A gene feature selection method based on orthogonal least squares method and meta-analysis

Abstract

The present invention belongs to the field of bioinformatics, and specifically relates to a gene feature selection method based on orthogonal least squares and meta-analysis, comprising the following steps: establishing a rapid feature selection model based on orthogonal least squares, converting the least squares optimization problem into solving an orthogonal squares optimization problem, using the effect size to select the features of each data set as a candidate feature set for a secondary learning machine; establishing a meta-analysis feature optimization model based on simulated annealing, calculating the variance of the effect size to obtain the weight of each data set, and ultimately determining T optimal potential biomarkers to classify cancer. The present invention first uses a primary learning machine to select features for each data set to ensure the interpretability of the model, and then uses a secondary learning machine to screen candidate genes to ensure the accuracy and stability of the model, thereby improving the accuracy of cancer classification and the effectiveness of feature selection.

Description

Technical Field

[0001] The present invention belongs to the field of bioinformatics, and in particular relates to a gene feature selection method based on orthogonal least squares method and meta-analysis. Background Art

[0002] By analyzing genetic data, we can identify potential biomarkers and provide reliable evidence for cancer risk assessment and precision cancer treatment. The greatest challenge in classifying genetic datasets lies in the imbalance between high dimensionality and small sample sizes. Furthermore, high noise, high variance, and uneven distribution make classifiers dataset-dependent, hindering the reproducibility of research. Obtaining more reliable biomarkers and reducing computational complexity are the core issues of genetic feature selection methods.

[0003] Biomarker selection algorithms are primarily divided into three categories based on feature selection techniques: filtering, wrapping, and embedded methods. Filtering methods identify features based on the difference in average expression values ​​between categories and the variance of values ​​within each category, and then train the learning machine. The feature selection process here assumes feature independence and is unrelated to the subsequent learner. In reality, genes function within interconnected network pathways. Wrapping methods continuously select feature subsets from the initial feature set and evaluate the subsets based on the performance of the learning machine until the optimal subset is selected. Since each feature subset evaluation requires training the learning machine, the computational overhead is high. Embedded feature selection methods automatically perform feature selection during the learner training process, using all features for each selection. Computational speed is also significantly affected by the base learning machine. Summary of the Invention

[0004] In order to solve the technical problems that the existing gene feature extraction methods are not repeatable enough and the accuracy and stability of prediction cannot be guaranteed, the present invention provides a gene feature selection method based on orthogonal least squares method and meta-analysis.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A gene feature selection method based on orthogonal least squares method and meta-analysis includes the following steps:

[0007] S1. Obtain D cancer gene expression datasets and standardize the data.

[0008] S2. Establish a fast feature selection model based on orthogonal least squares method, transform the least squares optimization problem into solving the orthogonal squares optimization problem, and use the effect size to select the features of each data set as the feature candidate set of the secondary learning machine;

[0009] S3. Establish a meta-analysis feature optimization model based on simulated annealing, obtain the weight of each data set by calculating the variance of the effect size, and ultimately determine the T optimal potential biomarkers;

[0010] S4. Determine the split point based on the ROC curve and perform binary classification on the cancer gene expression dataset.

[0011] The input of the fast feature selection model based on orthogonal least squares method established in S2 is: ① the feature variable X is an N×M matrix containing N samples and M features; ② the response variable y is an N×1 vector; ③ the number of features to be selected T is 10; the output is: X s The selected features.

[0012] The method of using effect size to select features of each data set in S2 is:

[0013] S2.1. Center the matrix X to X C , center the vector y to y C ;

[0014] S2.2, divide the matrix X into (X s ,X r ), where X s Represents the features that have been selected, X s =(x s1 ,...,x st ), X r Represents the remaining features, X r =(x r1 ,...,x rk ), where t represents the number of selected features and k represents the number of remaining features; the centralized matrix X C Also divided into (X Cs , X Cr ), where X Cs =(x Cs1 ,...,x Cst ),X Cr =(x Cr1 ,...,x Crk );

