CN104504305B - Supervise Classification of Gene Expression Data method - Google Patents

Abstract

The invention discloses a method for classifying supervised gene expression data, which mainly solves the problems of dimension disaster, loss of information and complex design of classifiers existing in the classification of gene expression data in the prior art. The technical scheme is: 1. Obtain the discriminant feature vector of the training sample by using the category-preserving projection method; 2. Obtain the projection matrix by using the regression optimization method by using the discriminant feature vector of the training sample; 3. Obtain the feature set of the training sample and the test feature set by the projection matrix Sample feature set; 4. From the training sample feature set and the test sample feature set, the nearest neighbor classifier is used to realize the classification and recognition of the test sample. The invention overcomes the problems of matrix singularity and overfitting in the category-preserving projection method, improves the accuracy of gene expression data classification, and can be used for tumor identification and tumor subtype classification in bioinformatics.

Description

Supervised Gene Expression Data Classification Methods

technical field

The invention belongs to the technical field of data processing and relates to a method for classifying supervised gene expression data, which can be used for tumor identification and tumor subtype classification in bioinformatics.

Background technique

With the development of gene chip technology, a large amount of gene expression data has been generated. How to obtain useful information from massive gene expression data has become a hot spot in bioinformatics research. The classification method is one of the important means to realize the biological information mining of gene expression data, but the high-dimensional and small-sample characteristics of gene expression data bring dimension disaster to the classification of gene expression data. To overcome this problem, gene selection or feature extraction is usually performed on gene expression data first, and then traditional classifiers are used for classification and identification. There are many existing gene selection methods, but in the face of different tumor classification tasks, there is no uniform standard for various gene selection algorithms. If the gene selection algorithm is not well designed, useful information genes for classification may be lost, thereby affecting classification performance. Feature extraction methods for gene expression data classification mainly fall into two categories:

(1) Unsupervised feature extraction method. Including principal component analysis PCA, independent component analysis ICA, non-negative matrix factorization method NMF and local projection LPP, etc. These feature extraction methods do not consider the category information of the sample, and often need to use some discriminant feature extraction methods to extract effective classification features, or use more complex classifiers such as support vector machines (SVM) to improve classification performance, thus increasing classification recognition. complexity.

(2) Supervised feature extraction method. The classic supervised feature extraction method is linear discriminant analysis LDA, but in the face of the high-dimensional small sample characteristics of gene expression data, LDA has problems such as matrix singularity, overfitting, and the optimal subspace dimension is limited by the number of sample categories, which limits LDA. Applications. Category-preserving projection CPP is a supervised feature extraction method proposed in 2012, see Wang Wenjun. A new method for feature extraction of gene expression data based on category-preserving projection. Electronic Journal. 40(2):358-364, 2012. CPP can effectively solve the problem that the optimal subspace dimension is limited by the number of sample categories, but in the face of the high-dimensional and small sample characteristics of gene expression data, CPP still has problems such as matrix singularity and overfitting.

Contents of the invention

The purpose of the present invention is to overcome the matrix singularity and overfitting problems existing in the category-preserving projection method, and propose a new supervised gene expression data classification method to improve the accuracy of gene expression data classification.

To achieve the above object, the technical solution of the present invention comprises the following steps:

(1) Let the training sample gene expression data set X={ _xi |i=1,2,...,m}, where x _i is an n-dimensional column vector, representing the expression of the i-th training sample on n genes Horizontal vector, m is the number of training samples; set the category of the i-th training sample as c _i ;

(2) Obtain the discriminative feature vector y'l of the training sample by using the category-preserving projection method, _l =1,2,...,d, d is the number of discriminative feature vectors, 1≤d<n;

(3) Using the discriminant feature vector _y'l , the regression optimization method is used to obtain the n×d-dimensional projection matrix A;

(4) Project the gene expression level vector x _i of the i-th training sample on the projection matrix A to obtain the feature vector y _i = ^AT xi of the _i -th training sample, where ^AT represents the transformation of the projection matrix A set; training sample feature set Y={y _i |i=1,2,...,m};

