A multiple imputation method and system for medical multi-view incomplete data

Abstract

The application discloses a multiple interpolation method and system for medical multi-view incomplete data, and relates to the technical field of machine learning.The method comprises the following steps: constructing a unified matrix and a binary observation indication matrix through feature-level splicing, combining missing perception standardization, adaptive neighbor selection, L2 regularization conditional regression to realize single interpolation; adopting an iteration strategy of missing proportion ordering to improve convergence, introducing random permutation and regression coefficient disturbance to generate m groups of candidate interpolation results to depict uncertainty; and finally outputting complete multi-view data based on missing rate adaptive weighted fusion, reverse standardization and view segmentation. Through multi-view feature splicing modeling, Pearson adaptive neighbor regression and missing proportion driven iterative interpolation, the application realizes precise multiple interpolation of medical multi-view incomplete data with high robustness, quantifiable uncertainty and restorable view structure.

Description

Technical Field

[0001] This invention relates to the field of machine learning technology, specifically to a multiple interpolation method and system for incomplete medical multi-view data. Background Technology

[0002] In core healthcare scenarios such as urban governance, public resource allocation, and social risk early warning, data-driven intelligent decision-making systems are highly dependent on data integrity. However, in actual engineering deployments, the medical data collection process is complex, cross-institutional sharing is limited, and data loss is extremely common and difficult to avoid: sensor malfunctions cause breakpoints in environmental monitoring data, upgrades and migrations of administrative approval systems result in the loss of historical fields, cross-departmental data sharing barriers prevent the acquisition of key indicators for specific views, and privacy anonymization further exacerbates the proportion of missing information. Under high missing rate conditions, the feature inputs on which the decision-making system relies are severely biased, directly transmitted to the model output level, leading to serious consequences such as erroneous resource allocation decisions, risk underreporting, and even policy failure.

[0003] Taking urban emergency management as an example, when there are significant gaps in multi-source sensor data (such as meteorological, traffic flow, and population heat maps), the confidence level of risk level prediction models will decrease significantly, potentially leading to inaccurate warning thresholds, misallocation of emergency resources, and irreversible negative impacts on public safety. In the social security field, if personal multi-dimensional profile data (such as employment, medical, and housing data) is missing, accurate assistance identification models will experience numerous missed and incorrect judgments, resulting in a severe misallocation of limited assistance resources. These problems demonstrate that data gaps are not merely a statistical loss of information, but a systemic risk that directly affects the quality of clinical decision-making and medical safety.

[0004] Despite widespread attention to the issue of missing data, current engineering practices primarily rely on simply deleting missing samples or imputing the mean. While these methods are acceptable in scenarios with low missing rates, they introduce significant selection bias under real-world conditions of high missing rates or non-random missing data (where the missing data is correlated with the feature value itself). This causes downstream models to perform well on the training set but fail severely in real-world government decision-making scenarios. How to efficiently and robustly reconstruct incomplete multi-view data within the computationally feasible limits of engineering deployment has become a key bottleneck restricting the practical effectiveness of clinical intelligent decision support systems. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a multi-view imputation method and system for incomplete medical multi-view data. Through multi-view feature splicing modeling, Pearson adaptive nearest neighbor regression, and iterative imputation driven by the missing proportion, it achieves accurate multi-view imputation with high robustness, quantifiable uncertainty, and reproducible view structure for incomplete medical multi-view data.

[0006] On the one hand, a multiple interpolation method for incomplete medical multi-view data includes:

[0007] S1. Acquire multi-view medical data. Each medical data view includes several medical samples and the feature dimensions corresponding to each medical sample. Based on the several medical samples and the feature dimensions corresponding to each medical sample, perform feature-level concatenation on the features of all medical data views to form a complete feature matrix including the feature dimensions of all views. Simultaneously, construct a binary observation indicator matrix to explicitly characterize the observable state of each sample on each feature dimension.

[0008] S2, based on the observable state, the values ​​of the observable part in each feature column of the complete feature matrix are preprocessed by mean-standard deviation standardization to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. Based on the preprocessed incomplete medical data, random permutation is performed on each feature column within each medical view to eliminate the column order bias that may be introduced by the original feature order and obtain randomly permuted medical data.