[0015] S2.3. If no feature is selected (t=0), let Q Cr =X Cr , that is, q Cri =X Cri ,i=1,...,k, where Q Cr It's X Cr is obtained after QR decomposition when the column is full rank, X Cr=Qcr·R, where R is an M×M reversible upper triangular matrix. If t is not zero, then X Cs Orthogonalized to Q Cs , here Q Cs =(q Cs1 ,...,q Cst )and Then X Cr Orthogonalized to Q Cr , Q Cr =(q Cr1 ,...,q Crk ), due to q Cri With Q Cs is orthogonal to Q Cr Orthogonal, q is obtained by Gram-Schmidt orthogonalization Cri The value of

[0016] S2.4. Calculate the square of the sample correlation coefficient r: where h i,i′ represents the effect size;

[0017] S2.5. Find the i that maximizes r, i.e. Then it will From X r Remove and move to X s In the equation, k = k-1, t = t+1 accordingly;

[0018] Repeat S2.1 to S2.5 until t == T.

[0019] In S2.3, q is obtained by Gram-Schmidt orthogonalization. Cri The value method is:

[0020]

[0021] in: is the feature variable X after the feature centering is not selected Cr The transpose of the i-th column vector; q Cri It's X Cr When the column is full rank, the vector of the i-th column of the matrix is ​​obtained after QR decomposition; is the feature variable X after the selected feature centering Cs The transpose of the i'th column vector.

[0022] The effect size h in S2.4 i,i′ The calculation formula is:

[0023]

[0024] Where: y Ci′┬ is the response variable y after centering C The transpose of the i'th column vector; is the feature variable X after the feature centering is not selected Cr When the column is full rank, the transpose of the i-th column vector of the matrix is ​​obtained after QR decomposition; y Ci′ is the response variable y after centering C The vector of the i'th column; q Cri is the feature variable X after the feature centering is not selected Cr When the column is full rank, the vector of the i-th column of the matrix is ​​obtained after QR decomposition.

[0025] The input of the meta-analysis feature optimization model based on simulated annealing in S3 is: ①X sd is the T features obtained by the primary learning machine for the dth data set; ②N e The number of samples in the experimental group, N c The number of control group samples, N e +N c =N; ③The initial solution state S0 is the non-repeated candidate feature set of all data sets, Random order of , that is, S0= <X S >; ④ Initial temperature г=100, number of iterations l, maximum number of iterations l m =500, and the end temperature г m =0.001; Output: T optimal feature rankings of all D data sets.

[0026] The method for classifying cancer in S3 is:

[0027] S3.1. Take the union of T features obtained by the primary learning machine from D data sets as the candidate feature set Here|X S |≥T; according to X S After dimensionality reduction to form a new feature matrix X', the corresponding effect size is calculated;

[0028] S3.2. Randomly select two features a and b from the current state S = <..., a, ..., b, ...>, and swap their positions to generate a new solution S' = <..., b, ..., a, ...>.

[0029] S3.3. Calculate the increment Δг = F(S') - F(S), where F(S) is the objective function, equivalent to energy: where ω d is the weight of the dth dataset, which is calculated by the feature variance of each dataset Var tdThe inverse value of the mean; if Δг<0, accept S' as the new current solution, otherwise accept S' as the new current solution with probability exp(-Δг / г);

[0030] S3.4, cooling complies with г(l+1)=αг(l), where the temperature attenuation coefficient α is between 0.8 and 0.99, that is, for each iteration, there are enough transfer attempts, and the number of generations updated is l=l+1;

[0031] Repeat S3.2 to S3.4 until г==г m Or l==l m .

[0032] The method for calculating the corresponding effect size in S3.1 is:

[0033]

[0034] where i = 1,...,|X S |, forming the effect size set H, including |X S | features, D data sets.

[0035] Var is calculated in S3.3 td The method for the mean reciprocal value of is:

[0036]

[0037] dist(X sd ,S) is used to measure the ranking of the selected features of the dataset X sd The SpearmanFootrule distance from the current state ranking S:

[0038]

[0039] Where loc(·) is the rank of the feature in the dataset. A smaller distance indicates a more similar arrangement, while a larger distance indicates a larger difference in the arrangement.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The gene feature selection method of the present invention is based on orthogonal least squares method and meta-analysis, which meets the three major criteria of prediction, stability and selection. First, a primary learning machine is used to select the features of each data set to ensure the interpretability of the model, and then a secondary learning machine is used to screen the candidate genes to ensure the accuracy and stability of the model, thereby improving the accuracy of cancer classification and the effectiveness of feature selection. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of this application, not all the embodiments. These descriptions are only to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0044] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following embodiments are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0045] A gene feature selection method based on orthogonal least squares method and meta-analysis includes the following steps:

[0046] Step 1: Obtain D cancer gene expression datasets and standardize the data;

[0047] Step 2: Establish a fast feature selection model based on orthogonal least squares method, transform the least squares optimization problem into solving the orthogonal squares optimization problem, and use the effect size to select the features of each data set as the feature candidate set of the secondary learning machine.

