Multi-task evolution semi-supervised feature selection method for high-dimensional data classification

Abstract

The invention discloses a high-dimensional data classification-oriented multi-task evolution semi-supervised feature selection method, which belongs to the field of high-dimensional data classification, and comprises the following steps of S1, constructing a common feature search space of main-auxiliary tasks; s2, respectively constructing objective functions for a packaging type main task and a filtering type auxiliary task in the main-auxiliary tasks, and calculating initial fitness; s3, realizing main-auxiliary task coevolution based on a self-adaptive knowledge sharing mechanism; s4, when the global feature subset of the auxiliary task is updated, regenerating a pseudo tag and reconstructing a main population; and S5, repeatedly executing the steps S3 and S4 until the maximum number of iterations is reached, and outputting a global optimal feature subset of the main task. By adopting the multi-task evolution semi-supervised feature selection method for high-dimensional data classification, the classification performance of the feature subsets is improved, the scale of the feature subsets is reduced and the diversity and convergence of populations are balanced while high-quality pseudo tags are generated.

Description

Technical Field

[0001] This invention relates to the field of high-dimensional data classification technology, and in particular to a multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification. Background Technology

[0002] With the rapid development of big data and machine learning technologies, high-dimensional data (such as medical images, financial transaction records, and text feature data) has emerged widely in fields such as healthcare, finance, and the internet. High-dimensional data contains a large number of redundant and irrelevant features, which can significantly reduce the efficiency and accuracy of classification models. Therefore, feature selection has become an indispensable core preprocessing step in high-dimensional data classification tasks.

[0003] In existing technologies, semi-supervised feature selection methods for high-dimensional data classification mostly employ evolutionary algorithms to achieve population-based feature subset search. Some methods attempt to combine multi-task learning to improve generalization ability, but they still have the following shortcomings in practical applications: 1. Insufficient adaptability of the population to the environment: When faced with the "environmental changes caused by pseudo-label updates" in semi-supervised scenarios, the population reconstruction process does not effectively inherit the key feature information of the original population, which is prone to problems such as unstable convergence (deviating from the global optimal neighborhood) or low convergence efficiency (difficult to converge to the local optimum before pseudo-label updates). 2. Individual improvement strategies lack specificity: The characteristics of high-quality individuals and low-quality individuals are not distinguished, and a uniform neighborhood search strategy is adopted. This makes it difficult to accurately preserve and develop the high-quality feature combinations of high-quality individuals, and it is also difficult to balance population convergence and diversity in the improvement of low-quality individuals. 3. Insufficient utilization of elite knowledge: Existing methods do not systematically integrate elite knowledge such as "historical best solutions and cross-task consensus features", which cannot guide the population to efficiently explore the feature space and easily leads to high feature subset redundancy and poor classification performance; 4. Coarse feature space partitioning: There is a lack of scientific quantification and partitioning strategies for the correlation stratification of high-dimensional features (strong correlation, weak correlation, redundant features), resulting in insufficient targeting of feature search, which wastes computing resources and makes it difficult to select efficient feature subsets. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification, thereby solving the aforementioned technical problems.

[0005] To achieve the above objectives, this invention provides a multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification, comprising the following steps: S1. Collect training datasets containing labeled and unlabeled sample sets in high-dimensional data classification scenarios, and evaluate the dual importance based on linear and nonlinear importance measures. Combine the inflection point selection strategy to remove consensus-based non-important features, construct the common feature search space for the main and auxiliary tasks, and achieve preliminary dimensionality reduction of the original high-dimensional feature space. S2. Construct objective functions for the encapsulated main task and the filtering auxiliary task in the main-auxiliary task respectively. At the same time, initialize the auxiliary population and the main population based on the common feature search space and calculate the initial fitness. S3. Based on the adaptive knowledge sharing mechanism, the main and auxiliary tasks are co-evolved. The auxiliary and main populations are updated through cross-task knowledge learning. When the global optimal feature subset of the auxiliary task is updated, pseudo-labels and confidence scores are generated using the label propagation algorithm. The population reconstruction strategy driven by the historical elite knowledge base is driven by environmental feedback. Variable neighborhood search is performed on high-quality individuals in the main population, and historical knowledge is used to guide the improvement or re-initialization of non-high-quality individuals to reconstruct the main population. S4. Repeat step S3 until the maximum number of iterations is reached. Output the globally optimal feature subset of the main task, apply it to the high-dimensional data classification scenario and verify the classification performance, feature sparsity and running efficiency to complete the semi-supervised feature selection.