[0009] S3, for each target feature column with missing values ​​in the randomly permuted medical data, adaptively select the K nearest neighbor features with the strongest correlation to the target feature column from all other feature columns based on the Pearson correlation coefficient, and fit a conditional linear regression model based on L2 regularization on the observable samples of the target feature column with the K nearest neighbor features as independent variables. Then, use the fitted conditional linear regression model to predict the missing values ​​in the target feature column to complete a single imputation.

[0010] S4, the single imputation process is sorted according to the missing proportion of each feature column from smallest to largest and executed sequentially, and repeated for T rounds of iteration. The entire iteration process is then repeated m times to generate m different candidate imputation matrices.

[0011] S5 integrates m different candidate imputation matrices through a missing rate-aware adaptive weighted fusion mechanism to obtain a complete matrix. After denormalization, the complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view, thus completing the multiple imputation of incomplete data.

[0012] Furthermore, in S1, feature-level concatenation is performed on the features of all medical data views based on several medical samples and the feature dimensions corresponding to each medical sample. The calculation formula is as follows:

[0013] ;

[0014] in Number of medical samples; Let be the feature dimension of the v-th medical view; J represents the total dimension of the medical data view; d represents the sum of the feature dimensions of all medical views.

[0015] Binary observation indicator matrix If the first The sample at the th If each feature dimension is observable, then otherwise ,defining the first The formula for the binary observation indicator matrix of the column is as follows:

[0016] ;

[0017] in, express The set of observable samples with index j; express The set of unobservable samples at index j; Indicates the i-th sample at the th... A feature-dimensional binary observation indicator matrix.

[0018] Furthermore, in S2, the values ​​of the observable portion in each feature column of the complete feature matrix are preprocessed using mean-standard deviation standardization based on the observable state to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. The calculation formula is as follows:

[0019] ;

[0020] ;

[0021] ;

[0022] Where j represents each feature column; This represents the mean; Indicates standard deviation; express The set of observable samples with index j; This represents the i-th data sample row; express The set of unobservable samples at index j; This represents the observation value of the i-th sample on the j-th feature; This represents the mean of the j-th feature column; This represents the standardized observation of the i-th sample on the j-th feature; This represents the j-th target feature column of the i-th data point.

[0023] Furthermore, in S3, the fitted conditional linear regression model with L2 regularization is used to predict the missing values ​​in the target column, completing a single imputation. The calculation formula is as follows:

[0024] ;

[0025] ;

[0026] in, The sub-vector of the i-th row of incomplete data on the set of K nearest neighbor features; For regularization parameters; This represents the optimal regression coefficient vector corresponding to the j-th feature obtained by minimizing the objective function; This represents the vector of regression coefficients to be determined; Indicates observable samples; The squared L2 norm of a vector; This represents the estimation result of the j-th missing feature value for the i-th sample; This represents the standardized observation of the i-th sample on the j-th feature; Indicates the weighted fusion coefficient; This indicates the optimization of interpolation for missing values ​​in the target feature column.

[0027] Furthermore, in S4, the single imputation process is sorted by the missing proportion of each feature column from smallest to largest and then executed sequentially, specifically including:

[0028] S41. For each feature in the medical data table, count the number of missing samples and divide it by the total number of samples in that column to obtain the missing percentage value for each column.

[0029] S42, Based on the calculated missing proportion values, sort the feature columns with missing values ​​in ascending order to generate a definite processing sequence.

[0030] S43, based on the generated sequence order, imputation starts from the first feature column, using only the original observable values ​​of all other columns in the current data table to build a prediction model and generate imputation values ​​for its missing positions;

[0031] S45, immediately write the imputed value back to the corresponding position of the original missing data to form the updated data. This updated data table is used as the input for the next imputation step to process the next feature column in the sequence.

[0032] Furthermore, in S4, to generate m different candidate imputation matrices, random perturbations are actively introduced into the random permutation and regression coefficient estimation: on the one hand, the sample order is randomly permuted, and on the other hand, a controllable perturbation is applied to the regression coefficients, so as to independently generate multiple sets of imputation results under various random conditions; by comparing and analyzing and fusing multiple sets of imputation results, the statistical uncertainty in the missing value recovery process is characterized, and the bias or overfitting caused by a single deterministic estimation is avoided.