[0048] The input is: ① The feature variable X is an N×M matrix containing N samples and M features; ② The response variable y is an N×1 vector; ③ The number of features to be selected T is 10.

[0049] The output is: X s The selected features.

[0050] Step 2.1. Center the matrix X to X C , center the vector y to y C ;

[0051] Step 2.2, divide the matrix X into (X s ,X r ), where X s Represents the features that have been selected, X s =(x s1 ,...,x st ), X r Represents the remaining features, X r =(x r1 ,...,x rk ), where t represents the number of selected features and k represents the number of remaining features; the centralized matrix X CAlso divided into (X Cs , X Cr ), where X Cs =(x Cs1 ,...,x Cst ),X Cr =(x Cr1 ,...,x Crk ).

[0052] Step 2.3: If no feature is selected (t=0), let Q Cr =X Cr , that is, q Cri =X Cri ,i=1,...,k, where Q Cr It's X Cr is obtained after QR decomposition when the column is full rank, X Cr =Qcr·R, where R is an M×M reversible upper triangular matrix. If t is not zero, then X Cs Orthogonalized to Q Cs , here Q Cs =(q Cs1 ,...,q Cst )and Then X Cr Orthogonalized to Q Cr , Q Cr =(q Cr1 ,...,q Crk ), due to q Cri With Q Cs is orthogonal to Q Cr Orthogonal, q is obtained by Gram-Schmidt orthogonalization Cri The value of .

[0053]

[0054] in: is the feature variable X after the feature centering is not selected Cr The transpose of the i-th column vector; q Cri It's X Cr When the column is full rank, the vector of the i-th column of the matrix is ​​obtained after QR decomposition; is the feature variable X after the selected feature centering Cs The transpose of the i'th column vector.

[0055] Step 2.4, calculate the square of the sample correlation coefficient r: where h i,i′ Indicates the effect size.

[0056]

[0057] Where: y Ci′ ┬ is the response variable y after centering C The transpose of the i'th column vector; is the feature variable X after the feature centering is not selected Cr When the column is full rank, the transpose of the i-th column vector of the matrix is ​​obtained after QR decomposition; y Ci′ is the response variable y after centering C The vector of the i'th column; q Cri is the feature variable X after the feature centering is not selected Cr When the column is full rank, the vector of the i-th column of the matrix is ​​obtained after QR decomposition.

[0058] Step 2.5, find the i that makes r maximum, that is Then it will From X r Remove and move to X s In the equation, k=k-1 and t=t+1 accordingly.

[0059] Repeat steps 2.1 to 2.5 until t == T.

[0060] Step 3: Establish a meta-analysis feature optimization model based on simulated annealing, obtain the weight of each data set by calculating the variance of the effect size, and ultimately determine the T optimal potential biomarkers to classify cancer.

[0061] Input: ①X sd is the T features obtained by the primary learning machine for the d-th data set. ②N e The number of samples in the experimental group, N c The number of control group samples, N e +N c = N. ③ The initial solution state S0 is the non-repeated candidate feature set of all data sets, Random order of , that is, S0= <X S >. ④ Initial temperature г=100, number of iterations l, maximum number of iterations l m =500, and the end temperature г m =0.001.

[0062] The output is: the T best feature rankings of all D data sets.

[0063] Step 3.1: Take the union of the T features obtained by the primary learning machine from the D data sets as the candidate feature set Here|X S |≥T. According to X S After dimensionality reduction to form a new feature matrix X', the corresponding effect size is calculated.

[0064]

[0065] where i = 1,...,|X S |, forming the effect size set H, including |X S | features, D data sets.

[0066] Step 3.2: Randomly select two features a and b from the current state S = <..., a, ..., b, ...>, and exchange their positions to generate a new solution S' = <..., b, ..., a, ...>.