[0006] Therefore, the present invention employs the above-mentioned multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification, which has the following beneficial effects: 1. By constructing a multi-task evolutionary semi-supervised feature selection framework assisted by a filtering method, a division of labor mode is adopted in which the auxiliary task quickly generates high-quality feature subsets and high-quality pseudo-labels, and the main task conducts global search through evolutionary algorithms. This not only significantly improves the labeling quality of pseudo-labels of semi-supervised samples, but also integrates the fast selection capability of filtering methods with the global search advantage of evolutionary algorithms, effectively improving the search efficiency of feature subsets. 2. Based on the feature search space construction method (DIM-FSC) with dual feature importance measurement and multi-form objective functions with different functions, by focusing on the exploration of important features, the auxiliary task ensures the prediction accuracy of pseudo-labels by means of the improved multi-manifold constrained Laplace score (MMC-LS) objective, while the main task effectively alleviates the interference of prediction bias on the search for the global optimal feature subset by means of the confidence-based Micro-F1 (CMicro-F1) objective, thereby improving the global quality of the feature subset; 3. The Adaptive Knowledge Sharing Mechanism (AKSM) dynamically adjusts the knowledge sharing probability by combining population convergence and diversity, and learns convergence and diversity knowledge simultaneously. This improves the learning efficiency of positive knowledge between multiple tasks, balances the development and exploration capabilities of the population, and avoids premature convergence of the population. 4. The Environmental Feedback-Based Population Reconstruction Strategy (EF-PRC) performs differentiated neighborhood searches for high-quality and low-quality individuals, while reinitializing some low-quality individuals. This enhances the adaptability of the main task to the new pseudo-label environment, ensures the convergence of the reconstructed population, improves population diversity, and optimizes the stability and generalization of feature selection.

[0007] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0008] Figure 1 This is a diagram illustrating the overall framework of the multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification described in this invention. Figure 2 This diagram illustrates the feature space construction process based on dual importance measurement in the multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification described in this invention. Figure 3 This is a schematic diagram illustrating the multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification described in this invention, where samples are located in different manifold structures under pairwise constraints. Figure 4 This is a schematic diagram of the operation of the multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification described in this invention on different neighborhood structures, wherein (a) is a diagram of the operation of three neighborhood structures for high-quality individuals, and (b) is a diagram of the operation of three neighborhood structures for non-high-quality individuals. Figure 5 The graph shows a comparison and significance test of the relative percentage growth (RPI(ACC)) between FAEMT-SSFS and four packaged EAs as described in the simulation experiment. Figure 6 The figures show the comparison and significance test of RPI(ACC) of FAEMT-SSFS and SSFS methods under different labeling rates described in the simulation experiment. Among them, (a) is the RPI(ACC) value result of each algorithm at a 10% labeling rate, (b) is the ANOVA significance test figure at a 10% labeling rate, (c) is the RPI(ACC) value result of each algorithm at a 20% labeling rate, (d) is the ANOVA significance test figure at a 20% labeling rate, (e) is the RPI(ACC) value result of each algorithm at a 30% labeling rate, (f) is the ANOVA significance test figure at a 30% labeling rate, (g) is the average RPI(ACC) value result of the entire dataset, and (h) is the overall significance test figure of the entire dataset. Detailed Implementation

[0009] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0010] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0011] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0012] like Figures 1-4 As shown, a multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification includes the following steps: S1. Collect training datasets containing labeled and unlabeled sample sets in high-dimensional data classification scenarios, and evaluate the dual importance based on linear and nonlinear importance measures. Combine the inflection point selection strategy to remove consensus-based non-important features, construct the common feature search space for the main and auxiliary tasks, and achieve preliminary dimensionality reduction of the original high-dimensional feature space. Step S1 specifically includes the following steps: S11. Collect labeled sample sets for high-dimensional data classification scenarios. Compared with unlabeled sample set training dataset ,Right now ;in, middle, Indicates the first One labeled sample, Indicates labeled samples Category , Indicates the total number of categories. Indicates the total number of labeled samples; , Indicates the first One unlabeled sample, This represents the total number of unlabeled samples, whose categories are the same as those of labeled samples. Consistent categories; S12. Define the linear importance metric. and nonlinear importance metrics : ; ; In the formula, Indicates the weighting coefficient; Indicates the first to be evaluated Features In the unlabeled sample set The normalized variance value in; express exist The normalized Pearson correlation coefficient value in the figure; express exist The normalized entropy value in; express exist The normalized mutual information value in; S13. Employ an inflection point-based selection strategy to evaluate the linear importance metrics. and nonlinear importance metrics After sorting, the features are filtered to remove those with linear importance metrics. and nonlinear importance metrics The unimportant features of consensus, and the remaining features, constitute the common feature search space for the primary and secondary tasks. This achieves initial dimensionality reduction of the original high-dimensional feature space.

[0013] Step S13 specifically includes the following steps: S131. Sort all features in descending order according to the calculation results of step S12 to obtain the feature importance curve. ; S132, Importance Curve of Connectivity Features The two endpoints generate a reference straight line and calculate Up to each point European distance And select Euclidean distance The largest point as The inflection point; S133, Feature Importance Curve Features whose importance measure is greater than the inflection point value are considered important features, resulting in four types of feature spaces, namely linear importance measures. Important feature set under guidance Set of unimportant features and nonlinear importance metrics Important feature set under guidance Set of unimportant features ; S134. Remove features from the feature space obtained in step S133. and The unimportant characteristic of consensus, namely The remaining features constitute the common feature search space for the primary and secondary tasks, i.e. .