[0033] Furthermore, in S5, the final complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view. The calculation formula is as follows: ;

[0034] ;

[0035] in, Indicates the perceived weight of missing rate; For characteristic columns The percentage of missing values; The maximum percentage of missing values ​​across all feature columns; A matrix representing the restoration of the original data scale; Represents the interpolation result matrix in the normalized space. The Line 1 Column elements; Indicates the first Standard deviation of the column features;

[0036] Finally, according to the column intervals used for splicing... Split back to each view This yields the fully interpolated multi-view data.

[0037] On the other hand, a multiple interpolation system for incomplete medical multi-view data includes:

[0038] The observation indicator matrix construction module is used to acquire multi-view medical data. Each medical data view includes several medical samples and the corresponding feature dimensions of each medical sample. Based on the several medical samples and the corresponding feature dimensions of each medical sample, the features of all medical data views are concatenated at the feature level to form a complete feature matrix including the feature dimensions of all views. At the same time, a binary observation indicator matrix is ​​constructed to explicitly characterize the observable state of each sample in each feature dimension.

[0039] The random permutation medical data acquisition module is used to perform mean-standard deviation standardization preprocessing on the values ​​of the observable part in each feature column of the complete feature matrix based on the observable state, to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. Based on the preprocessed incomplete medical data, random permutation is performed on each feature column within each medical view to eliminate the column order bias that may be introduced by the original feature order and obtain random permutation medical data.

[0040] The single imputation module is used to adaptively select the K nearest neighbor features with the strongest correlation to the target feature column from all other feature columns based on the Pearson correlation coefficient for each target feature column with missing values ​​in the randomly permuted medical data. On the observable samples of the target feature column, the K nearest neighbor features are used as independent variables to fit a conditional linear regression model based on L2 regularization. The fitted conditional linear regression model is then used to predict the missing values ​​in the target feature column, thus completing the single imputation.

[0041] The candidate interpolation matrix generation module is used to sort the single interpolation process according to the missing proportion of each feature column from smallest to largest and execute them sequentially, repeating the process for T rounds of iteration, and then repeating the entire iteration process m times to generate m different candidate interpolation matrices.

[0042] The multiple imputation module is used to integrate m different candidate imputation matrices through a missing rate-aware adaptive weighted fusion mechanism to obtain a complete matrix. After denormalization, the complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view, thus completing the multiple imputation of incomplete data.

[0043] The present invention adopts the above technical solution and has the following beneficial effects:

[0044] (1) This invention splices the features of multiple medical data views into a unified matrix by columns and simultaneously constructs a binary indicator matrix that marks whether each sample is actually observed on each feature. This achieves complete preservation of the overall structure of multi-source heterogeneous medical data and accurate and traceable recording of missing locations, laying a foundation for subsequent cross-view collaborative modeling with consistent structure and clear semantics.

[0045] (2) This invention sorts the feature columns by their missing degree from low to high, then performs iterative imputation column by column, and selects only the other features that are most relevant to the target feature to establish a constrained linear prediction model during each imputation. This effectively addresses common complex missing patterns in clinical data and improves the stability and accuracy of the imputation results under different missing levels and feature types.

[0046] (3) The present invention actively introduces random perturbation in the two key links of data order arrangement and model parameter solution, and repeatedly runs the whole imputation process multiple times to generate multiple sets of candidate results. Then, based on the severity of each feature missing, its contribution weight in the final fusion is automatically adjusted, realizing explicit modeling and quantitative expression of the inherent uncertainty of the missing value recovery process. Attached Figure Description

[0047] Figure 1 This is a flowchart of a multiple interpolation method for incomplete medical multi-view data according to an embodiment of the present invention;

[0048] Figure 2 This is a comparative analysis diagram of the accuracy ACC measurement in an embodiment of the present invention;

[0049] Figure 3 This is a diagram of a multiple interpolation system for incomplete medical multi-view data according to an embodiment of the present invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0051] like Figure 1 As shown, the present invention provides a multiple interpolation method for incomplete medical multi-view data, comprising:

[0052] S1. Acquire multi-view medical data. Each medical data view includes several medical samples and the corresponding feature dimensions of each medical sample. Based on the several medical samples and the corresponding feature dimensions of each medical sample, perform feature-level concatenation on the features of all medical data views to form a complete feature matrix including the feature dimensions of all views. Simultaneously, construct a binary observation indicator matrix to explicitly characterize the observable state of each sample on each feature dimension.

