Progressive spatial constraint feature selection method for ultrahigh-dimensional data

Abstract

The invention discloses a progressive spatial constraint feature selection method for ultrahigh-dimensional data, and relates to the field of feature selection, and the method comprises the steps: initializing a data feature set, a population and algorithm parameters, judging whether an iteration condition is satisfied, if yes, directly outputting a target result, and if not, entering S3; establishing a spatial constraint framework, and calculating a spatial convergence factor and a spatial diffusion factor; s3, judging whether the spatial convergence factor and the spatial diffusion factor obtained in S3 meet a convergence condition or not, selecting an operation strategy, and performing operation according to the operation strategy to generate a target feature space scheme; evaluating the advantages and disadvantages of the target feature space schemes, constructing fitness functions according to the indexes, performing calculation, sorting the fitness functions from low to high, reserving the target feature space scheme in the first order and the fitness value of the target feature space scheme as individual target schemes, updating iteration conditions, and performing iteration until a stop condition is met. According to the selection method provided by the invention, a more accurate and efficient feature selection process can be realized.

Description

Technical Field

[0001] The present invention relates to the field of feature selection, and in particular to a progressive spatial constraint feature selection method for ultra-high dimensional data. Background Art

[0002] The basic structure of this method is a heuristic encapsulated feature selection method, which is similar to the swarm intelligence algorithm and is aimed at high-dimensional and ultra-high-dimensional data that are widely present in medical and financial scenarios.

[0003] Mainstream encapsulated feature selection methods based on swarm intelligence / heuristics: First, an initial feature subset is generated through a certain heuristic algorithm (such as genetic algorithm, particle swarm algorithm, etc.); then, a fitness function is defined. The fitness function is usually related to the specific modeling task, which can be a performance indicator such as classification accuracy and regression error to evaluate the performance of this feature subset; then, some learning strategies are used to select or eliminate features, and the algorithm parameters are updated according to the selected feature subset and the evaluation results. The present invention aims to solve many challenges existing in high-dimensional and ultra-high-dimensional data, including the "curse of dimensionality" phenomenon and the "combinatorial explosion" problem that occurs during feature selection. In fields such as medicine, these challenges are particularly prominent because as the data dimension increases, the model search space grows exponentially, resulting in a large amount of computing resources and time consumption. In addition, the existing technology often finds it difficult to effectively evaluate the relationship between dimensionality reduction requirements and information retention when processing high-dimensional data. Most methods are too concerned about the loss of benefits of a single feature, resulting in excessive retention of data information, which greatly increases the running time, and it is very easy to form local convergence in the number of selected features. At the same time, existing studies often ignore the combination effect between features, that is, the interaction between different features may have a significant impact on the target variable, which can easily lead to local optimal solutions, resulting in poor performance of the selected feature scheme in various evaluation indicators.

[0004] Therefore, the present invention aims to propose an efficient progressive spatial constraint feature selection method to address these problems, which fully considers the combination effect between features to achieve a more accurate and efficient feature selection process. A new feature subset is generated again, and the cycle is iterated until the stopping criterion is reached. Summary of the invention

[0005] The purpose of the present invention is to provide a progressive spatially constrained feature selection method for ultra-high dimensional data, with the goal of achieving a more accurate and efficient feature selection process.

[0006] In this application, a progressive spatially constrained feature selection method for ultra-high dimensional data is provided, comprising the following steps:

[0007] S1. Initialize the data feature set, normalize the data feature set, and stratify the training set and test set;

[0008] S2, initialize the population and algorithm parameters, and determine whether the iteration conditions are met. If so, directly output the target result. If not, enter S3;

[0009] S3, establish a spatial constraint framework, and calculate the spatial convergence factor and spatial diffusion factor through the algorithm parameters and the spatial constraint framework;

[0010] S4, judging whether the spatial convergence factor and spatial diffusion factor obtained in S3 meet the convergence condition, and selecting a calculation strategy, and generating a target feature space solution according to the calculation strategy;

[0011] S5. Evaluate the quality of the target feature space solution, construct and calculate the fitness function according to the indicators, sort the fitness functions from low to high, and retain the target feature space solution with the first order and its fitness value as the individual target solution. The indicators include feature solution length, solution accuracy, solution AUC value, and solution F1 value.

[0012] S6, update the iteration condition, and determine whether the updated iteration condition is met. If it is met, directly output the target result. If it is not met, iterate S3 to S5 until the stop condition is met.

