ratio, where D_unlabel is used to simulate unlabeled data from the Internet.

[0059] Step 2: Missing value generation:

[0060] To simulate missing data in a real-world scenario, the MCAR mechanism is used to generate missing values. Then, the custom function `make_mcar`, which internally implements the MCAR mechanism, is called to generate missing values ​​for dataset D and the unlabeled dataset D_unlabel from the Yeast dataset, resulting in D_mcar and D_unlabel_mcar. (Missing value rate set to 25%)

[0061] Step 3: Implement the basic fill method, such as... Figure 2 As shown:

[0062] This embodiment employs eight basic imputation methods, covering traditional statistical methods, machine learning methods, and deep learning methods (such as...). Figure 2 (The basic interpolation algorithm in step 1)

[0063] KNNI: K-nearest neighbor distance-weighted fill;

[0064] GAIN: Generate adversarial padding network;

[0065] MICE: Chain equation multivariate filling;

[0066] XGBI: XGBoost Regression Filler;

[0067] MLPI: MLP Neural Network Filler;

[0068] Mean: Mean fill;

[0069] MFI: Median Filler;

[0070] RRSI: Random Forest Filling.

[0071] Each method is encapsulated in a class for direct use, and provides `fit_transform` and `transform` interfaces for easy unified invocation. Taking the Yeast dataset as an example, one of the basic methods is used on the dataset D_mcar to process each sample containing missing values ​​in the dataset D_mcar. missing features Perform basic imputation and remove missing features. The calculated fill value is After imputing all missing value samples, the dataset D_mcar_imputed is obtained. (The unlabeled dataset D_unlabel_mcar is not imputed; its purpose is to simulate the massive amount of unlabeled data on the Internet and to extract useful information to obtain auxiliary imputed values ​​for optimizing the basic imputed values.)

[0072] Step 4: Distance-weighted optimization adjustment based on unlabeled data (e.g.) Figure 2 (Step 2)

[0073] The basic fill result is optimized and adjusted by weighting the nearest neighbor distance of unlabeled data, as specifically implemented as follows:

[0074] 4.1 Distance Calculation ( Figure 2 Step 2 involves in-depth mining of internet data (in this example, the segmented unlabeled dataset is used to replace the internet data in the diagram): For each sample in dataset D containing missing values... Calculate the Euclidean distance to the non-missing features of all samples in the unlabeled dataset D_unlabel using the non-missing features (using the custom nan_euclidean_distances function).

[0075] 4.2 Calculation of weighted mean ( Figure 2 Step 2 (distance-based weighting): For each sample with missing values... missing features The 10 samples with the smallest Euclidean distance values ​​calculated in section 4.1 were selected, and the auxiliary imputation values ​​were calculated using the inverse distance squared weighted average. ,sample Missing values auxiliary fill value The following is a summary:

[0076]

[0077] 4.3 Optimization and adjustment of the filling results ( Figure 2 (The fusion function box in step 3): Adjust the parameters Blend base fill value With auxiliary fill value To obtain the final fill value The formula is:

[0078]

[0079] in .

[0080] For each sample containing missing values missing features After optimizing the auxiliary padding values, the dataset D_final_imputed was obtained.

[0081] 4.4 Calculation of evaluation indicators:

[0082] The following datasets were obtained through the previous steps:

[0083] (1) Original dataset D: No further operations were performed.

[0084] (2) D_mcar: The dataset obtained after performing the D operation on the dataset using the MCAR mechanism.

[0085] (3) D_mcar_imputed: The dataset obtained by performing basic imputation on the dataset D_mcar.

[0086] (4) D_auxiliary_imputed: The auxiliary imputed dataset obtained by performing nearest neighbor search and weighted calculation on the unlabeled dataset D_unlabel_mcar.

[0087] (5) D_final_imputed: The final dataset obtained by optimizing the dataset D_mcar_imputed with the auxiliary imputed dataset D_auxiliary_imputed.

[0088] The basic imputation result D_mcar_imputed and the original dataset D are evaluated using the AMAE evaluation criterion. The final imputed dataset D_final_imputed and the original dataset D are evaluated using the AMAE evaluation criterion. Then calculate .

[0089] The formula for fill precision is as follows:

[0090]

[0091] in, It is the sample size. It is the number of features. Indicates the first The first sample The true values ​​of each feature in the original dataset D, and It is a value in the corresponding basic imputed dataset D_mcar_imputed or a value in the final imputed dataset D_final_imputed.

[0092] Step 5: [Regarding...] Analyze the values ​​in:

[0093]

[0094] 5.1 Meaning of the Indicator

[0095] This represents the change in mean absolute error (AMAE) of each imputation method after optimization using unlabeled data compared to the original baseline method:

[0096] Positive value: Improved filling accuracy (reduced error)

[0097] Negative values ​​indicate decreased filling accuracy (increased error).