[0053] Specifically, based on several medical samples and the corresponding feature dimensions of each medical sample, the features of all medical data views are concatenated at the feature level. The calculation formula is as follows:

[0054] ;

[0055] in Number of medical samples; Let be the feature dimension of the v-th medical view; J represents the total dimension of the medical data view; d represents the sum of the feature dimensions of all medical views.

[0056] Binary observation indicator matrix If the first The sample at the th If each feature dimension is observable, then otherwise ,defining the first The formula for the binary observation indicator matrix of the column is as follows:

[0057] ;

[0058] in, express The set of observable samples with index j; This represents the i-th data sample row.

[0059] S2, based on the observable state, performs mean-standard deviation standardization preprocessing on the values ​​of the observable part in each feature column of the complete feature matrix to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. Based on the preprocessed incomplete medical data, performs random permutation on each feature column within each medical view to eliminate the column order bias that may be introduced by the original feature order and obtain randomly permuted medical data.

[0060] Specifically, based on the observable state, the values ​​of the observable portion in each feature column of the complete feature matrix are preprocessed using mean-standard deviation standardization to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. The calculation formula is as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] Where j represents each feature column; This represents the mean; Indicates standard deviation; express The set of observable samples with index j; This represents the i-th data sample row; This represents the observation value of the i-th sample on the j-th feature; This represents the mean of the j-th feature column; This represents the standardized observation of the i-th sample on the j-th feature; This represents the j-th target feature column of the i-th data point.

[0065] S3. For each target feature column with missing values ​​in the randomly permuted medical data, the K nearest neighbor features with the strongest correlation to the target feature column are adaptively selected from all other feature columns based on the Pearson correlation coefficient. On the observable samples of the target feature column, the K nearest neighbor features are used as independent variables to fit a conditional linear regression model with L2 regularization. The fitted conditional linear regression model with L2 regularization is used to predict the missing values ​​in the target feature column, thus completing a single imputation.

[0066] Specifically, the fitted conditional linear regression model with L2 regularization is used to predict missing values ​​in the target column to complete a single imputation. The calculation formula is as follows:

[0067] ;

[0068] ;

[0069] in, The sub-vector of the i-th row of incomplete data on the set of K nearest neighbor features; For regularization parameters; This represents the optimal regression coefficient vector corresponding to the j-th feature obtained by minimizing the objective function; This represents the vector of regression coefficients to be determined; Indicates observable samples; The squared L2 norm of a vector; This represents the estimation result of the j-th missing feature value for the i-th sample; This represents the standardized observation of the i-th sample in the j-th feature column; Indicates the weighted fusion coefficient; This indicates the optimization of interpolation for missing values ​​in the target feature column.

[0070] S4. The single imputation process is sorted according to the missing proportion of each feature column from smallest to largest and executed sequentially. This process is repeated for T iterations to gradually stabilize the imputation result. The entire iterative process is then repeated m times to generate m different candidate imputation matrices.

[0071] Specifically, the single imputation process is executed sequentially according to the missing proportion of each feature column, sorted from smallest to largest. This includes:

[0072] S41. For each feature in the medical data table, count the number of missing samples and divide it by the total number of samples in that column to obtain the missing percentage value for each column.

[0073] S42, Based on the calculated missing proportion values, sort the feature columns with missing values ​​in ascending order to generate a definite processing sequence.

[0074] S43, based on the generated sequence order, imputation starts from the first feature column, using only the original observable values ​​of all other columns in the current data table to build a prediction model and generate imputation values ​​for its missing positions;

[0075] S45, immediately write the imputed value back to the corresponding position of the original missing data to form the updated data. This updated data table is used as the input for the next imputation step to process the next feature column in the sequence.

[0076] Specifically, to generate m different candidate imputation matrices, random perturbations are proactively introduced in the two key stages of random permutation and regression coefficient estimation: on the one hand, the sample order is randomly permuted, and on the other hand, controllable perturbations are applied to the regression coefficients, so that the model can independently generate multiple imputation results under various random conditions; by comparing and analyzing and fusing multiple imputation results, the statistical uncertainty in the missing value recovery process is characterized, avoiding bias or overfitting caused by a single deterministic estimation.