[0013] Preferably, the specific contents of the population initialization and algorithm parameters in S2 are as follows:

[0014] Individuals are constructed using binary coding. The number of features in the input data set, i.e., the dimension, represents the maximum spatial range that the initial individual can choose as the spatial boundary, and the actual number of features selected is the spatial domain of the current individual.

[0015] The input parameters include the population size N, the number of iterations and the constraint factor, wherein the constraint factor generates the remaining control factors in the spatial constraint function;

[0016] The individuals in the initialized population need to calculate their fitness values ​​one by one to guide them to complete the space jump. The fitness value is obtained by weighted calculation after unified measurement of accuracy, number of features, F1 value, and AUC value.

[0017] Preferably, the spatial constraint function framework in S3 adopts the dimension adjustment function to progressively constrain the dimensional space, and the dimensional transformation is reflected in the spatial convergence part and the spatial diffusion part;

[0018] The spatial constraint function framework is divided into two stages according to the iteration parameters. The overall spatial constraint gradually decreases. The spatial constraint amplitude in the first stage changes from large to small, which is manifested as focusing on dimensionality reduction convergence and ignoring diffusion. The spatial constraint in the second stage changes from small to stable, which is manifested as focusing on diffusion and ignoring dimensionality reduction convergence.

[0019] Preferably, the expression of the spatial constraint function framework in S3 includes:

[0020]

[0021] Among them, t is the current iteration, i is the current individual, T length is the length of the iteration cycle, max is the upper bound of the spatial diffusion factor, min is the lower bound of the spatial diffusion factor, and N is the population size.

[0022] The spatial constraint function framework mainly controls the spatial convergence factor DRF and the spatial diffusion factor CLF through the dimension adjustment function, and indirectly controls the feature solution dimension in the feature selection in the transformation dimension of the control strategy.

[0023] Preferably, the spatial convergence factor of the spatial convergence part is expressed as follows:

[0024]

[0025] Among them, Tmid is the period division node, DRF_max and DRF_mid, DRF_min are the maximum and middle values ​​and minimum values ​​of two pre-defined spatial convergence factors, and DR is the characteristic convergence number.

[0026] Preferably, the expression of the spatial diffusion factor of the spatial diffusion part includes:

[0027] CLF=CF-f(t,i,T,para,DRF);

[0028]

[0029] Among them, CF is the spatial constraint factor, Nsf_diff is the dimension of the selected feature subset of the difference space obtained after the current agent individual selects a suitable strategy, and CL is the feature diffusion number.

[0030] Preferably, S4 determines whether the spatial convergence factor and spatial diffusion factor obtained in S3 meet the convergence condition, and selects a calculation strategy. The specific content of the target feature space solution generated by calculation according to the calculation strategy is as follows:

[0031] If the spatial convergence factor and the spatial diffusion factor meet the convergence conditions, the spatial convergence operation is performed, and the individual performs a spatial chain convergence strategy according to the spatial convergence factor, that is, the current spatial domain becomes the spatial boundary of the next dimensionality reduction, and the spatial mark will be inherited according to the spatial convergence factor;

[0032] If the spatial convergence factor and spatial diffusion factor do not meet the convergence conditions, a spatial diffusion operation is performed and the constraint strategy is executed according to the individual's own state;

[0033] The constraint strategies include group space constraint strategy, elite space constraint strategy and space domain constraint strategy;

[0034] Determine the individual's own state. If the individual is the target individual, implement the group space constraint strategy. If the individual is not the target individual, give it a jump probability and generate an individual once.

[0035] If an individual is a jump-out individual, the elite space constraint strategy is implemented. If an individual is not a jump-out individual, the space domain constraint strategy is implemented.

[0036] In summary, compared with traditional technologies, the present invention proposes a progressive spatial constraint feature selection method for ultra-high dimensional data, which proposes a spatial chain convergence strategy, which is controlled by a spatial convergence factor (generated by a spatial constraint function) to control the convergence stage and convergence degree of the algorithm, save computing resources and storage resources, and effectively improve the running time.

[0037] In addition, a spatial constrained diffusion strategy is proposed, which is controlled by the spatial diffusion factor (generated by the spatial constraint function) to control the learning strategy of the algorithm, so that the algorithm can fully explore the combined utility between features and escape from the local optimum.