[0014] S2. Construct objective functions for the encapsulated main task and the filtering auxiliary task in the main-auxiliary task respectively. At the same time, initialize the auxiliary population and the main population based on the common feature search space and calculate the initial fitness. Step S2 specifically includes the following steps: S21. Design the objective function for a multi-manifold constrained filtering-based auxiliary task. : ; in, ; In the formula, Represents the Laplace score for multi-manifold constraints. This represents the candidate solution of the feature subset to be optimized in the common feature search space of the main and auxiliary tasks for the auxiliary task; Indicates the weighting factor; Represents the trace operation of a matrix; Features in the search space representing common features of primary and secondary tasks transpose; The features in the search space representing the common features of the primary and secondary tasks, and ; and These represent the similarity matrices corresponding to Must-Link. Similarity matrix to Cannot-Link The Laplace operator, and , , Represents the set of sample pairs in Must-Link. Indicates the first in the labeled sample set A subset of samples of the class This represents the set of sample pairs that cannot be linked. Representation and Category Another different category, Indicates the first in the labeled sample set A subset of samples of the class; This represents the Laplacian matrix corresponding to the local manifold; This represents the degree matrix corresponding to the Laplacian matrix of the local manifold; Simultaneously, a confidence-guided encapsulated main task objective function is designed. : ; in, ; ; ; ; ; In the formula, Represents candidate sets based on feature subsets The calculated confidence-guided Micro-F1 value; and These represent precision and recall based on label confidence, respectively. and Representing categories Confidence-based true positives and confidence-based false positives; and Representing categories True positives and false negatives; Indicates when the sample Predicted pseudo-labels Reference Label Equal, and the reference label equals category When the condition is met, the value is 1; otherwise, the value is 0. Indicates when the sample Predicted pseudo-labels equals category And its reference label Not equal to category When the condition is met, the value is 1; otherwise, the value is 0. Indicates labeled samples Category Confidence level, and ; S22, Based on feature search space Auxiliary populations initialized separately and the main population Assisted population and the main population All include Individuals, and calculate auxiliary population. and the main population Initial fitness of each individual: ; ; In the formula, and They represent auxiliary populations respectively. and the main population The initial fitness; Update and record the local optima for the filtering-assisted task. and the global optimal solution And the local optimal solution of the encapsulated main task and the global optimal solution .

[0015] S3. Based on the adaptive knowledge sharing mechanism, the main and auxiliary tasks are co-evolved. The auxiliary and main populations are updated through cross-task knowledge learning. When the global optimal feature subset of the auxiliary task is updated, pseudo-labels and confidence scores are generated using the label propagation algorithm. The population reconstruction strategy driven by the historical elite knowledge base is driven by environmental feedback. Variable neighborhood search is performed on high-quality individuals in the main population, and historical knowledge is used to guide the improvement or re-initialization of non-high-quality individuals to reconstruct the main population. Step S3 specifically includes the following steps: S31, Based on the main population Local optimal fitness differences and auxiliary population Feature selection number distribution Adaptively determine the knowledge sharing probability threshold : ; In the formula, Indicates an indicator function; and They represent auxiliary populations respectively. The Middle , The feature selection index value corresponding to a locally optimal individual; Indicates the main population The objective function index value corresponding to the locally optimal individual; Indicates the main population The objective function index value corresponding to the globally optimal individual; Choose a function to calculate the number of features; S32. Using local and global optima as convergence knowledge, and the least similar local optima in the external population to the current individual as diversity knowledge, the similarity of feature subsets is measured using cosine similarity: ; In the formula, Represents the feature subset of the current individual The feature subset corresponding to a local optimum in the external population Cosine similarity between them; S33, Auxiliary Population Learning Main Population Diverse knowledge to escape local optima, main population Learning Auxiliary Population The convergence knowledge is used to accelerate convergence, and offspring individuals are generated through an improved particle update formula to update the auxiliary population. and the main population : ; in, ; In the formula, and They represent the first Second-rate, During the nth iteration, the 1st The particle in the first The state on the dimension; Operators that represent state updates; Indicates the first During the nth iteration, the 1st The particle in the first The individual's historical optimal position on the dimension, and , Indicates the first During the nth iteration, the 1st The best historical position found by each particle itself; Indicates the first In the nth iteration, the entire particle swarm is at the ... The global historical best position on the dimension; Indicates the first In the nth iteration, a certain neighborhood or elite subgroup is at the th... Local optimal position in dimension; Represents a random number generation function; for ,choose High-quality and diverse knowledge as external knowledge, i.e. ,for Then choose High-quality convergent knowledge is used as external knowledge, i.e. S34. Recalculate the fitness of individuals in the updated population, and update the local and global optima. S35. Determine the global optimal solution for the auxiliary population. Update or not? If updating, then based on... The corresponding feature subset-driven label propagation algorithm iteratively propagates label information to generate new pseudo-labels and confidence levels for unlabeled samples. The confidence level of the labeled samples is set to 1; S36. The global optimal solution of the auxiliary population. and the current global optimal solution of the main population Stored in the elite knowledge base; S37. Utilizing an elite knowledge base to drive an environment-feedback-oriented population reconstruction strategy to reconstruct populations capable of adapting to new pseudo-labeled environments. When pseudo-labels are regenerated, individuals are re-evaluated. fitness and reduce fitness Included in the high-quality individual set And the rest Classified into a set of non-superior individuals ; then and Each individual in the process performs a search of different neighborhood structures, collectively exploring the feature space of the current environment; among them, Indicates the first The main population set after the next iteration; and They represent the first and The fitness of an individual in the current environment after the next iteration; Indicates the first After the second iteration Individuals within.