[0077] S5 integrates m different candidate imputation matrices through a missing rate-aware adaptive weighted fusion mechanism to obtain the final complete matrix. After denormalization, the final complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view, thus completing the multiple imputation of incomplete data.

[0078] Specifically, the final complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view. The calculation formula is as follows: ;

[0079] ;

[0080] in, Indicates the perceived weight of missing rate; The proportion of missing values ​​in feature column j; The maximum percentage of missing values ​​across all feature columns; A matrix representing the restoration of the original data scale;

[0081] Finally, according to the column intervals used for splicing... Split back to each view This yields the fully interpolated multi-view data.

[0082] Furthermore, to illustrate the practical application process of this invention, let's take medical multimodal data completion as an example: First, input multi-view medical data corresponding to the same subject. Multi-view data may include clinical laboratory indicators, medical imaging features, vital sign data, electronic medical record text features, and other diagnosis-related information. Second, preprocess and standardize the data for each view, and then assemble them into an overall data matrix after sample alignment. When some subjects experience missing features in a certain view due to reasons such as missing examination items, equipment failure, limited acquisition conditions, interrupted follow-up, or incomplete data entry, incomplete multi-view medical data is obtained. Then, generate m sets of candidate imputation matrices using the aforementioned method, and calculate the missing rate-aware weight based on the missing proportion of each feature column. Adaptively weighted and fused the candidate imputation results to obtain a complete matrix restored to the original data scale. Finally, segment the complete matrix according to the original feature dimensions of each view to obtain the imputed complete multi-view medical data. The imputed multi-view medical data can be further used for tasks such as disease auxiliary diagnosis, patient stratification, prognostic assessment, risk prediction, and clinical decision support, thereby improving the completeness, accuracy, and robustness of medical data analysis.

[0083] Specifically, such as Figure 2 As shown, the experimental datasets used in this invention include: the 100 Leaves image dataset, the Outdoor Scene dataset, the WebKB1 web text dataset, and the Handwritten character dataset. These are all multi-view benchmark datasets, covering multiple modalities such as images, textures, and text. To evaluate the performance of the method under different missing values, five missing rate gradients of 10%, 20%, 30%, 40%, and 50% were set for each dataset. Accuracy (ACC) was used as the metric for evaluating the performance after imputation. ACC ∈ [0,1] is an indicator used to evaluate classification models. The best results are highlighted in bold. The values ​​above represent the average ACC for each dataset at the five missing rate gradients from 10% to 50%. According to the ACC metric, this method ranks first on all four datasets: the 100 Leaves image dataset, the Outdoor Scene dataset, the WebKB1 web text dataset, and the Handwritten character dataset, with an average ranking of 1.0, fully validating the overall superiority of this method in multi-view incomplete data reconstruction tasks.

[0084] like Figure 3 As shown, this embodiment also discloses a multiple interpolation system for incomplete medical multi-view data, including:

[0085] The observation indicator matrix construction module 31 is used to acquire multi-view medical data. Each medical data view includes several medical samples and the feature dimensions corresponding to each medical sample. Based on the several medical samples and the feature dimensions corresponding to each medical sample, the features of all medical data views are spliced ​​at the feature level to form a complete feature matrix including the feature dimensions of all views. At the same time, a binary observation indicator matrix is ​​constructed to explicitly characterize the observable state of each sample in each feature dimension.

[0086] The random permutation medical data acquisition module 32 is used to perform mean-standard deviation standardization preprocessing on the values ​​of the observable part in each feature column of the complete feature matrix based on the observable state, to eliminate the influence of the dimension, and obtain preprocessed incomplete medical data. Based on the preprocessed incomplete medical data, random permutation is performed on each feature column within each medical view to eliminate the column order bias that may be introduced by the original feature order, and obtain random permutation medical data.

[0087] The single imputation module 33 is used to adaptively select the K nearest neighbor features with the strongest correlation to the target feature column from all other feature columns based on the Pearson correlation coefficient for each target feature column with missing values ​​in the randomly permuted medical data. On the observable samples of the target feature column, the K nearest neighbor features are used as independent variables to fit a conditional linear regression model with L2 regularization. The fitted conditional linear regression model with L2 regularization is used to predict the missing values ​​in the target feature column to complete the single imputation.

