Tumor gene selection method and system and computer equipment

Abstract

The invention discloses a tumor gene selection method and system and computer equipment, and relates to the technical field of gene selection, and the method comprises the following steps: filtering genes irrelevant to tumors in a microarray gene expression data set sample by using a ReliefF algorithm to obtain an elite group; selecting feature subsets of a plurality of elite individuals in the elite group, then judging the classification error rate of the feature subsets, and obtaining the relationship between the feature subsets; combining all the feature subsets through the relationship among the feature subsets to obtain a first feature search space; selecting individuals in a Pareto frontier in the elite group by adopting a Pareto frontier strategy, and combining feature subsets of the individuals to obtain a second feature search space; recursion operation is carried out on the steps, and a global optimal solution and a Pareto frontier are obtained through an optimal solution generated by each round of recursion; and selecting the optimal gene subset of the tumor in the microarray gene expression data set through the globally optimal solution and the Pareto frontier. According to the method, multiple solutions are used for feature space merging instead of only considering a single optimal solution, so that not only can the feature space be optimized, but also the performance of the algorithm can be improved, and the selection precision of the tumor gene is improved.

Description

Technical Field

[0001] The present invention relates to the field of gene selection technology, and in particular to a method, system and computer equipment for selecting genes for tumors. Background Art

[0002] The normal process of cell division can cause damage to deoxyribonucleic acid (DNA), that is, changes in gene sequences during DNA replication. Normally, cells repair DNA damage through DNA repair mechanisms. However, abnormal DNA repair mechanisms can cause cells to become cancerous. Microarray technology plays a vital role in cancer identification, however, using microarray expression profile data for cancer identification or detection faces huge challenges. The reason is that microarray expression profile data contains tens of thousands of genes, but only a few samples are available for analysis. Irrelevant genes and redundant genes in microarray expression profile data can seriously affect the predictive performance of the classifier. How to identify the most relevant gene subsets from ultra-high-dimensional microarray expression profile data to improve the accuracy of cancer identification has brought great challenges to the gene selection task.

[0003] Classifying high-dimensional data usually requires reducing the data dimension to improve the performance of the classification model and reduce the consumed computing resources. At present, the mainstream FS algorithms can be roughly divided into filtering, packaging and hybrid methods. The filtering-based method obtains feature subsets according to the internal features of the data. The packaging-based method uses the evaluation of the classifier model to obtain the best feature subset. Therefore, compared with the packaging-based method, the filtering-based method can save time and computing resources, but the corresponding classification accuracy is low. The filtering-packaging-based hybrid method can complete feature selection in a short time and has a high classification accuracy, so it has been widely used. However, for high-dimensional microarray gene expression profile data, due to its huge gene space, finding the optimal solution is a particularly difficult task.

[0004] Multi-objective evolutionary algorithms (MOEAs) can obtain a set of trade-off solutions, which are often used to solve multi-objective optimization problems (MOPs). A richer set of non-dominated solutions can be evolved for different feature selection tasks. Compared with single-objective EA algorithms (i.e., EA algorithms that only consider classification accuracy), MOEAs can balance two objectives during the evolution process and find a solution that satisfies higher classification accuracy and fewer selected features. Although MOEAs have many advantages, they also have some limitations when solving FS problems. For example, Pareto dominance-based algorithms focus on finding solutions located at the center of the Pareto front (PF), which is not conducive to finding feature subsets with high classification performance, because FS is a partial multi-objective optimization problem (the importance of improving the prediction accuracy goal is greater than the importance of reducing the dimensionality goal), and a large number of repeated solutions will accelerate the convergence of EA and cause it to fall into the local optimum. In addition, whether the initialization population contains key features will also affect the performance of EA. Whether the end point of EA iteration is to fall into the local optimum or find the global optimum is still a question.

[0005] Therefore, the search path of the above recursive algorithm is likely to enter the local optimal space during gene selection. Then, the algorithm deviates from the exploration direction of the optimal solution. As the recursion continues, the search feature space will be further reduced. Subsequently, a large number of repeated individual iterations will cause the algorithm to converge prematurely, and ultimately the population will find it difficult to produce a better solution, resulting in greater difficulty in solving the gene selection task. Summary of the invention

[0006] The purpose of the present invention is to provide a tumor identification method for gene selection in view of the above-mentioned deficiencies of the prior art, so as to solve the problem that a large number of repeated individual iterations in the prior art methods lead to premature convergence of the algorithm, and ultimately it is difficult for the population to produce a better solution, resulting in great difficulty in solving the gene selection task.

[0007] The present invention provides the following technical solution: a gene-selected tumor identification method, comprising the following steps:

[0008] Obtain a sample of the tumor's microarray gene expression dataset;

[0009] Using the optimal elite strategy to select feature subsets of multiple elite individuals in a microarray gene expression data set sample, and obtaining the classification error rate of the feature subset, obtaining the inclusion relationship between the feature subsets through the classification error rate between each of the feature subsets, retaining the feature subsets that meet the conditions by using the inclusion relationship between the feature subsets, and spatially merging the feature subsets that meet the conditions, and using the merged feature space as the first feature search space;

[0010] The Pareto front strategy is adopted to select individuals that generate the Pareto front and the characteristic subsets of the individuals in the microarray gene expression dataset samples, and the characteristic subsets of the individuals are combined to generate a second characteristic search space;

[0011] Recursive operations are performed on the steps of generating the first characteristic search space and the second characteristic search space, and the global optimal solution and the Pareto front are obtained through the optimal solutions and optimal individuals generated in each round of recursion; wherein the global optimal solution and the Pareto front are the best gene subsets in the microarray gene expression dataset samples.

[0012] Preferably, the optimal elite strategy is used to select the characteristic subsets of multiple elite individuals in the microarray gene expression dataset samples, and the classification error rates of the characteristic subsets are obtained. The inclusion relationships between the characteristic subsets are obtained by the magnitudes of the classification error rates between the respective characteristic subsets, including the following steps:

[0013] The optimal elite strategy is used to select the microarray gene expression dataset samples to obtain elite individuals and the characteristic subsets corresponding to the elite individuals;

[0014] The magnitudes of the classification error rates of two characteristic subsets sub1 and sub2 in the characteristic subset are judged. If f1(sub1) < f1(sub2), then four relationships between the two characteristic subsets sub1 and sub2 are obtained;

[0015] Wherein, the f1(·) is the classification error rate, and the four relationships include the non - intersecting relationship Non - Intersect, the intersecting relationship Intersect, the first inclusion relationship Include - I or the second inclusion relationship Include - II.

[0016] Preferably, the four relationships include the non - intersecting relationship Non - Intersect, the intersecting relationship Intersect, the first inclusion relationship Include - I or the second inclusion relationship Include - II, specifically:

[0017] In the non - intersecting relationship Non - Intersect, sub1 and sub2 satisfy the following conditions:

[0018] sub1 ∩ sub2 = φ

[0019] Wherein, the characteristic subset selected by the elite individual Ind1 is completely different from the characteristic subset selected by the elite individual Ind2. In the next round of recursive search, the characteristic subsets selected by the two elite individuals are combined;

[0020] In the intersecting relationship Intersect, sub1 and sub2 satisfy the following conditions:

[0021]

[0022] Among them, the global optimal solution is found by combining the feature subsets selected by the elite individual Ind1 and the elite individual Ind2;

[0023] In the first inclusion relationship Include-I, sub1 and sub2 satisfy the following conditions:

[0024]

[0025] Among them, the feature subset selected by the elite individual Ind1 includes the feature subset selected by the elite individual Ind2. Since the classification performance of the elite individual Ind1 is better than that of the elite individual Ind2, in this case, the selected feature subset of the elite individual Ind1 is the new feature space;

[0026] In the second inclusion relationship Include-II, sub1 and sub2 meet the following conditions:

[0027]

[0028] Among them, the feature subset selected by the elite individual Ind1 is included in the feature subset selected by the elite individual Ind2. The classification performance of sub1 is better than that of sub2. The feature subset of the elite individual Ind1 is selected as the new feature space.