[0016] In this embodiment, the storage limit of the elite knowledge base is the most recent one. Substitute the global optimal solution. Indicates the maximum number of iterations; In step S37, for the set of high-quality individuals The steps for operating high-quality individuals are as follows: Step 1: Feature Space Division of High-Quality Individuals: Analyzing High-Quality Individuals The feature selection encoding state is used, and its encoded bits are regarded as the feature relevance evaluation result. The average relevance of each feature is calculated. The feature space of this high-quality individual is partitioned using a dual-inflection-point selection strategy. Features before the first inflection point are assigned to a strongly correlated feature subset, features after the second inflection point are assigned to a redundant feature subset, and the remaining features are assigned to a weakly correlated feature subset. Indicates the first The set of high-quality individuals after the next iteration; Represents a set of high-quality individuals The first individual The encoded value corresponding to the bit feature; Step 2, Parameter Initialization: Initialize the current high-quality individual As the solution to be enhanced, the neighborhood structure based on strong correlation features, the neighborhood structure based on weak correlation features, and the neighborhood structure based on redundancy features are used as input neighborhood structures, and the neighborhood search iteration threshold is initialized. Among them, the neighborhood structure based on strong correlation features Perturbation: Generate a zero-element mask vector matching the number of strongly correlated features, randomly select the encoding bits corresponding to the unselected strongly correlated features in the high-quality individual, and then apply this to the mask vector. Set the corresponding position to 1, and let ,generate New candidate solutions; Neighborhood structure based on weak correlation features Perturbation: Randomly select a portion of the encoding bits corresponding to weakly correlated features in the high-quality individual, reinitialize its encoding state, and generate... New candidate solutions; Neighborhood structure based on redundancy features Perturbation: Generate a zero-element mask vector that matches the number of redundant features. Randomly select the encoding bits corresponding to the selected redundant features in the high-quality individual, and then apply this to the mask vector. The corresponding position is set to 1, and the redundant feature encoding bits of high-quality individuals are perturbed to generate... New candidate solutions; Step 3, Fitness Verification of Candidate New Solutions: Calculate the fitness of candidate new solutions in the current neighborhood structure. The fitness of individuals under the pseudo-label environment in the next iteration is calculated and compared with the fitness of the original high-quality individuals to select those that meet the requirements of the current iteration. In the next iteration of the pseudo-label environment, candidate new solutions whose fitness is less than that of the original high-quality individual are considered. If there are multiple new solutions that meet the conditions, the one with the best fitness is selected as the updated solution for the high-quality individual. If there are no new solutions that meet the conditions, the original high-quality individual is retained. Step 4: Population Inheritance of Superior Individuals: Inherit the updated superior individuals or the original superior individuals into the reconstructed main population. middle.

[0017] In step S37, the following actions are taken for non-superior individuals: Step 1: Retrieve the historical best knowledge set, which consists of two parts: one is the set of historical best solutions searched by the encapsulated main task before each pseudo-label update, and the other is the feature set used to construct the consensus graph in the filtering auxiliary task; integrate the above two types of knowledge into a historical elite knowledge pool. Step 2, Parameter Initialization: Take the current non-high-quality individual as the solution to be enhanced, take each historical best solution in the historical elite knowledge pool as an independent neighborhood structure, and set the iterative search threshold of the VNS algorithm. Step 3, Neighborhood Structure Perturbation Guided by Historical Elite Knowledge: Initiate the iterative search of the VNS algorithm. For each historical best solution in the historical elite knowledge pool, perform neighborhood structure perturbation guided by historical elite knowledge: For each feature encoding bit of a non-superior individual, if the feature corresponding to the encoding bit is selected by both the non-superior individual and the current historical best solution, then retain the selection state of the feature; if the selection states of the two encoding bits are inconsistent, then randomly initialize the encoding bit and generate a new candidate solution under this neighborhood structure. Step 4: Fitness Verification of Candidate New Solutions: Calculate the fitness of candidate new solutions in the current neighborhood structure. The fitness of the next iteration under the pseudo-label environment is calculated and compared with the fitness of the original non-superior individuals; if there exists a... If the fitness of the pseudo-labeled individual in the next iteration is less than that of the original non-superior individual, then the candidate new solution with the best fitness is selected as the updated solution for the non-superior individual; if there is no candidate new solution that meets the conditions, then the feature encoding bits of the non-superior individual are globally randomly initialized to generate a new individual. Step 5: Inheritance of non-superior individuals: Incorporate the updated non-superior individuals or the re-initialized individuals into the reconstructed main population. .

[0018] S4. Repeat step S3 until the maximum number of iterations is reached. Output the globally optimal feature subset of the main task, apply it to the high-dimensional data classification scenario and verify the classification performance, feature sparsity and running efficiency to complete the semi-supervised feature selection.

[0019] Simulation Experiment To verify the performance of the proposed algorithm, experiments were conducted using 10 datasets of different sizes. Detailed descriptions of the selected datasets are shown in Table 1. PCMAC and BASEHOCK are from the scikit-feature open-source database, while the other eight datasets are from the UCI open-source database. To ensure fairness, a double five-fold cross-validation method was employed. Before the algorithm began, the dataset was divided into five mutually exclusive subsets, which were used alternately as the test set, while the remainder was used as the training set for the feature selection algorithm. During the encapsulated evaluation process, the training set was further divided into five mutually exclusive subsets, which were used alternately as the validation set to evaluate the fitness values ​​of the feature subsets. To highlight the semi-supervised nature of the training set, 30%, 20%, and 10% of the samples were randomly selected from each training set as labeled samples, and the remaining samples were stripped of their labels and used as unlabeled samples.