[0038] The spatial chain convergence strategy controls the convergence stage and degree of the algorithm. The chain structure further accelerates the convergence of the algorithm and greatly reduces the computation and storage of features, effectively improving the running time. The spatial constraint diffusion strategy effectively inherits and learns the combination and synergy between features through spatial constraints, avoiding falling into local optimality, thereby improving the overall effect of the model.

[0039] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flowchart of a progressive spatially constrained feature selection method for ultra-high-dimensional data according to the present invention;

[0041] Figure 2 This is a statistical analysis chart of the AUC value of a progressive spatial constraint feature selection method for ultra-high-dimensional data of the present invention;

[0042] Figure 3 This is a statistical analysis diagram of the F1 value of a progressive spatial constraint feature selection method for ultra-high-dimensional data according to the present invention;

[0043] Figure 4 It is an iterative operation record diagram of a progressive spatial constraint feature selection method for ultra-high dimensional data according to the present invention;

[0044] Figure 5This is a statistical analysis diagram of the average accuracy of a progressive spatial constraint feature selection method for ultra-high-dimensional data according to the present invention;

[0045] Figure 6 This is a statistical analysis diagram of the number of selected features of a progressive spatial constraint feature selection method for ultra-high-dimensional data according to the present invention;

[0046] Figure 7 This is a running time statistical analysis diagram of a progressive spatial constraint feature selection method for ultra-high-dimensional data according to the present invention;

[0047] Figure 8 The present invention is a flowchart of selecting an operation strategy for a progressive spatial constraint feature selection method for ultra-high dimensional data. DETAILED DESCRIPTION

[0048] The technical solution of the present invention is further described below by means of the accompanying drawings and embodiments. It should be noted that unless otherwise specifically stated, the relative arrangement of components and steps, numerical expressions and numerical values ​​described in these embodiments do not limit the scope of the present application.

[0049] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the present application, its application, or uses.

[0050] Technologies, systems, and devices known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, systems, and devices should be considered part of the specification.

[0051] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0052] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0053] This paper proposes a progressive spatial constraint feature selection method for ultra-high dimensional data, aiming to solve the problems of "curse of dimensionality" and "combinatorial explosion" that are prone to occur in high-dimensional or ultra-high-dimensional data in the traditional feature selection process, as well as the problems of insufficient local convergence and combination effect between features. This method achieves efficient and accurate feature selection through a progressive spatial constraint framework, a chain dimensionality reduction strategy and a mix-and-match diffusion strategy.

[0054] The progressive spatial constraint framework is the core of the present invention. It changes the traditional feature selection method dominated by the quality of a single feature or the quality of individuals in a population, and uses progressive spatial constraints to select features dominated by the number of features. The framework generates spatial convergence factors and spatial diffusion factors through functions, controls the variables and strategies related to the number of features in the algorithm flow, and allows the algorithm to converge quickly and jump out of the local optimum.

[0055] like Figure 1 As shown, the present invention provides a progressive spatial constraint feature selection method for ultra-high dimensional data, which is specifically as follows: S1, initialize the data feature set, uniformly process the null values ​​of the data set, normalize the features, and stratify the training set and the test set;

[0056] The experimental data set of this algorithm adopts data sets with different levels of feature numbers. At the same time, considering the ratio of the number of features to the number of samples, 12 real high-dimensional and ultra-high-dimensional data sets including gene microarrays and disease prediction are selected, as shown in Table 1. This data set comes from public databases such as UCI and Kaggle.

[0057] Table 1

[0058]

[0059] S2, initialize the population and algorithm parameters, and determine whether the iteration conditions are met. If so, directly output the target result. If not, enter S3;

[0060] Furthermore, the specific contents of the population initialization and algorithm parameters in S2 are as follows:

[0061] Individuals are constructed using binary coding. The number of features in the input data set, i.e., the dimension, represents the maximum spatial range that the initial individual can choose as the spatial boundary, and the actual number of features selected is the spatial domain of the current individual.

[0062] The input parameters include population size, number of iterations and constraint factors, and the constraint factors generate the remaining control factors in the spatial constraint function;

[0063] The individuals in the initialized population need to calculate their fitness values ​​one by one to guide them to complete the space jump. The fitness value is obtained by weighted calculation after unified measurement of accuracy, number of features, F1 value, and AUC value.