[0029] Preferably, spatially merging the feature subsets that meet the conditions and using the merged feature space as the first feature search space comprises the following steps:

[0030] According to the search space calculation method, the elite individual CA generated in each round of recursion is retained through the inclusion relationship between feature subsets, and the feature space of the retained feature subsets is merged, and the merged feature space is used as the search space for the next round of recursion;

[0031] nData=sub i ∪sub j i,j∈{1,…,N}

[0032] Among them, nData is the input data set of the new round of recursion, and N is the number of individuals contained in the CA array.

[0033] Preferably, the method of adopting the Pareto front strategy to select individuals and feature subsets of individuals that generate the Pareto front in the microarray gene expression data set sample, and combining the feature subsets of the individuals to generate the second feature search space comprises the following steps:

[0034] According to the Pareto dominance concept, the properties of the two Pareto frontier strategies in the elite group are obtained, specifically:

[0035] Attribute 1: For an individual yy ∈ P - PF, such that x.F1 < y.F1 and x.F2 < y.F2;

[0036] Attribute 2: For an individual x ∈ PF, such that y.F1 < x.F1 and y.F2 ≤ x.F2;

[0037] Through Attribute 1, for any individual in the non - dominated set, find an individual from the Pareto front PF, and the two objectives obtained are better than any individual in the non - dominated set;

[0038] In the case of Attribute 2, for the individuals in the Pareto front PF, there are no two objectives in the population P that are better than the individuals in the Pareto front PF;

[0039] Combine the characteristic subsets of the individuals in the Pareto front to generate a second characteristic search space;

[0040] Among them, the two objectives include minimizing the classification error rate and minimizing the feature selection number ratio.

[0041] Preferably, perform a recursive operation on the steps of generating the first characteristic search space and the second characteristic search space, and obtain the global optimal solution and the Pareto front through the optimal solutions and optimal individuals generated in each round of recursion, including the following steps:

[0042] In multiple rounds of recursive operations, use the non - dominated sorting method to obtain the next - generation population, obtain the optimal individuals, and update the global optimal solution based on the optimal solutions of the next - generation population generated in each round of recursive operations;

[0043] In f1(S L ) < f1(S G ) or (f1(S L ) = f1(S G ) and f2(S L ) < f2(S G )) cases, output the global optimal solution and the Pareto front PF.

[0044] Preferably, after obtaining the microarray gene expression dataset sample of the tumor, use the ReliefF algorithm to filter out the genes irrelevant to the tumor in the microarray gene expression dataset sample, including the following steps:

[0045] Set a feature selection threshold, and determine the number of selected features in the microarray gene expression dataset sample through the feature selection threshold;

[0046] Use the ReliefF algorithm to calculate the weight of each selected feature, and sort the selected features in descending order according to the weight;

[0047] The selected features after descending order were used to obtain an elite group in which genes irrelevant to tumors were removed.

[0048] Preferably, the weight of each selected feature is calculated using the ReliefF algorithm, and the specific expression is:

[0049]

[0050] Among them, W r is a weight vector used to store the ReliefF values ​​of all features, h represents the number of nearest neighbor samples, W[F a ] is feature F a The weight of s(R) is the class label of sample R, p(C) represents the prior probability of category C, and f(F a ,R i ,R j ) represents sample R i and R j In feature F a The difference on .

[0051] An acquisition module, used to obtain microarray gene expression dataset samples of tumors;

[0052] A first merging module is used to select feature subsets of multiple elite individuals in a microarray gene expression data set sample using an optimal elite strategy, and obtain a classification error rate of the feature subsets, obtain an inclusion relationship between the feature subsets through the classification error rates between the feature subsets, retain the feature subsets that meet the conditions by using the inclusion relationship between the feature subsets, and spatially merge the feature subsets that meet the conditions, and use the merged feature space as the first feature search space;

[0053] The second merging module is used to select individuals and feature subsets of individuals that generate Pareto fronts in the microarray gene expression data set samples by adopting the Pareto front strategy, and to combine the feature subsets of the individuals to generate a second feature search space;

[0054] A recursive module is used to recursively operate the steps of generating the first feature search space and the second feature search space, and obtain a global optimal solution and a Pareto front through the optimal solution and the optimal individual generated in each round of recursion; wherein the global optimal solution and the Pareto front are the best gene subsets in the microarray gene expression data set samples.

[0055] The present invention provides a computer device, including a memory and a processor, wherein a program is stored in the memory, and when the program is executed by the processor, the processor executes the steps of the gene selection method for a tumor.

[0056] Compared with the prior art, the present invention has the following significant advantages:

[0057] The present invention uses a recursive strategy to effectively reduce the search space of the optimal solution and improve the ability to search for the global optimal solution. In the proposed recursive strategy with the optimal elite and the Pareto front, the feature subsets that meet the conditions are obtained through various types of inclusion relationships between feature subsets, and the first feature search space in the recursion is obtained by merging these feature subsets. At the same time, the feature subsets of individuals on the Pareto front are selected through the Pareto front strategy and combined to obtain the second feature search space, and individuals that do not meet the conditions are eliminated. Multiple optimal solutions are used to merge the feature spaces instead of considering only a single optimal solution. The proposed feature space combination strategy not only reduces the recursive search space, but also improves the ability of the algorithm to find the global optimal feature subset, and can also improve the performance of the algorithm, and improves the selection accuracy of the gene subset. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is the JADE flow chart of the present invention;

[0059] Figure 2 It is a schematic diagram of the feature space change of the recursive EA of the present invention;

[0060] Figure 3 The four distribution types of the global optimal solution of the present invention relative to the solutions searched by the group individuals; (a) is type I, (b) is type II, (c) is type III, and (d) is type IV;

[0061] Figure 4 It is a recursive schematic diagram of RMODE-E / RMODE-P of the present invention;

[0062] Figure 5 Four relationship diagrams between two subsets selected for two elite individuals of the present invention; (a) is type I, (b) is type II, (c) is type III, and (d) is type IV;

[0063] Figure 6 It is the PF graph obtained by RMODE-P of the present invention in one round of recursive execution; wherein F1 represents the classification error rate, and F2 represents the ratio of the number of selected features;

[0064] Figure 7 It is the RMODE-E / RMODE-P flow chart of the present invention;

[0065] Figure 8 It is the PF distribution diagram generated by the round recursion of the present invention; F1 represents the classification error rate, and F2 represents the ratio of the number of selected features; wherein (a)-(d) are the PF distribution diagrams under different conditions respectively;

[0066] Fig. 9It is a Pareto front subset graph obtained by RMODE-E-1, RMODE-E-5, RMODE-E-10 and RMODE-P of the present invention; wherein, (a)-(h) are Pareto front subset graphs of different data sets obtained under the conditions of RMODE-E-1, RMODE-E-5, RMODE-E-10 and RMODE-P respectively;

[0067] Fig.10 The Pareto front graph obtained by applying SparseEA, CMODE, MOFS-BDE, MOBGA-AOS, GR-MOEA, NSGA-II and RMODE in the present invention; wherein (a)-(h) are Pareto front graphs of different data sets obtained under parseEA, CMODE, MOFS-BDE, MOBGA-AOS, GR-MOEA, NSGA-II and RMODE conditions, respectively;

[0068] Fig.11 is a convergence diagram of the classification performance of the present invention; F1 represents the classification error rate; wherein (a)-(f) are respectively the convergence diagrams of the classification performance under different conditions;