[0020] Table 1. Details of the selected dataset

[0021] To comprehensively evaluate the performance of the FAEMT-SSFS described in this invention, three sets of experiments were conducted: parameter sensitivity analysis, ablation experiments, and comparative experiments. All experiments were simulated on an Intel(R) Core(TM) i5-13500 @ 2.50 GHz computer and implemented in the MATLAB 2024a environment. Each experiment was run independently 30 times, and the average value of each evaluation metric was used as the final experimental result for analysis. Detailed comparison algorithms and performance evaluation metrics are described below: Algorithm Comparison: To verify the performance advantage of the proposed algorithm in SSFS, FAEMT-SSFS is compared with five representative SSFS methods: HSFS, AGLRM, RRPC, SSNDI, and SemiACO. HSFS and RRPC represent traditional embedded and filtered SSFS methods, respectively; AGLRM and SSNDI represent state-of-the-art embedded and filtered SSFS methods, respectively; and SemiACO is a novel filtered evolutionary SSFS method.

[0022] On the other hand, to highlight the global search performance of FAEMT-SSFS, four typical evolutionary feature selection algorithms were selected for comparison. Since research on EA-based encapsulated SSFS is relatively limited, this simulation experiment selected GA, PSO, CSO, and MFEA, which are widely used in supervised FS, and made improvements specifically for the SSFS problem. Specifically, the designed encapsulated objective function, which relies solely on supervised data, was used as the objective function for the four evolutionary algorithms. These constitute the corresponding EA-based encapsulated SSFS algorithms: GA-W, PSO-W, CSO-W, and MFEA-W. The remaining modules all follow the design of the original algorithm.

[0023] To ensure the reliability of the comparative experimental results, the relevant parameters involved in the five SSFS methods and four EA algorithms mentioned above all followed the recommended settings. Furthermore, to balance the running efficiency and solution quality of the evolutionary algorithms, the key parameters NP, T, and... of all EA-based SSFS algorithms were... The values ​​are uniformly set to 50, 100, and 0.5.

[0024] The performance of the proposed algorithm and the baseline algorithm is evaluated using classification accuracy and overall performance difference as evaluation metrics.

[0025] To demonstrate that the high-quality pseudo-labels generated by the auxiliary task can improve the global feature subset search capability of the main task, FAEMT-SSFS is compared with GA-M, PSO-M, CSO-M, and MFEA-M. The ACC values ​​obtained for datasets with different labeling rates are shown in Table 4.

[0026] Table 2 Comparison of average ACC values ​​obtained from FAEMT-SSFS and four different packaged EAs

[0027] As shown in Table 2, (1) FAEMT-SSFS differs from MFEA-W by 1.22% in the Isolet dataset with a 30% labeling rate, from CSO-W by 0.5% in the ORL dataset with a 20% labeling rate, and from PSO-W by 1.19% in the WarpPIE10P dataset with a 20% labeling rate. This proves that the pseudo-labeling technique can improve the feature selection results of the encapsulation method on most semi-supervised datasets; (2) From the perspective of different labeling rates, the performance of all algorithms decreases as the labeling rate decreases, with a decrease of approximately 0.55%-1.99%, which verifies the dependence of the encapsulation method on the amount of supervised data. However, FAEMT-SSFS had the lowest average decrease, at about 1.21%, indicating that FAEMT-SSFS was less affected by the number of labeled samples; (3) In terms of average ACC and RPI performance, FAEMT-SSFS had the best overall performance, improving by 4.02%, 3.82%, 3.97%, and 3.73% respectively compared to GA-W, PSO-W, CSO-W, and MFEA-W. This shows that the improvement of the accuracy of pseudo-label prediction by the auxiliary task can effectively improve the performance of the encapsulated task.

[0028] like Figure 5 As shown, FAEMT-SSFS achieved the best RPI (ACC) result, and the p-value = 2.964727E-4 < 0.05, indicating that FAEMT-SSFS also has a significant performance advantage over the four encapsulated evolutionary algorithms. Therefore, FAEMT-SSFS is significantly applicable to most semi-supervised datasets.

[0029] In summary, while filtering methods can quickly optimize feature subsets, they are limited by the one-sidedness of the filtering evaluation function, resulting in only suboptimal feature subsets. On the other hand, although encapsulation methods have the potential to search for globally optimal feature subsets, the resulting feature subsets are biased due to the limited amount of supervised data. Therefore, the additional computational cost of the FAEMT-SSFS algorithm can effectively improve the performance of finding globally optimal feature subsets.

[0030] 2. To verify the superior performance of the proposed algorithm on the SSFS problem, it is compared with five popular SSFS methods shown in Table 3.

[0031] Table 3 Comparison of average ACC values ​​obtained by FAEMT-SSFS and five SSFS algorithms.