[0064] S3, establish a spatial constraint framework, and calculate the spatial convergence factor and spatial diffusion factor through the algorithm parameters and the spatial constraint framework;

[0065] The spatial convergence factor determines the decrease of the spatial domain of the individual in the current population under the current iteration cycle, and affects the convergence of the algorithm. In addition, another important metric for chain convergence is "chain". A single individual in the entire population presents a chain state in the entire convergence cycle, that is, the change of the individual spatial domain has nothing to do with the population, the optimal individual, other individuals, and the unselected feature space, but only with the individual's historical feature space. "Chain dimensionality reduction" further accelerates the convergence of the algorithm and greatly reduces the computation and storage of features.

[0066] The core of the spatial constraint diffusion strategy is the constraints between spatial domains and the constraints between spatial markers. Under the constraints of spatial domains, the newly generated spatial domain must be smaller than the current spatial domain. Under the constraints of spatial markers, the spatial markers of the newly generated spatial scheme must be a subset of the original spatial markers. Through spatial constraint diffusion, the combination and synergy between features will be effectively inherited and learned. In the diffusion, it is mainly manifested in three steps: the first is the group spatial constraint for the optimal individual, the second is the elite spatial constraint for the mass individual, and the third is the optimal spatial domain constraint for the individual who jumps out.

[0067] Furthermore, the spatial constraint function framework in S3 uses the dimension adjustment function to progressively constrain the dimensional space, and the dimensional transformation is reflected in the spatial convergence part and the spatial diffusion part;

[0068] The spatial constraint function framework is divided into two stages according to the iteration parameters. The overall spatial constraint gradually decreases. The spatial constraint amplitude in the first stage changes from large to small, which is manifested as focusing on dimensionality reduction convergence and ignoring diffusion. The spatial constraint in the second stage changes from small to stable, which is manifested as focusing on diffusion and ignoring dimensionality reduction convergence.

[0069] Furthermore, the expressions of the spatial constraint function framework in S3 include:

[0070]

[0071] Among them, t is the current iteration, i is the current individual, T length is the length of the iteration cycle, max is the upper bound of the spatial diffusion factor, min is the lower bound of the spatial diffusion factor, and N is the population size.

[0072] The progressive spatial constraint framework uses a dimensionality adjustment function to progressively constrain the dimensional space. The dimensionality transformation is reflected in two parts: spatial convergence and spatial diffusion. The spatial constraint function framework mainly controls the dimension of the feature scheme in feature selection through the inverse "S" dimensionality adjustment function of the sigmoid function and the function of generating the spatial convergence factor DRF and the spatial diffusion factor, so that the algorithm can converge quickly and jump out of the local optimum.

[0073] In high-dimensional and ultra-high-dimensional data, if the dimension is not restricted and optimized, the computational cost of the algorithm will increase exponentially. Therefore, the overall algorithm cycle is divided into two stages according to the number of iterations and input parameters. The early stage focuses on spatial convergence and rapid dimensionality reduction, and the later stage focuses on spatial diffusion and rapid optimization of feature combinations. Figure 8 shown.

[0074] The two-stage design of the algorithm is mainly presented in stages through spatial convergence operations. Different convergence factors will be generated in the early stage that focuses on dimensionality reduction convergence and the later stage that focuses on diffusion. The convergence speed of the algorithm is controlled by the spatial convergence factor DRF, which determines the decrease of the individual spatial domain of the current population under the current iterative cycle and affects the convergence of the algorithm.

[0075] Furthermore, the spatial convergence factor expression of the spatial convergence part is as follows:

[0076]

[0077] Among them, Tmid is the period division node, DRF_max and DRF_mid, DRF_min are the maximum and middle values ​​and minimum values ​​of two pre-defined spatial convergence factors, and DR is the characteristic convergence number.

[0078] The convergence factor controls the convergence speed, and the spatial chain convergence strategy controls how to converge. One of its important criteria is "chain": a single individual in the entire population presents a chain state in the entire convergence cycle, that is, the change of the individual's spatial domain has nothing to do with the population, the optimal individual, other individuals, and the unselected feature space, but only with the individual's historical feature space. The spatial chain convergence strategy accelerates the convergence of the algorithm and greatly saves computing resources and storage resources.

[0079] If the current individual agent meets the spatial convergence operation rules, the DRF of the current individual in the current iteration is calculated, and the DR is obtained through the DRF. The features selected by the current historical optimal individual feature scheme are randomly deleted through the DR.