[0069] Fig.12 The diagrams are comparative diagrams of the classification accuracy and running time of RMOD-P at different maxIter of the present invention; wherein (a) is a diagram of the classification accuracy of RMOD-P at different maxIter, and (b) is a diagram of the running time of RMOD-P at different maxIter. DETAILED DESCRIPTION

[0070] The following is a clear and complete description of the technical solutions of the embodiments of the present invention in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0071] In the existing EAs-based recursive FS algorithm, the termination condition of the algorithm is no longer the number of iterations (or the maximum number of evaluations), but whether the optimal solution obtained in this round of recursion is better than the optimal solution found previously. If the recursive termination condition is not met, the optimal feature subset obtained in this round is used as the search space for the next round of recursion and the search continues. Figure 2As shown in the figure, at the end of each round of recursion, an optimal solution (feature subset) (red) will be returned, and the optimal solution (feature subset) will be used as the search space for the next round of recursive search. The remaining features (blue) will be ignored. This means that if the optimal solution does not contain the global optimal solution, the next round of recursive search will not be able to find the global optimal solution (although a better solution than the previous round may be found). Since the global optimal solution may appear in different solution spaces, greedy recursive search often falls into the dilemma of local optimality. That is, the optimal solution determined by the algorithm in a round of recursion may not contain the global optimal solution. The global optimal solution may be contained in the solution space of one (some) suboptimal solution, or it may exist in the combined space of multiple solutions.

[0072] Figure 3 are the four distributions of the global optimal solution relative to the top solutions found. Figure 3 Solution 1～3 represents the first three solutions in the population, each corresponding to a feature subset. The three solutions are ranked according to their fitness (f1(·) classification error), that is, solution1 is the best optimal solution, solution2 is the second best solution, and solution3 is the third best solution. The dark area is the feature that constitutes the global optimal solution. In the existing recursive algorithm, the optimal solution solution1 will be used as the feature search space for the next round of recursion. However, if Figure 3 As shown in the figure, except for type I, solution 1 does not contain (or completely contain) the global optimal solution. If only the optimal solution is used as the search space for the next round of recursion, it is easy to fall into the local optimum.

[0073] In view of the limitations of the above existing algorithms, two new recursive multi-objective differential evolution (RMODE) algorithms (RMODE-E / RMODE-P) with different recursive strategies are proposed to search for the global optimal gene subset from microarray gene expression datasets. In order to avoid missing the global optimal search, RMODE-E / RMODE-P does not use a single optimal solution as the search space for the next round of recursion, but combines multiple excellent solutions into the search space for the next round of recursion. This not only effectively narrows the search space, but also avoids avoiding the global optimal solution as much as possible. In addition, in order to solve the problem that the existing algorithms waste computing resources due to the stagnation of individual evolution in the later iterations when converging, RMODE-E / RMODE-P controls the number of iterations of each round of recursion, which not only saves computing time, but also reinitializes the population in the new round of recursion, which is conducive to exploring more feature combinations and further expanding the search ability of the algorithm.

[0074] The goal of EA-based FS is to find a global (or approximately global) optimal feature subset for classification. This requires ensuring that the search space of the group contains the global optimal feature subset. Although the current recursive EA can reduce the feature space by recursion, the feature space does not necessarily contain the global optimal solution. If the feature space searched by the individual does not contain the global optimal solution, the algorithm will inevitably fall into the local optimum. Therefore, for the EA-based recursive FS algorithm, how to reduce the search space in the recursive process while ensuring that the search space contains the global optimal solution is the most critical issue.

[0075] refer to Figure 7 , an embodiment of the present invention provides a method for selecting genes for a tumor, comprising the following steps:

[0076] Step S1: Obtain a sample of a tumor microarray gene expression dataset.

[0077] Step S2: Use the ReliefF algorithm to filter out genes irrelevant to tumors in the microarray gene expression dataset sample to obtain an elite group.

[0078] This step specifically includes the following steps:

[0079] Step S21: setting a feature selection threshold, and determining the number of selected features in the microarray gene expression data set sample by the feature selection threshold.

[0080] Step S22: Use the ReliefF algorithm to calculate the weight of each feature, and sort the selected features in descending order according to the weight.

[0081] According to ReliefF, the weight of a feature is calculated based on its ability to distinguish samples of the same and different classes. Formula (1) is used to calculate the weight of each feature in distinguishing a sample from its neighboring samples. In short, the higher the weight, the more important the feature. Using ReliefF to calculate the weight of each feature, the specific expression is:

[0082]

[0083] Among them, W r is a weight vector used to store the ReliefF values ​​of all features, h represents the number of nearest neighbor samples, W[F a ] is the feature F a The weight of s(R) is the class label of sample R, p(C) represents the prior probability of category C, and f(F a ,R i ,R j ) represents sample R i and R j In feature F a The difference on .

[0084] The proposed RMODE-E / RMODE-P has two stages: the filtering stage and the packaging stage. The ReliefF algorithm is used to evaluate the importance of each feature in the filtering stage. The features are arranged in descending order according to their importance, and the most important features among the N (percentage) features will be used in the packaging stage. Therefore, the ReliefF algorithm used to filter data requires a threshold to determine the number (or proportion) of selected features. A threshold that is too low will cause important features to be discarded, while a threshold that is too high will include many redundant features and irrelevant features. For high-dimensional microarray expression profile data, the top 3%-5% of genes are usually selected. In the present invention, the top 3% of genes were extracted in all experiments.

[0085] The goal of solving a multi-objective optimization problem is to find a set of trade-off solutions that can satisfy all conflicting objectives. The general description of a multi-objective optimization problem is as follows. The search space of multi-objective optimization problem is expressed in the following form:

[0086] minimize F(x)=(f1(x),f2(x),…,f M (x)) (2)

[0087] Among them, f1(x),f2(x),…,f M (x) is M different minimization objectives, F(x) is the target vector, and x∈X is the decision vector. According to the concept of Pareto dominance, if and This means that solution x1 dominates solution x2 (iex1<x2). In short, if no solution dominates x * Then x * is the Pareto optimal solution. In the present invention, the two goals of FS are to minimize the classification error rate (f1) and the number of selected features (f2). Specifically, the two goals are defined as follows:

[0088] f1(X i )=1-Acc(X i ) (3)

[0089]

[0090] Among them, X i represents the i-th individual in the population; Acc(X i ) represents individual X i The classification accuracy of f1(X i ) represents individual X i The classification error rate, f2(X i ) represents individual X i The ratio of the number of selected features.

[0091] Differential evolution: The differential evolution algorithm (DE) proposed by Storn and Price is one of the most effective evolutionary algorithms. The differential evolution algorithm includes mutation operator, crossover operator and selection operator. The mutation operator generates a mutation vector V according to the vector X of the current population. Eq. (5) is a commonly used mutation strategy.

[0092]

[0093] Among them, F and represent the scaling factor between (0, 1) and one of the top p% individuals selected from the current (generation t) population

[44] . i,t represents the i-th individual in the parent population. rj,t Represents a randomly selected individual, rj∈{1,2,…,N}, rj≠i, j belongs to {1,2}.

[0094] The mutation operator perturbs the vector X i,t , thus affecting the vector X i,t In Eq. (5), the vector X i,t Towards the best vector Move, and there is a perturbation in a random direction, so that the vector X i,t You can explore vectors The archive A in the algorithm JADE stores the area around the top p% of excellent individuals in the parent population. JADE is the baseline algorithm of the proposed RMODE-E / RMODE-P, and its flowchart is as follows: Figure 1 As shown in Eq. (6), the test vector U i,t is based on the mutation vector V i,t With the target vector X i,t The crossover operation is obtained.

[0095]

[0096] Where CR is the crossover rate between [0,1], j rand ∈{1,2,…,D} is a random integer that ensures that at least one value in the generated trial vector comes from the V vector.