[0098] 0: In line with the benchmark method

[0099] 5.2 Validity Analysis

[0100] Based on the revised indicator definition: Positive values ​​represent the percentage improvement in fill accuracy after optimization using unlabeled data; negative values ​​represent a decrease in accuracy. This example analyzes the effectiveness of this unlabeled data-assisted fill method from three dimensions: positive enabling capability, cross-algorithm adaptability, and practical value.

[0101] 5.2.1 The core method achieves a significant improvement in accuracy, and the optimization effect is substantial.

[0102] Among the eight basic imputation methods, Mean, KNNI, MFI, and GAIN methods show good performance on most datasets. The result >0 proves that the unlabeled data-assisted optimization strategy can bring stable performance gains to a variety of mainstream filling algorithms, and the improvement effect is outstanding in key scenarios.

[0103] Statistical learning methods (Mean, KNNI): Achieved stable accuracy improvements on multiple datasets such as Yeast, Statlog, and Letter Recognition. For example, on the Pen-Based Digits dataset, the Mean method... =0.4917, KNNI method =0.6390, both of which represent a significant improvement in accuracy, validating the effective empowerment of simple statistical methods by unlabeled data.

[0104] Machine Learning (MFI): Performs excellently on datasets such as Statlog, Letter Recognition, and Optical Digits, especially on the Optical Digits dataset. =0.5109, which shows that unlabeled data can provide richer reference information for instance-based fill methods, effectively improving fill accuracy.

[0105] Deep learning class (GAIN): Achieved large positive values ​​on all datasets, such as the LetterRecognition dataset. =0.8191, on the Statlog dataset =0.7886, proving that the introduction of unlabeled data can greatly expand the effective information of deep models and significantly improve their filling performance in complex missing value scenarios.

[0106] 5.2.2 Adaptability across algorithms and datasets highlights the practical value of the method.

[0107] The effectiveness of unlabeled data-assisted optimization methods is not only reflected in the performance improvement of a single algorithm, but also in their adaptability across algorithm types and data scenarios, laying a solid foundation for their practical application.

[0108] 1. Cross-algorithm type coverage: Methods for achieving stable accuracy improvements cover three core categories: statistical learning (Mean, KNNI, XGBI), traditional machine learning (MICE, MFI, RRSI), and deep learning (MLPI, GAIN). This proves that the optimization strategy is not a "customized improvement" for a specific type of algorithm, but rather provides a general performance optimization path for imputation methods of different technical approaches based on the distribution characteristics of unlabeled data.

[0109] 2. Cross-data scenario adaptation: The accuracy improvement effect covers datasets from multiple fields, including wine quality assessment, astronomical data (MAGIC Gamma Telescope), image segmentation (Statlog), and handwritten digit recognition (LetterRecognition), encompassing both low-dimensional structured data and high-dimensional feature data. This demonstrates that the method can adapt to the missing value imputation needs of different industries and data distributions, exhibiting strong scenario transfer capabilities.

[0110] 5.2.3 Performance fluctuations in a few methods provide direction for subsequent optimizations.

[0111] The negative values ​​(precision degradation) observed for XGBI, MICE, RRSI, and MLPI on some datasets are primarily due to their high sensitivity to data distribution or the fact that their utilization of unlabeled data in specific scenarios has not yet reached its optimal level. However, it's noteworthy that these methods still show positive improvements on other datasets without exhibiting a systematic performance collapse. This result is significant.

[0112] The results demonstrate that the unlabeled data-assisted optimization method has good robustness and will not have a destructive impact on the original performance of the basic filling method.

[0113] Performance fluctuations in a few scenarios provide a clear direction for subsequent targeted optimizations (such as designing more robust iteration strategies for MICE and adjusting the fusion weights of unlabeled data for MLPI).

[0114] 5.2.4 Validity Conclusion

[0115] In summary, the method of using unlabeled data to assist in optimizing imputation values ​​has clear effectiveness and extremely high practical value:

[0116] 1. This method can significantly improve the accuracy of most of the eight basic imputation methods on different datasets. In particular, in complex scenarios, the performance of deep learning methods (such as GAIN) is optimized by orders of magnitude, which fully verifies its core enabling capability.

[0117] 2. The optimization effect covers multiple algorithm types and data scenarios across multiple industries, and has strong adaptability to practical applications. It can be widely used in fields such as healthcare, finance, and industry where there are a large number of missing values.

[0118] 3. The method exhibits excellent robustness, and the performance fluctuations in a few scenarios leave clear room for improvement in subsequent full-scenario optimization.

[0119] Despite performance fluctuations on individual datasets, this unlabeled data optimization strategy has demonstrated its core value overall, proving to be an effective and highly promising missing value imputation optimization solution.

[0120] The innovation of this example lies in the distance-weighted adjustment of the unlabeled data in step 4, specifically:

[0121] 1. Knowledge Source Expansion: Breakthroughly introduces unlabeled datasets as external knowledge sources into the imputation optimization process, changing the limitation of existing technologies that rely solely on their own data distribution. This is the essential difference from all existing imputation methods.