[0080] In the later stages of the algorithm, the focus shifts to diffusion optimization, where the feature dimensions are controlled by a spatial diffusion operation. This operation carefully adjusts the learning path of the algorithm through the spatial diffusion factor CLF, aiming to deeply explore the utility of the combination of features to achieve a breakthrough from the local optimum.

[0081] Furthermore, the expression of the spatial diffusion factor of the spatial diffusion part includes:

[0082] CLF=CF-f(t,i,T,para,DRF);

[0083]

[0084] Among them, CF is the spatial constraint factor, Nsf_diff is the dimension of the selected feature subset of the difference space obtained after the current agent individual selects a suitable strategy, and CL is the feature diffusion number.

[0085] The core of spatial diffusion operation is spatial constraint, that is, constraining the problem search space. On the one hand, in the high-dimensional and ultra-high-dimensional problem search space, there are too many meaningless or low-value spaces, and searching for this part of the space will waste a lot of resources. On the other hand, when the search space increases, the effective information in the feature space is more difficult to capture, making the synergy of features more difficult to be mined. Through the spatial constraint diffusion of this article, the combination and synergy between features will be effectively inherited and learned, which is mainly manifested in three steps in diffusion: first, a group space constraint strategy is implemented for the optimal individual agent, second, an elite space constraint strategy is implemented for the general individual, and third, a spatial domain constraint strategy is implemented for the individual who jumps out.

[0086] In S4, it is determined whether the spatial convergence factor and spatial diffusion factor obtained in S3 meet the convergence condition, and an operation strategy is selected. The specific contents of the target feature space solution generated by the operation strategy are as follows:

[0087] If the spatial convergence factor and the spatial diffusion factor meet the convergence conditions, the spatial convergence operation is performed, and the individual performs a spatial chain convergence strategy according to the spatial convergence factor, that is, the current spatial domain becomes the spatial boundary of the next dimensionality reduction, and the spatial mark will be inherited according to the spatial convergence factor;

[0088] If the spatial convergence factor and spatial diffusion factor do not meet the convergence conditions, a spatial diffusion operation is performed and the constraint strategy is executed according to the individual's own state;

[0089] The constraint strategies include group space constraint strategy, elite space constraint strategy and space domain constraint strategy;

[0090] Determine the individual's own state. If the individual is the target individual, implement the group space constraint strategy. If the individual is not the target individual, give it a jump probability and generate an individual once.

[0091] If an individual is a jump-out individual, the elite space constraint strategy is implemented. If an individual is not a jump-out individual, the space domain constraint strategy is implemented.

[0092] The group space constraint strategy targets the best individual. The group advantage space is constructed from the historical best spatial set of individuals in the proxy population (i.e., the historical best feature selection scheme set of individuals). The group advantage space is used to constrain the problem search space of the best individual. First, the feature space of the current best individual is matched to remove duplications, and the feature difference space between the best individual and the group is generated. Then, the best individual is allowed to generate the feature diffusion number CL according to the spatial diffusion factor CLF, and the features that meet the feature diffusion number are randomly selected in the feature difference space, thereby updating the best individual space, i.e., the new feature scheme.

[0093] The elite space constraint strategy targets the general public and randomly selects individuals who are better than the current individual as elite individuals. The feature scheme is defined as the elite space, and the elite space is used to constrain the problem search space of the current individual. Subsequently, the feature difference space is generated by removing the duplication of the feature space of the current individual and the elite space, and then the current individual is allowed to generate the feature diffusion number CL according to the spatial diffusion factor CLF, and the matching feature difference space randomly selects features that meet the feature diffusion number, thereby updating the current individual space. Among the elites, there is also a situation of selecting the best from the best, that is, individuals can only match the elite space of better individuals. In the cycle of the group, the worse the performance of the individual, the lower the probability of being selected. Therefore, elite individuals of different levels have invisible spatial diffusion advantages.

[0094] The spatial domain constraint strategy targets individuals that have jumped out. There is a certain probability of individuals jumping out during diffusion, which strengthens the algorithm to jump out of the local optimum and guides it through the constraints of the optimal spatial domain to ensure that its exploration direction is consistent with the optimal solution. Individuals that have jumped out will completely abandon the current feature space, but will be constrained by the spatial domain of the current optimal individual and regenerate a new feature space solution.

[0095] S5. Evaluate the quality of the target feature space solution, construct and calculate the fitness function according to the indicators, sort the fitness functions from low to high, and retain the target feature space solution with the first order and its fitness value as the individual target solution. The indicators include feature solution length, solution accuracy, solution AUC value, and solution F1 value.