[0067] Step 3.3. Calculate the increment Δг = F(S') - F(S), where F(S) is the objective function, equivalent to energy: where ω d is the weight of the dth dataset, which is calculated by the feature variance of each dataset Var td If Δг<0, accept S' as the new current solution, otherwise accept S' as the new current solution with probability exp(-Δг / г).

[0068] Step 3.4: Cooling complies with г(l+1)=αг(l), where the temperature attenuation coefficient α is between 0.8 and 0.99, that is, for each iteration, there are enough transfer attempts, and the number of generations is updated to l=l+1.

[0069]

[0070] dist(X sd ,S) is used to measure the ranking of the selected features of the dataset X sd The SpearmanFootrule distance from the current state ranking S:

[0071]

[0072] Where loc(·) is the rank of the feature in the dataset. A smaller distance indicates a more similar arrangement, while a larger distance indicates a larger difference in the arrangement.

[0073] Repeat steps 3.2 to 3.4 until г == г m Or l==l m .

[0074] Step 4: Determine the split point based on the ROC curve and perform binary classification on the cancer gene expression dataset.

[0075] The present invention selected the gene expression dataset of lung cancer from the public database TCGA, extracted normal samples and cancer samples from it as research objects, and the information is summarized as shown in Table 1:

[0076] Table 1 Comparison of normal samples and cancer samples

[0077]

[0078]

[0079] Table 2 compares the performance of this method with three other popular methods of the same type in terms of AUC values, accuracy, precision, and recall after extracting the 10 best potential biomarkers from a cancer gene dataset. The methods were tested on five classifiers: logistic regression, support vector machine, K-nearest neighbor, naive Bayes, and adaptive boosting (AdaBoost).

[0080] This method is a gene feature selection method based on orthogonal least squares and meta-analysis, mRMR_MA is a gene feature selection method based on mutual information and meta-analysis, based on the orthogonal least squares OLS feature selection method and the difference and quotient scheme mRMR feature selection method, which selects features by maximizing the mutual information between features and categories while minimizing the redundancy between features.

[0081] Table 2 Comparison of the effects of the present invention and other two feature selection methods

[0082]

[0083]

[0084] As can be seen in Table 2, the present invention performs best across most metrics, particularly in terms of AUC, accuracy, precision, and recall. The OLS method's high computational efficiency (running time as short as 2.045 seconds) is a key factor in the present invention's rapid selection of candidate feature sets based on orthogonal least squares, rather than other popular methods such as mutual information. The meta-analysis-based feature optimization model then serves as a secondary learning machine, ensuring model accuracy and stability, significantly improving the accuracy of cancer classification and the effectiveness of feature selection.

[0085] The above only describes in detail the preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the scope of protection of the present invention.

Claims

1. A gene feature selection method based on orthogonal least squares method and meta-analysis, characterized in that: The following steps are involved: S1. Obtain D cancer gene expression datasets and standardize the data. S2. Establish a fast feature selection model based on orthogonal least squares method, transform the least squares optimization problem into solving the orthogonal squares optimization problem, and use the effect size to select the features of each data set as the feature candidate set of the secondary learning machine; The method of using effect size to select features of each data set in S2 is: S2.

1. Center the matrix X to X C , center the vector y to y C ; S2.2, divide the matrix X into (X s ,X r ), where X s Represents the features that have been selected, X s =(x s1 ,...,x st ), X r Represents the remaining features, X r =(x r1 ,..., x rk ), where t represents the number of selected features and k represents the number of remaining features; the centralized matrix X C Also divided into (X Cs , X Cr ), where X Cs = (x Cs1 ,...,x Cst ), X Cr = (x Cr1 ,...,x Crk ); S2.

3. If no feature is selected (t=0), let Q Cr = X Cr , that is, q Cri = X Cri , i = 1,...,k, where Q Cr It's X Cr is obtained after QR decomposition when the column is full rank, X Cr = Qcr·R, where R is a M × M An invertible upper triangular matrix, if t is not zero, X Cs Orthogonalized to Q Cs , here Q Cs =(q Cs1 , ...,q Cst )and =0, i≠i', then X Cr Orthogonalized to Q Cr , Q Cr =(q Cr1 , ...,q Crk ), due to q Cri With Q Cs is orthogonal to Q Cr Orthogonal, q is obtained by Gram-Schmidt orthogonalization Cri The value of S2.