[0097] The selection operation selects the better one from the target vector X and the test vector U to survive to the next generation according to the fitness value f1(·) (as shown in Eq. (7)). The description of the selection operator is as follows:

[0098]

[0099] Where f1(U i,t ) indicates U i,tThe classification error rate. The representation of an individual in DE is a vector encoded with real values, and the dimension of each individual is the number of features in the dataset. The threshold θ is used to determine whether to select a feature. If the corresponding value in the vector is greater than θ, the feature is selected; otherwise, it is not selected.

[0100] Step S23: Obtain an elite population that removes genes irrelevant to tumors through the selected features arranged in descending order.

[0101] Step S3: Use the optimal elite strategy to select the feature subsets of multiple elite individuals in the microarray gene expression dataset samples, obtain the classification error rates of the feature subsets, obtain the inclusion relationship between the feature subsets through the magnitudes of the classification error rates among the feature subsets, retain the eligible feature subsets using the inclusion relationship between the feature subsets, and perform a spatial merge on the eligible feature subsets. Take the merged feature space as the first feature search space.

[0102] In the optimal elite recursive strategy, the top E elite individuals are selected according to f1(·) (i.e., the classification error rate), rather than the feature subset of the first elite individual, thereby generating a recursive search space, which avoids the situation where a single optimal subset does not contain the global optimal solution. However, if the feature subsets corresponding to the optimal elite individuals are simply combined for a new round of recursion, it will lead to a large amount of computational redundancy. To further improve the efficiency of the algorithm, a feature space combination method based on the relationship of the feature subsets corresponding to the optimal elite individuals is proposed. Taking the top two elite individuals as an example, this feature space combination strategy is illustrated.

[0103] This step specifically includes the following steps:

[0104] Step S31: Obtain the elite individuals in the elite population and the feature subsets corresponding to the elite individuals. Let Ind1 and Ind2 be two elite individuals in the population, and the selected subsets (feature subsets) corresponding to them are sub1 and sub2 respectively.

[0105] Step S32: Judge the magnitudes of the classification error rates of the two feature subsets sub1 and sub2 in the feature subsets. If f1(sub1) < f1(sub2), then obtain the four relationships between the two feature subsets sub1 and sub2.

[0106] Among them, f1(·) is the classification error rate, and the four relationships include the non-intersecting relationship Non-Intersect, the intersecting relationship Intersect, the first inclusion relationship Include-I, or the second inclusion relationship Include-II, as Figure 5 .

[0107] Case 1: In the non-intersect relationship, sub1 and sub2 satisfy the following conditions:

[0108]

[0109] Among them, the feature subset selected by Ind1 is completely different from the feature subset selected by Ind2. In the next round of recursive search, combining the feature subsets selected by the two elites is very important to prevent the algorithm from falling into the local optimum. Therefore, Ind1 and Ind2 should be merged.

[0110] Case 2: In the intersection relation Intersect, sub1 and sub2 satisfy the following conditions:

[0111]

[0112] Among them, it is of great significance to find the global optimal solution through the combination of the elite selected feature subsets of Ind1 and Ind2. Therefore, sub1 and sub2 should be merged.

[0113] Case 3: In the first inclusion relationship Include-I, sub1 and sub2 meet the following conditions:

[0114]

[0115] Among them, the feature subset selected by Ind1 includes the feature subset selected by Ind2. Since the classification performance of Ind1 is better than that of Ind2, it can be concluded that removing features from Ind1 will reduce the classification performance. In this case, the selected feature subset of Ind1 is the new feature space.

[0116] Case 4: In the second inclusion relationship Include-II, sub1 and sub2 meet the following conditions:

[0117]

[0118] Among them, the feature subset selected by Ind1 is included in the feature subset selected by Ind2, and the classification performance of sub1 is better than that of sub2. Therefore, it can be concluded that removing features from Ind1 will reduce the classification performance. In this case, the feature subset of Ind1 is selected as the new feature space.

[0119] By combining the feature subsets of the first E elite individuals, a new feature search space is generated, and its pseudo code is shown in Algorithm 1. First, the array CA containing E elite individuals is passed into Algorithm 1 and sorted in ascending order according to f1(·) (Eq. (3)) (line 1). Secondly, two individuals are extracted from the CA array in turn (lines 3-4), and the relationship between the selected feature subsets of the individuals is determined. According to the relationship between them (non-intersecting, intersecting, inclusion-I, and inclusion-II), the qualified individuals will be retained in CA for the final feature space combination, as shown in lines 3-9 of Algorithm 1. The algorithm eliminates the unqualified individuals.

[0120] Finally, according to Eq. (12), the feature subsets retained in CA are merged into the feature space (line 10), and the merged feature space is used as the search space for the next round of recursion. This step specifically includes the following steps:

[0121] According to the search space calculation method, the feature subsets retained in the elite individual CA generated in each round of recursion are merged into the feature space, and the merged feature space is used as the search space for the next round of recursion.

[0122] nData=sub i ∪sub j i,j∈{1,…,N} (12)

[0123] Among them, nData is the input data set of the new round of recursion, and N is the number of individuals contained in the CA array.

[0124] Table 1 Feature subset combination algorithm based on elite strategy

[0125]

[0126] Step S4: using the Pareto front strategy to select individuals that generate the Pareto front in the microarray gene expression data set samples, and obtaining feature subsets of the individuals, and combining the feature subsets of the individuals to generate a second feature search space.

[0127] In feature combination, can the excellent feature subset extracted based on classification performance contain most of the key features? This is not always the case. As far as DE is concerned, the essence of individual evolution is its movement in the solution space. Under the influence of Eq. (5), the movement of individuals in the search space will be disturbed by the optimal solution, and individuals will gradually approach and eventually converge. Therefore, the population after convergence often contains many of the same optimal individuals. In this case, if an excellent feature subset is extracted based on classification performance, the same individual is usually selected, which is no different from selecting a single best individual.

[0128] in short, Figure 4The excellent feature subsets in come from the individuals in PF, and the feature subsets corresponding to these individuals are combined to generate the search space for the next round of recursion.

[0129] Figure 6 In it, F1 represents the classification error rate, F2 represents the ratio of the number of selected features, and the figure shows the PF subset obtained by the RMODE-P algorithm in one round of recursion. The individuals closer to the bottom have a lower classification error rate (better classification performance), and the individuals closer to the right have more selected features. Assume that PF is the set of non-dominated individuals in the population P, that is, PF is the Pareto front of P, and P - PF is the set of dominated solutions. According to the concept of Pareto dominance, the properties of two Pareto front strategies are obtained, specifically:

[0130] Property 1: For the individual yy ∈ P - PF, such that x.F1 < y.F1 and x.F2 < y.F2. Property 2: For the individual x ∈ PF, such that y.F1 < x.F1 and y.F2 ≤ x.F2.

[0131] Through Property 1, for any individual in the non-dominated set, find an individual in the Pareto front PF whose two objectives are better than any individual in the non-dominated set. Through Property 2, for the individuals in the Pareto front PF, there are no two objectives in the population P that are better than the individuals in the Pareto front PF.

[0132] The pseudocode is shown in Algorithm 2. The feature subsets of the individuals in the Pareto front are combined to generate the second feature search space. The two objectives among them include minimizing the classification error rate and minimizing the feature selection number ratio.

[0133] Table 2 Feature Subset Combination Algorithm Based on Pareto Front

[0134]

[0135] Step S5: Recursively operate on the steps of generating the first feature search space and the second feature search space, and obtain the global optimal solution and the Pareto front through the optimal solutions and optimal individuals generated in each round of recursion. The global optimal solution and the Pareto front are the best gene subsets in the microarray gene expression dataset samples.