[0096] S6, update the iteration condition, and determine whether the updated iteration condition is met. If it is met, directly output the target result. If it is not met, iterate S3 to S5 until the stop condition is met.

[0097] The curse of dimensionality in previous technologies caused the model search space to grow exponentially, consuming a lot of computing power and time, resulting in high costs and slow response speeds.

[0098] In addition, the number of features is prone to local convergence, which greatly increases the running time, resulting in unclear optimization of the feature subset solution and a long time. Failure to fully consider the combination effect between processing features makes the method prone to local optimality, affecting the overall effect of the model.

[0099] This application can improve the efficiency of model search, search within the effective space, reduce computing power and time consumption, and thus solve the problems of high cost and slow response speed.

[0100] Avoid local convergence problems in the number of features, optimize feature subset solutions, and shorten running time to solve the problem of unclear optimization and long running time caused by too many features.

[0101] like Figure 4 As shown by the experiment Figure 1 It can be seen from the iteration record diagram that the proposed algorithm GSCFS can show faster convergence effect in most data sets than the comparison algorithm and is not trapped in local optimality.

[0102] In the experiment Figure 2 It can be seen from the feature quantity chart that the proposed algorithm GSCFS is more streamlined than the feature solutions obtained by the same type of swarm intelligence and evolutionary computing methods, and the optimization of the number of features can reach more than 90%. Compared with filtering and feature sorting methods, it has a roughly streamlined solution, but retains more effective features for complex data. At the same time, the output result is not a quantitative feature ranking or importance, but a valid feature subset that can be directly used.

[0103] From the running time graph, we can see that the proposed algorithm is simpler, faster and more efficient than similar swarm intelligence and evolutionary computing methods. It far exceeds similar algorithms while ensuring the results. The time efficiency is not much different from other faster sorting algorithms or new heuristic algorithms, but at the same time it ensures the combination relationship between features, fully mining and retaining the relationship between features. The proposed algorithm GSCFS can show faster convergence effect in most data sets than the comparison algorithm, and is not trapped in local optimality.

[0104] like Figure 6 As shown in the figure, the proposed algorithm GSCFS is more streamlined than the feature solutions obtained by the same type of swarm intelligence and evolutionary computing methods, and can achieve more than 90% optimization of the number of features. Compared with filtering and feature sorting methods, it has a roughly streamlined solution, but retains more effective features for complex data. At the same time, the output result is not a quantitative feature ranking or importance, but a valid feature subset that can be directly used.

[0105] like Figure 7As shown, the algorithm of the present application is simpler, faster and more efficient than similar swarm intelligence and evolutionary computing methods. It far exceeds similar algorithms while ensuring the results. The time efficiency is not much different from other faster sorting algorithms or new heuristic algorithms, but at the same time it ensures the combination relationship between features and fully explores and retains the connection between features.

[0106] Accuracy ACC is the ratio of correctly predicted samples to the total number of samples, providing a quick overview of the overall performance of the model. When the data set is relatively balanced, accuracy is a useful indicator. The F1 value is the harmonic mean of the model's precision and recall, taking into account the model's accuracy and recall. It is particularly suitable for unbalanced data sets. When both precision and recall are important, the F1 value is a very good performance indicator. The AUC value usually refers to the area under the ROC curve (Receiver Operating Characteristic Curve). The ROC curve is a graph that plots the true positive rate (TPR) and false positive rate (FPR) at different thresholds. The AUC value provides a measure of the overall classification ability of the model. The higher the AUC value, the better the classification performance of the model. It is not affected by the distribution of the data set and is suitable for unbalanced data sets. For example Figure 2 , Figure 3 , Figure 5 As shown, the method proposed in this application can maintain the best accuracy, F1 value, and AUC value compared with the comparison algorithm. The constructed model has excellent generalization performance and is not prone to overfitting in the face of noisy data.