4. Calculate the square of the sample correlation coefficient r: , i=1, ...,k, where represents the effect size; Effect size in S2.4 The calculation formula is: in: is the response variable y after centering C The transpose of the i'th column vector; is the feature variable X after the feature centering is not selected Cr When the column is full rank, the transpose of the i-th column vector of the matrix is ​​obtained after QR decomposition; is the response variable y after centering C The vector of the i'th column; is the feature variable X after the feature centering is not selected Cr When the column is full rank, the vector of the i-th column of the matrix is ​​obtained after QR decomposition; S2.

5. Find the i that maximizes r, i.e. , and then From X r Remove and move to X s In the equation, k=k-1, t=t+1 accordingly; Repeat S2.1 to S2.5 until t == T; S3. Establish a meta-analysis feature optimization model based on simulated annealing, obtain the weight of each data set by calculating the variance of the effect size, and ultimately determine the T optimal potential biomarkers; S4. Determine the split point based on the ROC curve and perform binary classification on the cancer gene expression dataset.

2. The gene feature selection method based on orthogonal least squares method and meta-analysis according to claim 1, characterized in that: The method for determining T optimal potential biomarkers in S3 is: S3.

1. Take the union of T features obtained by the primary learning machine from D data sets as the candidate feature set , here | |≥T; according to After dimensionality reduction to form a new feature matrix X', the corresponding effect size is calculated; S3.

2. Randomly select two features a and b from the current state S = <..., a, ..., b, ...> and swap their positions to generate a new solution S' = <..., b, ..., a, ...>. S3.

3. Calculate the increment Δг = F(S') - F(S), where F(S) is the objective function, equivalent to energy: ,in is the weight of the dth dataset, which is calculated by the feature variance of each dataset Var td The inverse value of the mean; if Δг<0, accept S' as the new current solution, otherwise accept S' as the new current solution with probability exp(-Δг / г); Calculation in S3.3 The method for the mean reciprocal value of is: Used to measure the ranking of selected features of the dataset The Spearman Footrule distance from the current state ranking S: in is the rank of the feature in the dataset. A smaller distance indicates a more similar arrangement, while a larger distance indicates a greater difference in arrangement. S3.4, cooling complies with г( l +1)=αг( l ), where the temperature attenuation coefficient α is between 0.8 and 0.99, which means that for each iteration, there are enough transfer attempts and the number of generations is updated. l = l +1; Repeat S3.2 to S3.4 until г == г m or l==l m .

3. The gene feature selection method based on orthogonal least squares method and meta-analysis according to claim 1, characterized in that: The input of the fast feature selection model based on orthogonal least squares method in S2 is: ① The feature variable X is a N × M Matrix, containing N samples, M Features ②The response variable y is a N ×1 vector; ③The number of features to be selected is T, which is 10; the output is: X s The selected features.

4. The gene feature selection method based on orthogonal least squares method and meta-analysis according to claim 1, characterized in that: In S2.3, q is obtained by Gram-Schmidt orthogonalization. Cri The value method is: in: is the feature variable X after the feature centering is not selected Cr The transpose of the i-th column vector; It's X Cr When the column is full rank, the vector of the i-th column of the matrix is ​​obtained after QR decomposition; is the feature variable X after the selected feature centering Cs The transpose of the i'th column vector.

5. The gene feature selection method based on orthogonal least squares method and meta-analysis according to claim 1, characterized in that: The input of the meta-analysis feature optimization model based on simulated annealing in S3 is: ① is the T features obtained by the primary learning machine for the dth data set; ②N e The number of samples in the experimental group, N c The number of control group samples, N e +N c =N; ③The initial solution state S0 is the non-repeated candidate feature set of all data sets, Random sorting, that is, S0=< > ④ Initial temperature г=100, number of iterations l , maximum number of iterations l m =500, and the termination temperature г m =0.001; the output of the feature optimization model is: the T optimal feature rankings of all D data sets.

6. The gene feature selection method based on orthogonal least squares method and meta-analysis according to claim 2, characterized in that: The method for calculating the corresponding effect size in S3.1 is: where i=1,...,| |, forming the effect size set H, including | | features, D data sets.

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