[0136] This step specifically includes the following steps:

[0137] In multiple rounds of recursive operations, use the non-dominated sorting method to obtain the next generation population, generate the best Pareto front PF (obtain the optimal individuals), and update the global optimal solution based on the optimal solutions of the next generation population generated in each round of recursion.

[0138] In f1(S L ) < f1(SG )or(f1(S L )=f1(S G )andf2(S L ) <f2(S G )), the final Pareto front PF and the optimal solution are output.

[0139] Specifically:

[0140] Algorithm 3 describes the framework of RMODE-E / RMODE-P. Since RMODE-E / RMODE-P is a hybrid algorithm, the ReliefF method is needed to filter out irrelevant features in the data. In lines 1-2, ReliefF calculates the weight vector W of the feature and filters the data according to the weight value.

[0141] In the population initialization phase (lines 3-4), the algorithm initializes a population P i , a file A for storing the global optimal individual G , a file A for storing the best individuals generated in each round of recursion L (Line 3), the optimal solution S found in each round of recursion L (Line 4), and update the global optimal solution S at the end of each recursive round G Among them, the optimal solution S G and S L is used as a condition for continuing the recursion. As shown in line 15, the two optimal solutions S are compared respectively. G and S L The classification error rate (Formula (3)) and the selection feature ratio (Formula (4)) of .

[0142] (1)f1(S L ) <f1(S G ) indicates S L The classification performance is better than S G , which means that the solution S found by this round of recursion is L Better than the global optimal solution S G . So, is there a better solution in the current feature space? The answer is uncertain, and there may be many redundant features in the current feature space that interfere with the individual search. Therefore, RMODE-E / RMODE-P will continue to recurse and control the feature space of the group search in the next round of recursion (line 14). In order to retain as many relevant features as possible, RMODE-E / RMODE-P optimizes the feature space by combining the features in the archive A_G.

[0143] (2)f1(S L )=f1(S G ), and f2(SL ) <f2(S G ), which means that the solution S L Not only has S G The classification performance is better than that of the original model, and the number of selected features is smaller. This shows that better solutions can be explored in the current feature space. In the same way, RMODE-E / RMODE-P will continue to recurse until the above two conditions are no longer met.

[0144] In the search phase (lines 8-12), the DE-based evolutionary operator (line 9) and the current optimal solution S L (Line 10) Generate the offspring population. The proposed benchmark algorithm for the RMODE-E / RMODE-P algorithm is JADE. The main reason for choosing JADE as the benchmark function for the RMODE-E / RMODE-P algorithm is JADE's powerful global search capability. Recursive algorithms usually consume a lot of running time due to the out-of-control number of recursions. To ensure that the running time is within a suitable range, the number of iterations of the benchmark algorithm is controlled to balance the performance and running time of the algorithm.

[0145] The set of excellent solutions generated by each round of recursion is stored in A L Middle (row 11), A G According to A L Update (line 13). In addition, different recursive strategies have different update methods. In the optimal elite strategy, A L What is saved is the E best elites (or Pareto frontiers) extracted according to the classification performance ranking in the current round of recursion, A G What is saved are E global optimal individuals. L Merged into A G , A G Select E optimal individuals (or Pareto frontiers) and use them to merge feature spaces. The basic flow chart of RMODE is as follows: Figure 7 shown.

[0146] Since FS is a multi-objective optimization problem, the non-dominated sorting method is used to obtain the next generation population (line 11). Figure 8 As shown in , it is the PF (Pareto front) distribution under 5 rounds of recursion. Figure 8 In the example, the PF generated by the first round of recursion is closest to the upper right corner, and as the recursion continues, the PF gradually moves to the lower left corner. Therefore, each round of recursion will produce a better PF.

[0147] Table 3 Pseudo code of RMODE-E / RMODE-P

[0148]

[0149]

[0150] To evaluate the proposed RMODE-E / RMODE-P, comprehensive experiments were conducted on 11 publicly available microarray gene expression datasets. First, the benchmark datasets and experimental framework are introduced. Then, the experimental results and analysis are presented. All experiments were conducted on a personal computer equipped with an Intel Core i5-7300HQ CPU, 2.50GHz, 16GB memory, and Windows 11 64-bit operating system.

[0151] This experiment used 11 microarray datasets, including Arcane, BreastCancer1, BreastCancer2, CLLSUB, CrohnDisease, GLI, Leukemia, Lung Cancer, Ovarian Cancer, Prostate Cancer, and SMKCAN. Table 1 describes the characteristics of the microarray data used in this experiment. As shown in Table 1, the features of all datasets ranged from 7192 to 24481, and the sample size ranged from 72 to 253, covering both binary and multi-class datasets.

[0152] Table 4 Microarray gene expression dataset

[0153] Dataset Number of samples Number of features Number of categories Arcene 200 10000 2 Breast Cancer1 97 24481 2 Breast Cancer2 104 22283 2 CLLSUB 111 11340 3 CrohnDisease 127 22283 3 GLI 85 22283 2 Leukemia 72 7129 2 LungCancer 181 12533 2 Ovarian 253 15154 2 Prostate 102 12600 2 SMKCAN 187 19993 2

[0154] All experiments are divided into four parts. In the first part, the effectiveness of the two proposed recursive search strategies is analyzed and compared. In the second part, experiments are designed to prove that the recursive framework can significantly improve the performance of the baseline algorithm and verify that the proposed recursive strategy is an effective improvement. In the third part, the proposed algorithm is compared with the state-of-the-art algorithms and the advantages of the proposed algorithm are analyzed. In the fourth part, the parameter effectiveness of RMODE-P is analyzed. The schemes of each part will be introduced in detail below.

[0155] Part I: In this part, four multi-objective recursive EAs are designed for experiments to compare the performance of the proposed recursive search strategy. The four versions of the proposed algorithm will be compared, and the version with the best overall performance (i.e., RMODE-P with the best performance) will be selected for the next experiment.

[0156] RMODE-E-1: The RMODE-E algorithm uses the feature subset selected by the best elite individuals as a new recursive search space. RMODE-E-5: The RMODE-E algorithm combines the feature subsets selected by the top 5 best elite individuals as a new recursive search space. RMODE-E-10: The RMODE-E algorithm combines the feature subsets selected by the top 10 best elites as a new recursive search space. RMODE-P: The RMODE-P algorithm combines the feature spaces of individuals in the PF into a new recursive search space.

[0157] Part II: In this part, four methods are designed for comparison according to the characteristics of the proposed RMODE-P algorithm. These methods are Origin, R-filter, JADE, and REJADE. Brief information of all compared algorithms is given below.

[0158] Origin: The experimental results are based on the original dataset without feature selection. R-filter: ReliefF is used to select the top 3% of features, and all EA experimental results are based on a subset of its selected features. JADE: JADE is an efficient differential evolution algorithm that improves performance by introducing external archived mutation operators and adaptively updating parameters. REJADE: This method adds a recursive framework to JADE, and the search space of the new round of recursion is the feature corresponding to the optimal solution found in the current recursion.

[0159] Section III: In this section, RMODE-P is compared with several state-of-the-art multi-objective methods. These algorithms include NSGA-II, CMODE, SparseEA, MOFS-BDE, GR-MOEA and MOBGA. Brief information of all compared algorithms is as follows.