[0032] Table 3 shows that (1) FAEMT-SSFS can obtain the feature subset with the best classification performance in most datasets with different labeling rates. It only performs slightly worse than SemiACO in the Isolet dataset with a 20% labeling rate and the ORL dataset with a 30% labeling rate. This indicates that FAEMT-SSFS can select feature subsets with better classification performance in most semi-supervised datasets. (2) From the average results, FAEMT-SSFS obtained the feature subsets with the highest classification accuracy at labeling rates of 10%, 20%, and 30%, which were 79.62%, 80.50%, and 82.06%, respectively. In addition, the impact of labeling rate on FAEMT-SSFS is about 1.22%, which is significantly lower than the 3.33%, 2.18%, 2.98%, 2.53%, and 2.05% of the other five comparison algorithms. This shows that FAEMT-SSFS has stronger stability than the semi-supervised feature selection algorithm of manifold. (3) From the overall performance evaluation analysis, FAEMT-SSFS achieved the highest overall performance, and improved by 10.69%, 6.34%, 8.62%, 9.88%, and 7.41% respectively compared with HSFS, AGLRM, RRPC, SSNDI, and SemiACO. This shows that FAEMT-SSFS is more competitive than the SSFS method of manifold.

[0033] like Figure 6 As shown in (a) and (b), FAEMT-SSFS achieved the highest RPI (ACC) value on the dataset with a 10% labeling rate, and significantly outperformed other SSFS methods. This demonstrates that FAEMT-SSFS exhibits significantly superior performance in environments with scarce labeled samples. This is primarily due to the fact that the candidate feature subset optimized by the auxiliary task improves the quality of pseudo-labels, making the classifier in the main task more accurate, thus leading to the globally optimal feature subset. Figure 6 As shown in (c) and (d), in the dataset with a 20% labeling rate, FAEMT-SSFS only shows a performance gap with SemiACO in Ioslet. However, according to the ANOVA results, FAEMT-SSFS still achieves the highest RPI (ACC) result, and This demonstrates a significant advantage. It indicates that as the number of labeled samples increases, the gap between FAEMT-SSFS and some other algorithms decreases. The main reason for this phenomenon is the interference of some erroneous pseudo-labels with the optimization direction of the main task. However, compared to independent supervised and unsupervised evaluation methods, the filling of pseudo-labeled samples can still compensate for the bias of encapsulated evaluation. For example... Figure 6 As shown in (e) and (f), in the ten datasets with a 30% labeling rate, the performance gap between FAEMT-SSFS and some of the comparative algorithms was further narrowed. Specifically, FAEMT-SSFS outperformed SemiACO and SSNDI by 3.77% and 1.42%, respectively, in the ORL dataset. However, the ANOVA results still show that FAEMT-SSFS significantly outperforms the other SSFS methods. This demonstrates that FAEMT-SSFS can efficiently utilize scarce labeled samples, thereby improving the classification accuracy of feature subsets. For example... Figure 6 As shown in (g) and (h), FAEMT-SSFS achieved the highest average RPI (ACC) across all datasets, and The above results demonstrate that FAEMT-SSFS has significant advantages over popular SSFS methods.

[0034] In summary, the FAEMT-SSFS framework proposed in this invention overcomes the limitation of encapsulated methods that rely on a sufficient number of labeled samples, enabling efficient semi-supervised feature selection. Furthermore, based on the experimental and result analysis above, FAEMT-SSFS has advantages over current competitive SSFS methods, especially when dealing with datasets with lower labeling rates.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification, characterized by: Includes the following steps: S1. Collect training datasets containing labeled and unlabeled sample sets in high-dimensional data classification scenarios, and evaluate the dual importance based on linear and nonlinear importance measures. Combine the inflection point selection strategy to remove consensus-based non-important features, construct the common feature search space for the main and auxiliary tasks, and achieve preliminary dimensionality reduction of the original high-dimensional feature space. S2. Construct objective functions for the encapsulated main task and the filtering auxiliary task in the main-auxiliary task respectively. At the same time, initialize the auxiliary population and the main population based on the common feature search space and calculate the initial fitness. S3. Based on an adaptive knowledge sharing mechanism, the main and auxiliary tasks are co-evolved, and the auxiliary and main populations are updated through cross-task knowledge learning. S4. When the global optimal feature subset of the auxiliary task is updated, the label propagation algorithm is used to generate pseudo-labels and confidence scores. The population reconstruction strategy oriented towards environmental feedback is used to explore the exploration potential of the main population in the new environment and regenerate the main population that takes into account both convergence and diversity. S5. Repeat steps S3 and S4 until the maximum number of iterations is reached. Output the globally optimal feature subset of the main task, apply it to the high-dimensional data classification scenario and verify the classification performance, feature sparsity and running efficiency to complete the semi-supervised feature selection.

2. The multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Collect labeled sample sets for high-dimensional data classification scenarios. Compared with unlabeled sample set training dataset ,Right now ;in, middle, Indicates the first One labeled sample, Indicates labeled samples Category , Indicates the total number of categories. Indicates the total number of labeled samples; , Indicates the first One unlabeled sample, This represents the total number of unlabeled samples, whose categories are the same as those of labeled samples. Consistent categories; S12. Define the linear importance metric. and nonlinear importance metrics : ； ； In the formula, Indicates the weighting coefficient; Indicates the first to be evaluated Features In the unlabeled sample set The normalized variance value in; express exist The normalized Pearson correlation coefficient value in the figure; express exist The normalized entropy value in; express exist The normalized mutual information value in; S13. Employ an inflection point-based selection strategy to evaluate the linear importance metrics. and nonlinear importance metrics After sorting, the features are filtered to remove those with linear importance metrics. and nonlinear importance metrics The unimportant features of consensus, and the remaining features, constitute the common feature search space for the primary and secondary tasks. This achieves initial dimensionality reduction of the original high-dimensional feature space.