[0122] 2. Distance-weighted fusion mechanism: By calculating sample-level distance, selecting nearest neighbors, and weighting by inverse squared distance, the distribution information most relevant to the current sample is extracted from the unlabeled data and linearly fused with the basic imputation value, thus realizing the organic combination of local information and global knowledge.

[0123] 3. Post-optimization architecture: The modular design of "basic filling + post-optimization" makes this example compatible with any existing filling algorithm as an independent optimization layer without modifying the internal structure of the original algorithm, and has plug-and-play engineering practicality.

[0124] Differences from existing technologies:

[0125] Unlike traditional semi-supervised learning, this example does not directly use unlabeled data to train downstream models, but instead uses it to optimize the quality of input data;

[0126] Unlike transfer learning: unlabeled data does not need to be distributed in the same way as labeled data, only that the feature space is consistent;

[0127] Unlike integrated filling: This example is not a multi-method voting, but rather uses external data to optimize the result of a single method.

Claims

1. A method for optimizing missing value imputation based on unlabeled data, characterized in that, Includes the following steps: Step 1: Dataset Preparation: Prepare a complete and unmissing dataset D, where D contains n samples, each denoted as . ,in Indicates the first There are 10 samples, each containing multiple features. and a label , Indicates the first in the sample One feature; Step 2: Generate a dataset with missing values: Apply the MCAR missing value mechanism to the complete and non-missing dataset D to generate missing values ​​proportionally in all data features, resulting in a dataset D_mcar with missing values; Step 3: Basic Imputation: Perform basic imputation on the dataset D_mcar with missing values ​​using any imputation method from statistical learning, machine learning, or deep learning. Assume the first step is... Sample The Features It is missing; after filling it using the above filling method, The value is After filling in all missing values, the basic imputed result D_mcar_imputed is obtained; Step 4: In-depth mining of effective information from massive unlabeled data: For each sample with missing values ​​in the dataset D_mcar, k similar samples are selected from the internet using the KNN method for matching. Distance-based weights are assigned to each of the k similar samples, and then weighted multiplication is performed to obtain multiple auxiliary imputation results. After integrating and verifying the sample integrity, the samples are reconstructed to obtain the complete auxiliary imputation dataset D_auxiliary_imputed. Then, a linear fusion function is used to fuse and optimize the basic and auxiliary imputation values ​​at the same positions in the two matrices D_mcar_imputed and D_auxiliary_imputed, and the values ​​are returned to their original positions to obtain the final imputation dataset D_final_imputed. The basic imputation result D_mcar_imputed obtained in Step 3 is compared with the complete and missing-free dataset D from Step 1 using the AMAE evaluation criterion. The final imputed dataset D_final_imputed and the complete, non-missing dataset D from step 1 are evaluated using the AMAE evaluation criteria. Then calculate ; Step 5: Calculate the result obtained in Step 4. Create a table to observe the changes in filling accuracy of each basic filling method after using unlabeled data to assist in optimizing the filling values. If more than 3 / 4 of the filling methods used can improve the filling accuracy, it can prove that this method of optimizing filling values ​​with unlabeled data is effective and practical.

2. The missing value imputation framework based on unlabeled data optimization according to claim 1, characterized in that, The specific steps in step 4 of using a linear fusion function to optimize the basic and auxiliary padding values ​​at the same positions in the two matrices using D_mcar_imputed and D_auxiliary_imputed are as follows: 4.1 Distance Calculation: For samples containing missing values ​​in the dataset D_mcar ,calculate The Euclidean distance values ​​between the samples and all samples in the massive unlabeled data on the Internet are calculated based solely on the samples. Calculate all observable features; 4.2 Nearest Neighbor Selection: For samples containing missing values Select the k samples with the smallest Euclidean distance values ​​from all the Euclidean distance values ​​calculated in step 4.1 to form a set. ,in For the sample The distance set corresponding to the j-th nearest neighbor sample is , in For the sample With the j-th nearest neighbor sample The Euclidean distance value; 4.3 Distance-weighted calculation: For samples Missing values ​​in ,exist nearest neighbor set In the middle, let set ,in For sample set Medium Euclidean distance value Calculate the reciprocal of the product. The formula is as follows: in To prevent small constants with zero denominators ; sample Missing values auxiliary fill value The formula is as follows: 4.4 Fill Value Adjustment: Adjust the base fill value With auxiliary fill value Perform linear optimization adjustments to obtain the final optimized fill value: in The parameters are adjusted to optimize and control the extent to which unlabeled data information is introduced.

3. The missing value imputation framework based on unlabeled data optimization according to claim 2, characterized in that, In step 4.4 To optimize and adjust parameters to control the degree of introduction of unlabeled data information, when When =0, the basic padding value is retained. When the value is 1, it is filled with unlabeled data.

4. The missing value imputation framework based on unlabeled data optimization according to claim 1, characterized in that, In step 2, the MCAR missing values ​​mechanism is used to generate missing values ​​proportionally across all data features in the complete and unmissing dataset D. That is, missing values ​​are generated only for the feature data in dataset D, not for the labels. Generate missing values, with the missing value ratio configured to 0.15-0.35.

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