[0160] NSGA-II: NSGA-II is one of the most classic multi-objective algorithms and is also used in FS due to its efficient performance. Each iteration generates the next population based on the fast non-dominated sorting of the parent and child populations. CMODE CMODE is a multi-objective DE based on Pareto dominance in FS, which is used to ensure the diversity of solutions. CMODE selects elite individuals according to the competition mechanism, and the elite individuals guide the evolution of other individuals through a novel mutation operator. SparseEA: This method has a novel population initialization strategy and genetic operators to solve sparse Pareto optimal solutions, and the algorithm ensures the sparsity of the solution results. MOFS-BDE: It is a new binary multi-objective differential evolution algorithm for FS. It improves the one-bit purification search operator (OPS) and the binary mutation operator based on probability difference, which makes DE have strong exploration and exploitation capabilities. GR-MOEA: This method is a multi-objective FS algorithm based on the NSGA-II paradigm, which inherits the advantages of NSGA-II. The filter population and the wrapper population in GR-MOEA interact with each other according to the guidance and repair strategies during the evolution process. MOBGA-AOS: This method is one of the variants of NSGA-II for FS, which uses penalty and reward matrices to evolve individuals through an adaptive crossover operator in an iterative process.

[0161] Part IV: In this part, the number of iterations (maxIter) of the RMODE algorithm in each round of recursion is analyzed, and the advantages and disadvantages of the parameter values ​​are evaluated by comparing the classification performance and the algorithm consumption time.

[0162] Table 5 lists the parameter values ​​of RMODE-E / RMODE-P and all compared algorithms. Each algorithm is run independently 30 times on each dataset, and then the average results are compared to further reduce the impact of variance. All DE algorithms use a threshold of θ = 0.6 for decoding.

[0163] In the experiment, the non-recursive algorithm and the recursive algorithm differ in the number of group iterations. The main reason is that in the non-recursive algorithm, the total number of iterations TI is a constant, while in the recursive algorithm, it is a variable affected by the number of recursions. In order to conduct a fair experiment, the design of Formula 13 balances the number of group iterations of the two algorithms.

[0164]

[0165] Among them, M represents the number of data sets, TR i represents the total number of recursions of RMODE-P on the i-th dataset, maxIter represents the number of group iterations of RMODE-P in each recursion, and TI i represents the number of group iterations of the non-recursive EA on the i-th data set. Experiments show that when maxIter is set to 50, the number of recursions of RMODE-P is usually less than 4. Therefore, let TI i =max{TI i ,200} to ensure that the non-recursive algorithm has enough iterations.

[0166] Table 5 Parameters of all algorithms

[0167]

[0168] Results and Analysis: The experimental results were analyzed in detail. The experimental results of the algorithms on the microarray expression profile datasets are compared, including average time (seconds), average size (number of selected features), best accuracy, and average accuracy (standard). The values ​​in bold are the best results for each dataset under each indicator. The gap between the algorithms can be seen based on these four evaluation indicators. The Wilcoxon signed rank test with a significance level of 0.05 was also used to statistically analyze the difference in average accuracy between RMODE-P and other comparison algorithms. In Table 5, the symbols "+", "≈", and "-" indicate that the results of RMODE-P are better, similar, and worse than the corresponding comparison algorithms, respectively. For fair comparison, all comparison algorithms use KNN and 10-fold cross validation to evaluate the classification error rate. The K value in KNN is set to 10 to balance accuracy and efficiency.

[0169] Four versions of the proposed algorithm: RMODE-E-1, RMODE-E-5, RMODE-E-10, and RMODE-E-1 are analyzed and compared to evaluate the best recursive search strategy. Table 6 shows the results of the four algorithms on the eight datasets listed in Table 1. For the Leukemia, LungCancer, and Ovarian datasets, since the four algorithms all selected the same feature subsets, the results are not shown in Table 6.

[0170] As shown in Table 6, except for the BreastCancer2 and GLI datasets, RMODE-E-1 has the worst best accuracy and average accuracy on all datasets. In most datasets, RMODE-E-1 selects the least number of features. The reason is that RMODE-E-1 uses the feature subset selected by the best individual as the feature space for the new round of recursion. As the recursion continues, the space available for individual search becomes smaller and smaller.

[0171] In terms of classification performance, RMODE-E-10 is closer to the RMODE-P algorithm because RMODE-E-10 has a higher probability of including the optimal feature subset in the search space and a higher probability of selecting a better feature subset. The classification performance of RMODE-E-5 is close to RMODE-E-10, especially on the BreastCancer1 and SMKCAN datasets, achieving better results.

[0172] exist Fig. 9 In the comparison of Pareto fronts, RMODE-E-5 and RMODE-E-10 have similar fronts, but both are weaker than the RMODE-P algorithm. The RMODE-P algorithm has unparalleled performance advantages in terms of optimal accuracy and average accuracy. The reason is that the individuals in the Pareto front have heterogeneous elite features, and the combination of their search space provides an accurate search direction for recursive search. However, RMODE-E-5 and RMODE-E-10 need to select the top-ranked solutions for feature space combination, and the selected solutions are likely to converge to the same position, which is not conducive to a new round of recursive search. In contrast, RMODE-P, which adopts the Pareto front strategy, outperforms RMODE-E, which adopts the optimal elite strategy, in classification performance.

[0173] Table 6 Comparison of three variants of RMODE-P and RMODE-E

[0174]

[0175] The effectiveness of the recursive framework is demonstrated by comparing five methods on 11 data sets. From the time consumption in Table 7, the Origin method takes the least time because it does not require any data processing, followed by the R-filter method that only uses ReliefF. Other EA-based feature selection methods (JADE, REJADE, and RMODE) require multiple evaluations and evolution operations on the population, which takes more time than the Origin and R-filter methods.

[0176] As shown in Table 7, except for the CLLSUB and GLI datasets, the classification performance of the R-filter method is better than that of the Origin method on all datasets. The reason is that the original dataset contains many irrelevant redundant features, and the presence of these features will seriously affect the classification performance. The Relief-based R filter can remove a large number of irrelevant features. For the CLLSUB and GLI datasets, the classification performance of the R-filter method is not better than that of the Origin method, because the ReliefF method focuses on evaluating the classification performance of a single feature and cannot evaluate the correlation between features. This means that even if the top-ranked individual features are combined, better classification performance may not necessarily be achieved.

[0177] It is obvious from Table 7 that using EA-based feature selection methods often leads to better classification performance. For BreastCancer1, CLLSUB, CrohnDisease, and SMKCAN datasets, the classification performance of the feature subsets selected using the EA-based method is 30% higher than that of the R-screening method on average. As for the remaining datasets, the classification performance of the feature subsets selected based on the EA method is also significantly improved compared with the R-screening method. This illustrates the global search capability of the EA method. However, this method may fall into local optimality. For example, the average and best accuracy of the JADE algorithm are lower than those of the REJADE algorithm and the RMODE-P algorithm. This proves that the recursive framework provides a stronger search capability for the population. Compared with JADE, REJADE achieved better classification performance on all datasets. However, it can be found that the performance improvement of the REJADE algorithm is not significant. The average performance improvement on the Arcane, BreastCancer1, and CLLSUB datasets is about 1%. Compared with the JADE algorithm, the proposed RMODE-P algorithm can improve the performance by 4% to 5%, and the number of selected features is only 10% to 30% of that of the JADE algorithm. In particular, RMODE-P can achieve 100% classification accuracy on eight datasets, demonstrating the effectiveness of the recursive framework of RMODE-P.

[0178] Table 7 evaluates the effectiveness of RMODE-P in 11 datasets

[0179]

[0180]

[0181] RMODE-P is compared with six state-of-the-art multi-objective feature selection methods. Table 8 shows the comparison of the average time (seconds), average size, best accuracy, and average accuracy of the compared methods on 11 datasets. Fig.10 The Pareto fronts of seven multi-objective algorithms on eight datasets are shown. In addition, Fig.11 Iterative convergence plots of the classification performance of all compared algorithms are shown.