3. The multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification according to claim 2, characterized in that: Step S13 specifically includes the following steps: S131. Sort all features in descending order according to the calculation results of step S12 to obtain the feature importance curve. ; S132, Importance Curve of Connectivity Features The two endpoints generate a reference line and calculate Up to each point European distance And select Euclidean distance The largest point as The inflection point; S133, Feature Importance Curve Features whose importance measure is greater than the inflection point value are considered important features, resulting in four types of feature spaces, namely linear importance measures. Important feature set under guidance Set of unimportant features and nonlinear importance metrics Important feature set under guidance Set of unimportant features ; S134. Remove features from the feature space obtained in step S133. and The unimportant characteristic of consensus, namely The remaining features constitute the common feature search space for the primary and secondary tasks, i.e. .

4. The multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification according to claim 1, characterized in that: Step S2 specifically includes the following steps: S21. Design the objective function for a multi-manifold constrained filtering-based auxiliary task. : ； in, ； In the formula, Represents the Laplace score for multi-manifold constraints. This represents the candidate solution of the feature subset to be optimized in the common feature search space of the main and auxiliary tasks for the auxiliary task; Indicates the weighting factor; Represents the trace operation of a matrix; Features in the search space representing common features of primary and secondary tasks Transpose of; The features in the common feature search space of the primary and secondary tasks are represented, and ; and These represent the similarity matrices corresponding to Must-Link. Similarity matrix corresponding to Cannot-Link The Laplace operator, and , , Represents the set of sample pairs in Must-Link. Indicates the first in the labeled sample set A subset of samples of the class This represents the set of sample pairs that cannot be linked. Representation and Category Another different category, Indicates the first in the labeled sample set A subset of samples of the class; This represents the Laplacian matrix corresponding to the local manifold; This represents the degree matrix corresponding to the Laplacian matrix of the local manifold; Simultaneously, a confidence-guided encapsulated main task objective function is designed. : ； in, ； ； ； ； ； In the formula, Represents candidate sets based on feature subsets The calculated confidence-guided Micro-F1 value; and These represent precision and recall based on label confidence, respectively. and Representing categories Confidence-based true positives and confidence-based false positives; and Representing categories True positives and false negatives; Indicates when the sample Predicted pseudo-labels Reference Label Equal, and the reference label equals category When the condition is met, the value is 1; otherwise, the value is 0. Indicates when the sample Predicted pseudo-labels equals category And its reference label Not equal to category When the condition is met, the value is 1; otherwise, the value is 0. Indicates labeled samples Category Confidence level, and ; S22, Based on feature search space Auxiliary populations initialized separately and the main population Assisted population and the main population All include Individuals, and calculate auxiliary population. and the main population Initial fitness of each individual: ； ； In the formula, and They represent auxiliary populations respectively. and the main population The initial fitness; Update and record the local optima for the filtering-assisted task. and the global optimal solution And the local optimal solution of the encapsulated main task and the global optimal solution .

5. The multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification according to claim 4, characterized in that: Step S3 specifically includes the following steps: S31, Based on the main population Local optimal fitness differences and auxiliary population Feature selection number distribution Adaptively determine the knowledge sharing probability threshold : ； In the formula, Indicates an indicator function; and They represent auxiliary populations respectively. The Middle , The feature selection index value corresponding to a locally optimal individual; Indicates the main population The objective function index value corresponding to the locally optimal individual; Indicates the main population The objective function index value corresponding to the globally optimal individual; Choose a function to calculate the number of features; S32. Using local and global optima as convergence knowledge, and the least similar local optima in the external population to the current individual as diversity knowledge, the similarity of feature subsets is measured using cosine similarity: ； In the formula, Represents the feature subset of the current individual The feature subset corresponding to a local optimum in the external population Cosine similarity between them; S33, Auxiliary Population Learning Main Population Diverse knowledge to escape local optima, main population Learning Auxiliary Population The convergence knowledge is used to accelerate convergence, and offspring individuals are generated through an improved particle update formula to update the auxiliary population. and the main population : ； in, ； In the formula, and They represent the first Second-rate, During the nth iteration, the 1st The particle in the first The state on the dimension; Operators that represent state updates; Indicates the first During the nth iteration, the 1st The particle in the first The individual's historical optimal position on the dimension, and , Indicates the first During the nth iteration, the 1st The best historical position found by each particle itself; Indicates the first In the nth iteration, the entire particle swarm is at the ... The global historical best position on the dimension; Indicates the first In the nth iteration, a certain neighborhood or elite subgroup is at the th... Local optimal position in dimension; This represents a random number generation function; S34. Recalculate the fitness of individuals in the updated population, and update the local and global optima. S35. Determine the global optimal solution for the auxiliary population. Update or not? If updating, then based on... The corresponding feature subset-driven label propagation algorithm iteratively propagates label information to generate new pseudo-labels and confidence levels for unlabeled samples. The confidence level of the labeled samples is set to 1; S36. The global optimal solution of the auxiliary population. and the current global optimal solution of the main population Stored in the elite knowledge base; S37. Utilizing an elite knowledge base to drive an environment-feedback-oriented population reconstruction strategy to reconstruct populations capable of adapting to new pseudo-labeled environments. When pseudo-labels are regenerated, individuals are re-evaluated. fitness and reduce fitness Included in the high-quality individual set And the rest Classified into a set of non-superior individuals ; then and Each individual in the process performs a search of different neighborhood structures, collectively exploring the feature space of the current environment; among them, Indicates the first The main population set after the next iteration; and They represent the first and The fitness of an individual in the current environment after the next iteration; Indicates the first After the second iteration Individuals within.