[0107] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A progressive spatially constrained feature selection method for ultra-high dimensional data, characterized in that: The following steps are involved: S1. Initialize the data feature set, normalize the data feature set, and stratify the training set and test set; S2, initialize the population and algorithm parameters, and determine whether the iteration conditions are met. If so, directly output the target result. If not, enter S3; S3, establish a spatial constraint framework, and calculate the spatial convergence factor and spatial diffusion factor through the algorithm parameters and the spatial constraint framework; S4, judging whether the spatial convergence factor and spatial diffusion factor obtained in S3 meet the convergence condition, and selecting a calculation strategy, and generating a target feature space solution according to the calculation strategy; S5. Evaluate the quality of the target feature space solution, construct and calculate the fitness function according to the indicators, sort the fitness functions from low to high, and retain the target feature space solution with the first order and its fitness value as the individual target solution. The indicators include feature solution length, solution accuracy, solution AUC value, and solution F1 value. S6, update the iteration condition, and determine whether the updated iteration condition is met. If it is met, directly output the target result. If it is not met, iterate S3 to S5 until the stop condition is met.

2. The method for progressive spatially constrained feature selection for ultra-high-dimensional data according to claim 1, characterized in that: The specific contents of initializing the population and algorithm parameters in S2 are as follows: Individuals are constructed using binary coding. The number of features in the input data set, i.e., the dimension, represents the maximum spatial range that the initial individual can choose as the spatial boundary, and the actual number of features selected is the spatial domain of the current individual. The input parameters include the population size N, the number of iterations T, and the constraint factor CF, which generates a dimensionality control factor in the spatial dimensionality adjustment function; The individuals in the initialized population need to calculate their fitness values ​​one by one to guide them to complete the space jump. The fitness value is obtained by weighted calculation after unified measurement of accuracy, number of features, F1 value, and AUC value.

3. The method for progressive spatially constrained feature selection for ultra-high dimensional data according to claim 2, characterized in that: The spatial constraint function framework in S3 uses the dimension adjustment function to progressively constrain the dimensional space, and the dimensional transformation is reflected in the spatial convergence part and the spatial diffusion part; The spatial constraint function framework is divided into two stages according to the iteration parameters. The overall spatial constraint gradually decreases. The spatial constraint amplitude in the first stage changes from large to small, which is manifested as focusing on dimensionality reduction convergence and ignoring diffusion. The spatial constraint in the second stage changes from small to stable, which is manifested as focusing on diffusion and ignoring dimensionality reduction convergence.

4. The method for progressive spatially constrained feature selection for ultra-high-dimensional data according to claim 2, characterized in that: The expression of the spatial constraint function framework in S3 is: Among them, t is the current iteration, i is the current individual, T length is the length of the iteration cycle, max is the upper bound of the spatial diffusion factor, min is the lower bound of the spatial diffusion factor, and N is the population size. The spatial constraint function framework mainly controls the spatial convergence factor DRF and the spatial diffusion factor CLF through the dimension adjustment function, and indirectly controls the feature solution dimension in the feature selection in the transformation dimension of the control strategy.

5. The method for progressive spatially constrained feature selection for ultra-high dimensional data according to claim 3, characterized in that: The spatial convergence factor expression of the spatial convergence part is as follows: Among them, Tmid is the period division node, DRF_max and DRF_mid, DRF_min are the maximum and middle values ​​and minimum values ​​of two pre-defined spatial convergence factors, and DR is the characteristic convergence number.

6. The method for progressive spatially constrained feature selection for ultra-high dimensional data according to claim 3, characterized in that: The expression of the spatial diffusion factor of the spatial diffusion part includes: CLF=CF-f(t,i,T,para,DRF); Among them, CF is the spatial constraint factor, Nsf_diff is the dimension of the selected feature subset of the difference space obtained after the current agent individual selects a suitable strategy, and CL is the feature diffusion number.

7. The method for progressive spatially constrained feature selection for ultra-high dimensional data according to claim 2, characterized in that: S4 determines whether the spatial convergence factor and spatial diffusion factor obtained in S3 meet the convergence condition, and selects an operation strategy. The specific contents of the target feature space solution generated by the operation strategy are as follows: If the spatial convergence factor and the spatial diffusion factor meet the convergence conditions, the spatial convergence operation is performed, and the individuals carry out the spatial chain convergence strategy according to the spatial convergence factor; If the spatial convergence factor and spatial diffusion factor do not meet the convergence conditions, a spatial diffusion operation is performed and the constraint strategy is executed according to the individual's own state; The constraint strategies include group space constraint strategy, elite space constraint strategy and space domain constraint strategy; Determine the individual's own state. If the individual is the target individual, implement the group space constraint strategy. If the individual is not the target individual, give it a jump probability and generate an individual once. If an individual is a jump-out individual, the elite space constraint strategy is implemented. If an individual is not a jump-out individual, the space domain constraint strategy is implemented.

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