[0182] As shown in Table 8, on all datasets, the average accuracy and best accuracy of RMODE-P are better than other multi-objective feature algorithms. Specifically, RMODE-P found feature subsets with 100% classification accuracy on 8 datasets, and the RMODE-P algorithm also found feature subsets with the highest classification performance on the remaining 3 datasets, and outperformed other algorithms in terms of average accuracy. In terms of average size, RMODE-P selected subsets with the least number of features on 7 datasets, and the feature subsets selected by RMODE-P on these datasets have an absolute advantage in classification performance. This is mainly because the proposed recursive framework based on the Pareto frontier strategy can effectively improve the quality of group search.

[0183] For the Arcene dataset, the best accuracy of the other six multi-objective comparison algorithms did not exceed 97.5%, while the best accuracy of RMODE-P reached 99.5%. Fig.11 From Arcene in Figure 1, we can see that the six compared algorithms are stuck in evolutionary stagnation between the 50th and 150th iterations, and it is difficult to jump out of the local optimum. The RMODE-P algorithm reinitializes the population in each round of recursion and searches in the new search space to obtain a better solution. Fig.10 It can also be seen from Arcene in that the Pareto front subset of the RMODE-P algorithm is better than that of other methods, and the distribution of non-dominant solutions in the subset is more uniform. When the number of features is the same, the classification error rate (F1) of the solution obtained by the RMODE-P algorithm is lower. As the number of features increases, the classification error rate of the solution obtained by the RMODE-P algorithm is also lower than that of other algorithms.

[0184] Table 8 also shows that on the CLLSUB dataset, RMODE-P outperforms other algorithms in all comparison indicators and has the smallest standard deviation of average accuracy, which indicates that the performance of RMODE-P is more stable and effective. For the BreastCancer1 and SMKCAN datasets, RMODE-P outperforms other algorithms in classification performance, i.e., the selected feature subset has the least number of features and the highest classification accuracy, while only SparseEA obtains similar indicators in terms of average accuracy.

[0185] Fig.11 It shows that RMODE-P can quickly find better solutions to update the population in each recursion, unlike other algorithms that are prone to long-term evolutionary stagnation. Fig.10 It shows that when the number of selected features is small, the classification performance difference between RMODE-P and SparseEA is small. As the number of features increases, the RMODE-P algorithm will select a feature subset with better classification performance. It is worth noting that the Pareto front solution set generated by the RMODE-P algorithm dominates the Pareto front solution sets generated by all other algorithms. This means that the RMODE-P algorithm is more likely to select a more optimized feature subset. The reason can be seen from Fig.11 It can be seen that there is an overlap between the two recursive search spaces. In simple terms, the feature space of the latter round of recursive search is derived from the in-depth optimization of the feature space of the previous round, so the solution obtained is also an in-depth exploration of the optimal solution of the previous round. In the recursive process, some unimportant features will be excluded and the interference between features will be reduced. In short, the recursive mechanism of RMODE-P gives it a better chance to search for a better solution.

[0186] For the remaining data sets, the RMODE-P algorithm can find the feature subset with the highest accuracy (100%), which can reflect the advantages of the RMODE-P algorithm. Fig.10 In the above analysis, RMODE-P has a better Pareto front and the generated Pareto front solution set is more evenly distributed. Therefore, RMODE-P is superior to other multi-objective algorithms on microarray expression profile data.

[0187] Experimental results show that RMODE-P has great potential in solving multi-objective feature selection problems for high-dimensional datasets, improving classification performance while reducing the number of selected features. The recursive framework based on feature space combination not only maintains the convergence speed of the algorithm in each round of recursion, but also improves the search ability of the group and the performance of the algorithm.

[0188] Table 8. Overall ranking comparison of 4 criteria

[0189]

[0190] The proposed RMODE-P is an EA that combines the feature space to form a recursive framework. The only parameter that needs to be analyzed is the number of iterations of the population in each round of recursion. The number of iterations limits the exploration ability of the algorithm to a certain extent. The parameter (maxIter) will be experimentally analyzed. The parameter value maxIter is selected from the array [10, 30, 50, 70, 90, 100]. Fig.12 The comparison of classification accuracy and time consumption of the RMODE-P algorithm under different maxIter parameters is shown. Fig.12 Only some of the datasets are shown, because on other datasets, most parameters can achieve 100% classification accuracy and the performance gap between parameters is not obvious. Fig.12 In the comparison, the classification performance of the algorithm with maxIter=100 is the best, but it consumes the most running time. In the comparison of classification accuracy, it can be found that the classification accuracy of the RMODE-P algorithm with maxIter=50 is only weaker than that of the RMODE-P algorithm with maxIter=100, and is similar to that of the RMODE-P algorithm with maxIter=90. In the time comparison, the RMODE-P algorithm with maxIter=50 has a greater advantage. Therefore, the algorithm with maxIter=50 is considered in the experiment.

[0191] Different from the existing EA-based recursive FS algorithm, the RMODE-E / RMODE-P recursive feature search space proposed in the present invention is composed of excellent feature subsets. Compared with the existing recursive algorithms, RMODE-E / RMODE-P ensures that each round of recursive search space can remove many irrelevant features as much as possible, and contains the global optimal feature subset by merging those excellent feature subsets. Figure 4 The recursive schematic diagram of the RMODE-E / RMODE-P algorithm is shown. Figure 4ES1, ES2 and ES3 are excellent feature subsets found in the current round of recursion, and these feature subsets are merged into the search space of the next round of recursion. The present invention proposes a recursive multi-objective differential evolution algorithm (RMODE-E) using an elite recursive strategy and a recursive multi-objective differential evolution algorithm (RMODE-P) using a Pareto front recursive strategy to find the best gene subsets from microarray expression data for cancer identification. RMODE-E / RMODE-P is a two-stage gene selection algorithm based on filtering-wrapping. In the first stage, the ReliefF method is used to filter out many irrelevant redundant genes, thereby reducing the interference of redundant and irrelevant genes to the algorithm and reducing the time consumption of the Wrapper search stage. In the second stage, a novel recursive multi-objective DE is used to select the optimal gene subset. The recursive strategy of the RMODE-E / RMODE-P algorithm can effectively narrow the search space of the optimal solution and improve the ability to search for the global optimal solution. In the proposed recursive strategies with optimal elite (RMODE-E) and Pareto front (RMODE-P), multiple solutions are used for feature space merging instead of considering only a single optimal solution, which can not only be used to optimize the feature space but also improve the performance of the algorithm. Extensive experiments were conducted to compare the proposed algorithm with eight state-of-the-art evolutionary algorithms (including six multi-objective algorithms) to verify its effectiveness. The results show that RMODE-P performs far better than other algorithms on microarray expression profile datasets.

[0192] Based on the above methods and discussions, the present invention provides a tumor gene selection system, including: a collection module, a filtering module, a judgment module, a combination module, a selection module, a recursive module and a selection module.

[0193] Among them, the acquisition module is used to obtain microarray gene expression data set samples of tumors; the filtering module is used to use the ReliefF algorithm to filter out genes that are irrelevant to the tumor in the microarray gene expression data set samples to obtain an elite group; the judgment module is used to use the optimal elite strategy to select feature subsets of multiple elite individuals in the elite group, and judge the classification error rate of the feature subsets to obtain various types of relationships between the feature subsets; the combination module is used to spatially merge all feature subsets through various types of relationships between the feature subsets, and use the merged feature space as the first feature search space; the selection module is used to use the Pareto front strategy to select individuals that generate the Pareto front in the elite group, and to obtain the feature subsets of the individuals, and combine the feature subsets to generate the second feature search space; the recursive module is used to recursively operate the steps of generating the first feature search space and the second feature search space, and obtain the global optimal solution and Pareto front through the optimal solution and optimal individual generated by each round of recursion; the selection module is used to select the best gene subset in the microarray gene expression data set samples through the global optimal solution and Pareto front.

[0194] The present invention provides a computer device, including a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor executes the steps of a tumor gene selection method.