6. The multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification according to claim 5, characterized in that: In step S37, for the set of high-quality individuals The steps for operating high-quality individuals are as follows: Step 1: Feature Space Division of High-Quality Individuals: Analyzing High-Quality Individuals The feature selection encoding state is used, and its encoded bits are regarded as the feature relevance evaluation result. The average relevance of each feature is calculated. The feature space of this high-quality individual is partitioned using a dual-inflection-point selection strategy. Features before the first inflection point are assigned to a strongly correlated feature subset, features after the second inflection point are assigned to a redundant feature subset, and the remaining features are assigned to a weakly correlated feature subset. Indicates the first The set of high-quality individuals after the next iteration; Represents a set of high-quality individuals The first individual The encoded value corresponding to the bit feature; Step 2, Parameter Initialization: Initialize the current high-quality individual As the solution to be enhanced, the neighborhood structure based on strong correlation features, the neighborhood structure based on weak correlation features, and the neighborhood structure based on redundancy features are used as input neighborhood structures, and the neighborhood search iteration threshold is initialized. Among them, the neighborhood structure based on strong correlation features Perturbation: Generate a zero-element mask vector matching the number of strongly correlated features, randomly select the encoding bits corresponding to the unselected strongly correlated features in the high-quality individual, and then apply this to the mask vector. Set the corresponding position to 1, and let ,generate New candidate solutions; Neighborhood structure based on weak correlation features Perturbation: Randomly select a portion of the coding bits corresponding to weakly correlated features in the high-quality individual, reinitialize its coding state, and generate... New candidate solutions; Neighborhood structure based on redundancy features Perturbation: Generate a zero-element mask vector that matches the number of redundant features. Randomly select the encoding bits corresponding to the selected redundant features in the high-quality individual, and then apply this to the mask vector. The corresponding position is set to 1, and the redundant feature encoding bits of high-quality individuals are perturbed to generate... New candidate solutions; Step 3, Fitness Verification of Candidate New Solutions: Calculate the fitness of candidate new solutions in the current neighborhood structure. The fitness of individuals under the pseudo-label environment in the next iteration is calculated and compared with the fitness of the original high-quality individuals to select those that meet the requirements of the current iteration. In the next iteration of the pseudo-label environment, candidate new solutions whose fitness is less than that of the original high-quality individual are considered. If there are multiple new solutions that meet the conditions, the one with the best fitness is selected as the updated solution for the high-quality individual. If there are no new solutions that meet the conditions, the original high-quality individual is retained. Step 4: Population Inheritance of Superior Individuals: Inherit the updated superior individuals or the original superior individuals into the reconstructed main population. middle.

7. The multi-task evolutionary semi-supervised feature selection method for high-dimensional data classification according to claim 5, characterized in that: In step S37, the following actions are taken for non-superior individuals: Step 1: Retrieve the historical best knowledge set, which consists of two parts: one is the set of historical best solutions searched by the encapsulated main task before each pseudo-label update, and the other is the feature set used to construct the consensus graph in the filtering auxiliary task; integrate the above two types of knowledge into a historical elite knowledge pool. Step 2, Parameter Initialization: The current non-high-quality individual is taken as the solution to be enhanced, and each historical best solution in the historical elite knowledge pool is taken as an independent neighborhood structure. At the same time, the iterative search threshold of the VNS algorithm is set. Step 3, Neighborhood Structure Perturbation Guided by Historical Elite Knowledge: Initiate the iterative search of the VNS algorithm. For each historical best solution in the historical elite knowledge pool, perform neighborhood structure perturbation guided by historical elite knowledge: For each feature encoding bit of a non-superior individual, if the feature corresponding to the encoding bit is selected by both the non-superior individual and the current historical best solution, then retain the selection state of the feature; if the selection states of the two encoding bits are inconsistent, then randomly initialize the encoding bit and generate a new candidate solution under this neighborhood structure. Step 4: Fitness Verification of Candidate New Solutions: Calculate the fitness of candidate new solutions in the current neighborhood structure. The fitness of the next iteration under the pseudo-label environment is calculated and compared with the fitness of the original non-superior individuals; if there exists a... If the fitness of the pseudo-labeled individual in the next iteration is less than that of the original non-superior individual, then the candidate new solution with the best fitness is selected as the updated solution for the non-superior individual; if there is no candidate new solution that meets the conditions, then the feature encoding bits of the non-superior individual are globally randomly initialized to generate a new individual. Step 5: Inheritance of non-superior individuals: Incorporate the updated non-superior individuals or the re-initialized individuals into the reconstructed main population. .

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