[0088] The candidate interpolation matrix generation module 34 is used to sort the single interpolation process according to the missing proportion of each feature column from smallest to largest and execute them sequentially, and repeat the process for T rounds of iteration to make the interpolation result gradually stabilize. Then, the entire iterative process is repeated m times to generate m different candidate interpolation matrices.

[0089] The multiple imputation module 35 is used to integrate m different candidate imputation matrices through a missing rate-aware adaptive weighted fusion mechanism to obtain the final complete matrix. After denormalization, the final complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view to complete the multiple imputation of incomplete data.

[0090] A specific implementation of a multiple interpolation system for incomplete medical multi-view data is described in this embodiment, which is the same as the multiple interpolation method for incomplete medical multi-view data.

[0091] Although the invention has been specifically shown and described in conjunction with preferred embodiments, those skilled in the art should understand that various changes in form and detail may be made to the invention without departing from the spirit and scope of the invention as defined in the appended claims, all of which shall be within the scope of protection of the invention.

Claims

1. A multiple interpolation method for incomplete medical multi-view data, characterized in that, Includes the following steps: S1. Acquire multi-view medical data. Each medical data view includes several medical samples and the feature dimensions corresponding to each medical sample. Based on the several medical samples and the feature dimensions corresponding to each medical sample, perform feature-level concatenation on the features of all medical data views to form a complete feature matrix including the feature dimensions of all views. Simultaneously, construct a binary observation indicator matrix to explicitly characterize the observable state of each sample on each feature dimension. S2, based on the observable state, the values ​​of the observable part in each feature column of the complete feature matrix are preprocessed by mean-standard deviation standardization to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. Based on the preprocessed incomplete medical data, random permutation is performed on each feature column within each medical view to eliminate the column order bias introduced by the original feature order and obtain randomly permuted medical data. S3, for each target feature column with missing values ​​in the randomly permuted medical data, adaptively select the K nearest neighbor features with the strongest correlation to the target feature column from all other feature columns based on the Pearson correlation coefficient, and fit a conditional linear regression model based on L2 regularization on the observable samples of the target feature column with the K nearest neighbor features as independent variables. Then, use the fitted conditional linear regression model to predict the missing values ​​in the target feature column to complete a single imputation. S4, the single imputation process is sorted according to the missing proportion of each feature column from smallest to largest and executed sequentially, and repeated for T rounds of iteration. The entire iteration process is then repeated m times to generate m different candidate imputation matrices. S5 integrates m different candidate imputation matrices through a missing rate-aware adaptive weighted fusion mechanism to obtain a complete matrix. After denormalization, the complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view, thus completing the multiple imputation of incomplete data.

2. The multiple interpolation method for incomplete medical multi-view data according to claim 1, characterized in that, In S1, feature-level concatenation is performed on the features of all medical data views based on several medical samples and the feature dimensions corresponding to each medical sample. The calculation formula is as follows: ； in Number of medical samples; Let be the feature dimension of the v-th medical view; J represents the total dimension of the medical data view; d represents the sum of the feature dimensions of all medical views. Binary observation indicator matrix If the first If a data sample row is observable in j feature columns, then otherwise ,defining the first The formula for the binary observation indicator matrix of the column is as follows: ； in, Represents the set of observable samples for feature column j; express The set of unobservable samples in the j-th feature column; Indicates the i-th data sample row at the i-th position. A feature-dimensional binary observation indicator matrix.

3. The multiple interpolation method for incomplete medical multi-view data according to claim 1, characterized in that, In S2, the values ​​of the observable portion in each feature column of the complete feature matrix are preprocessed using mean-standard deviation standardization based on the observable state to eliminate the influence of dimensions and obtain the preprocessed incomplete medical data. The calculation formula is as follows: ； ； ； Where j represents each feature column; This represents the mean; Indicates standard deviation; Represents the set of observable samples for feature column j; Indicates a data sample row; This represents the observation value of the i-th data sample row in the j-th feature column; This represents the mean of the j-th feature column; This represents the standardized observation value of the i-th data sample row in the j-th feature column; This represents the j-th target feature column of the i-th data point.