[0195] The above content is a further detailed description of the present invention in combination with a specific preferred embodiment. For technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for selecting genes for tumors, characterized in that: It includes the following steps: Obtain a microarray gene expression dataset sample of a tumor; Use the optimal elite strategy to select the feature subsets of multiple elite individuals in the microarray gene expression dataset sample, and obtain the classification error rate of the feature subsets. Obtain the inclusion relationship between the feature subsets through the size of the classification error rate between each of the feature subsets. Use the inclusion relationship between the feature subsets to retain the qualified feature subsets, and spatially merge the qualified feature subsets. Take the merged feature space as the first feature search space; Adopt the Pareto front strategy to select the individuals and the feature subsets of the individuals that generate the Pareto front in the microarray gene expression dataset sample, and combine the feature subsets of the individuals to generate a second feature search space; Perform a recursive operation on the steps of generating the first feature search space and the second feature search space, and obtain the global optimal solution and the Pareto front through the optimal solutions and optimal individuals generated in each round of recursion; wherein the global optimal solution and the Pareto front are the best gene subsets in the microarray gene expression dataset sample.

2. A method for tumor identification by gene selection as claimed in claim 1, characterized in that: The step of using the optimal elite strategy to select the feature subsets of multiple elite individuals in the microarray gene expression dataset sample, and obtaining the classification error rate of the feature subsets, and obtaining the inclusion relationship between the feature subsets through the size of the classification error rate between each of the feature subsets includes the following steps: Use the optimal elite strategy to select the microarray gene expression dataset sample to obtain elite individuals and the feature subsets corresponding to the elite individuals; Judge the size of the classification error rate of two feature subsets sub1 and sub2 in the feature subset. If f1(sub1) < f1(sub2), then obtain the four relationships between the two feature subsets sub1 and sub2; Wherein, the f1(·) is the classification error rate, and the four relationships include the non-intersecting relationship Non-Intersect, the intersecting relationship Intersect, the first inclusion relationship Include-I or the second inclusion relationship Include-II.

3. A method for tumor identification by gene selection as claimed in claim 2, characterized in that: The four relationships include the non-intersecting relationship Non-Intersect, the intersecting relationship Intersect, the first inclusion relationship Include-I or the second inclusion relationship Include-II, specifically: In the non-intersecting relationship Non-Intersect, sub1 and sub2 satisfy the following conditions: Wherein, the feature subset selected by the elite individual Ind1 is completely different from the feature subset selected by the elite individual Ind2. In the next round of recursive search, combine the feature subsets selected by the two elite individuals; In the intersecting relationship Intersect, sub1 and sub2 satisfy the following conditions: Wherein, search for the global optimal solution through the combination of the feature subsets selected by the elite individuals Ind1 and Ind2; In the first inclusion relationship Include-I, sub1 and sub2 satisfy the following conditions: Among them, the feature subset selected by the elite individual Ind1 includes the feature subset selected by the elite individual Ind2. Since the classification performance of the elite individual Ind1 is better than that of the elite individual Ind2, in this case, the selected feature subset of the elite individual Ind1 is the new feature space; In the second inclusion relationship Include-II, sub1 and sub2 meet the following conditions: Among them, the feature subset selected by the elite individual Ind1 is included in the feature subset selected by the elite individual Ind2. The classification performance of sub1 is better than that of sub2. The feature subset of the elite individual Ind1 is selected as the new feature space.

4. A method for tumor identification by gene selection as claimed in claim 3, characterized in that: The feature subsets meeting the conditions are spatially merged, and the merged feature space is used as the first feature search space, including the following steps: According to the search space calculation method, the elite individual CA generated in each round of recursion is retained through the inclusion relationship between feature subsets, and the feature space of the retained feature subsets is merged, and the merged feature space is used as the search space for the next round of recursion; nData=sub i ∪sub j i,j∈{1,…,N} Among them, nData is the input data set of the new round of recursion, and N is the number of individuals contained in the CA array.

5. A method for tumor identification by gene selection as claimed in claim 1, characterized in that: The method of adopting the Pareto front strategy to select individuals and feature subsets of individuals that generate the Pareto front in the microarray gene expression data set sample, and combining the feature subsets of the individuals to generate a second feature search space, comprises the following steps: According to the Pareto dominance concept, the properties of the two Pareto frontier strategies in the elite group are obtained, specifically: Attribute 1: For individual yy ∈ P - PF, such that x.F1 < y.F1 and x.F2 < y.F2; Attribute 2: For an individual x ∈ PF, such that y.F1 < x.F1 and y.F2 ≤ x.F2; Through property 1, any individual in the non-dominated set is found from the Pareto frontier PF, and both objectives obtained are better than any individual in the non-dominated set; In property 2, for individuals in the Pareto frontier PF, there is no individual in the population P whose two goals are better than those in the Pareto frontier PF; Combining the feature subsets of individuals in the Pareto front to generate a second feature search space; Among them, the two objectives include minimizing the classification error rate and minimizing the feature selection ratio.

6. A method for tumor identification by gene selection as claimed in claim 5, characterized in that: The steps of generating the first feature search space and the second feature search space are recursively operated, and a global optimal solution and a Pareto front are obtained through the optimal solution and the optimal individual generated in each round of recursion, including the following steps: In multiple rounds of recursive operations, the non-dominated sorting method is used to obtain the next generation population and the optimal individual, and the global optimal solution is updated based on the optimal solution of the next generation population generated in each round of recursive operations; In f1(S L ) <f1(S G )or(f1(S L )=f1(S G )andf2(S L ) <f2(S G )), the global optimal solution and Pareto front PF are output.

7. A method for tumor identification by gene selection as claimed in claim 1, characterized in that: After obtaining the microarray gene expression data set sample of the tumor, using the ReliefF algorithm to filter out genes in the microarray gene expression data set sample that are irrelevant to the tumor includes the following steps: Setting a feature selection threshold, and determining the number of selected features in the microarray gene expression data set sample by the feature selection threshold; The weight of each feature is calculated using the ReliefF algorithm, and the selected features are sorted in descending order according to the weight; The selected features after descending order were used to obtain an elite group in which genes irrelevant to tumors were removed.

8. A method for tumor identification by gene selection as claimed in claim 7, characterized in that: The ReliefF algorithm is used to calculate the weight of each selected feature. The specific expression is: Among them, W r is a weight vector used to store the ReliefF values ​​of all features, h represents the number of nearest neighbor samples, W[F a ] is the feature F a The weight of s(R) is the class label of sample R, p(C) represents the prior probability of category C, and f(F a ,R i ,R j ) represents sample R i and R j In feature F a The difference on .

9. A tumor gene selection system, characterized in that: include: An acquisition module, used to obtain microarray gene expression dataset samples of tumors; A first merging module is used to select feature subsets of multiple elite individuals in a microarray gene expression data set sample using an optimal elite strategy, and obtain a classification error rate of the feature subsets, obtain an inclusion relationship between the feature subsets through the classification error rates between the feature subsets, retain the feature subsets that meet the conditions by using the inclusion relationship between the feature subsets, and spatially merge the feature subsets that meet the conditions, and use the merged feature space as the first feature search space; The second merging module is used to select individuals and feature subsets of individuals that generate Pareto fronts in the microarray gene expression data set samples by adopting the Pareto front strategy, and to combine the feature subsets of the individuals to generate a second feature search space; A recursive module is used to recursively operate the steps of generating the first feature search space and the second feature search space, and obtain a global optimal solution and a Pareto front through the optimal solution and the optimal individual generated in each round of recursion; wherein the global optimal solution and the Pareto front are the best gene subsets in the microarray gene expression data set samples.

10. A computer device, characterized in that: It comprises a memory and a processor, wherein the memory stores a program, and when the program is executed by the processor, the processor executes the steps of a gene selection method for a tumor as described in any one of claims 1 to 8.

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