4. The multiple interpolation method for incomplete medical multi-view data according to claim 1, characterized in that, In S3, the fitted conditional linear regression model with L2 regularization is used to predict the missing values ​​in the target feature column, completing a single imputation. The calculation formula is as follows: ； ； in, The sub-vector representing the i-th data sample row of incomplete data on the set of K nearest neighbor features; For regularization parameters; This represents the optimal regression coefficient vector corresponding to the j-th feature column obtained by minimizing the objective function; This represents the vector of regression coefficients to be determined; Indicates observable samples; The squared L2 norm of a vector; This represents the estimation result of the j-th missing feature value for the i-th sample; This represents the standardized observation value of the i-th data sample row in the j-th feature column; Indicates the weighted fusion coefficient; This indicates the optimization of interpolation for missing values ​​in the target feature column.

5. The multiple interpolation method for incomplete medical multi-view data according to claim 1, characterized in that, In S4, the single imputation process is sorted by the missing proportion of each feature column from smallest to largest and then executed sequentially, specifically including: S41. For each feature in the medical data table, count the number of missing samples and divide it by the total number of samples in that column to obtain the missing percentage value for each column. S42, Based on the calculated missing proportion values, sort the feature columns with missing values ​​in ascending order to generate a definite processing sequence. S43, based on the generated sequence order, imputation starts from the first feature column, using only the original observable values ​​of all other columns in the current data table to build a prediction model and generate imputation values ​​for its missing positions; S45, immediately write the imputed value back to the corresponding position of the original missing data to form the updated data. This updated data table is used as the input for the next imputation step to process the next feature column in the sequence.

6. The multiple interpolation method for incomplete medical multi-view data according to claim 1, characterized in that, In S4, to generate m different candidate imputation matrices, random perturbations are actively introduced into the random permutation and regression coefficient estimation: on the one hand, the sample order is randomly permuted, and on the other hand, controllable perturbations are applied to the regression coefficients, so as to generate multiple sets of imputation results independently under various random conditions. By comparing and analyzing and fusing multiple sets of imputation results, the statistical uncertainty in the missing value recovery process is characterized, and the bias or overfitting caused by a single deterministic estimation is avoided.

7. The multiple interpolation method for incomplete medical multi-view data according to claim 1, characterized in that, In S5, the final complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view. The calculation formula is as follows: ; ； in, Indicates the perceived weight of missing rate; For characteristic columns The percentage of missing values; The maximum percentage of missing values ​​across all feature columns; A matrix representing the restoration of the original data scale; Represents the interpolation result matrix in the normalized space. The The first data sample row Each feature column element; Indicates the first Standard deviation of the column features; Finally, according to the column intervals used for splicing... Split back to each view This yields the fully interpolated multi-view data.

8. A multiple interpolation system for incomplete medical multi-view data, characterized in that, include: The observation indicator matrix construction module is used to acquire multi-view medical data. Each medical data view includes several medical samples and the feature dimensions corresponding to each medical sample. Based on several medical samples and the feature dimensions corresponding to each medical sample, the features of all medical data views are spliced ​​at the feature level to form a complete feature matrix including all view feature dimensions. At the same time, a binary observation indicator matrix is ​​constructed to explicitly characterize the observable state of each sample in each feature dimension. The random permutation medical data acquisition module is used to perform mean-standard deviation standardization preprocessing on the values ​​of the observable part in each feature column of the complete feature matrix based on the observable state, to eliminate the influence of dimensions and obtain preprocessed incomplete medical data. Based on the preprocessed incomplete medical data, random permutation is performed on each feature column within each medical view to eliminate the column order bias introduced by the original feature order and obtain random permutation medical data. The single imputation module is used to adaptively select the K nearest neighbor features with the strongest correlation to the target feature column from all other feature columns based on the Pearson correlation coefficient for each target feature column with missing values ​​in the randomly permuted medical data. On the observable samples of the target feature column, the K nearest neighbor features are used as independent variables to fit a conditional linear regression model based on L2 regularization. The fitted conditional linear regression model is then used to predict the missing values ​​in the target feature column, thus completing the single imputation. The candidate interpolation matrix generation module is used to sort the single interpolation process according to the missing proportion of each feature column from smallest to largest and execute them sequentially, repeating the process for T rounds of iteration, and then repeating the entire iteration process m times to generate m different candidate interpolation matrices. The multiple imputation module is used to integrate m different candidate imputation matrices through a missing rate-aware adaptive weighted fusion mechanism to obtain a complete matrix. After denormalization, the complete matrix is ​​segmented according to the original feature dimensions of each view and restored to each view, thus completing the multiple imputation of incomplete data.

Images