(5) Let the test sample gene expression data set U={u _j |j=1,2,...,p}, where u _j is an n-dimensional column vector, representing the expression of the jth test sample on n genes Horizontal vector, p is the number of test samples;

(6) Project the gene expression level vector u _j of the jth test sample on the projection matrix A to obtain the feature vector q _j = A ^T u _j of the jth test sample, where ^AT represents the transformation of the projection matrix A setting; test sample feature set Q＝{q _j |j＝1,2,...,p};

(7) Use the nearest neighbor classifier to classify the test samples, calculate the Euclidean distance from the jth test sample feature vector _qj to each training sample feature vector y _i , and take the category of the training sample with the closest Euclidean distance as the jth category of test samples.

Compared with the prior art, the present invention has the following advantages:

1) The present invention overcomes the problems of matrix singularity and over-fitting in the category-preserving projection method due to converting the category-preserving projection method into a regression framework;

2) The present invention extracts classification features of samples in combination with sample category information, which reduces the burden of classifier design and improves the accuracy of gene expression data classification.

Description of drawings

Fig. 1 is the realization flowchart of the present invention;

Fig. 2 is a graph of the classification correct recognition rate of the first group of gene expression data used in the simulation of the present invention;

Fig. 3 is a curve diagram of the classification correct recognition rate of the second group of gene expression data used in the simulation of the present invention.

Detailed ways

With reference to Fig. 1, the concrete realization steps of the present invention are as follows:

Step 1, given the gene expression data of the training sample and the category information of the training sample.

Given the expression data of m training samples on n genes, it is represented by an n×m-dimensional matrix X, the rows of matrix X represent genes, and the columns represent training samples: the element x _ki of matrix X represents the i-th training sample The expression level on the k-th gene, the i-th column x _i of matrix X represents the expression level vector of the i-th training sample on n genes, i=1,2,...,m, k=1,2, ...,n;

Given the category information C={c _i |i=1,2,...,m} of m training samples, where c _i represents the category of the i-th training sample.

Step 2, according to the category information C of the training sample and the gene expression data X of the training sample, the discriminant feature vector y' _l of the training sample is obtained by using the category-preserving projection method.

(2.1) Define the element values of the m×m-dimensional homogeneous relationship matrix W ¹ respectively and the element values of m×m-dimensional heterogeneous relationship matrix W ² as follows:

Among them, c _t represents the category of the tth training sample;

(2.2) Calculate the diagonal element values of the same kind of diagonal matrix D ¹ of m×m dimension and the values of the diagonal elements of the heterogeneous diagonal matrix ^D2 of m×m dimension

The off-diagonal element values of the homogeneous diagonal matrix D ¹ and the heterogeneous diagonal matrix D ² are all 0;

(2.3) Calculate m×m dimensional intra-class scatter matrix L ¹ and m×m dimensional inter-class scatter matrix L ² :

L ¹ =D ¹ -W ¹ ,

L ² =D ² -W ² ;

(2.4) Define the generalized characteristic equation L ¹ y'=λL ² y', where λ is an eigenvalue, and y' is an m-dimensional eigenvector;

(2.5) Solve the eigenvectors corresponding to the first d minimum eigenvalues of the above-mentioned generalized eigenvalues as the d discriminative feature vectors y' _l of the training samples, l=1,2,...,d, d is the number of discriminative feature vectors , 1≤d<n.

Step 3, using the discriminative feature vector _y'l of the training sample and the gene expression data X of the training sample, the regression optimization method is used to obtain the n×d-dimensional projection matrix A.

(3.1) Let a _l be the n-dimensional optimal projection vector, define the following regression optimization formula:

Among them, α and β are two regression coefficients with different values, and satisfy 0<α<1, 0<β<1, α≠β;

(3.2) Solve the above regression optimization formula to obtain d n-dimensional projection vectors a _l , l=1, 2,...,d, and form an n×d-dimensional projection matrix A=[a ₁ ,a ₂ ,...,a _l ,..., a _d ].

Step 4: Calculate the training sample feature set Y according to the training sample gene expression data X and the projection matrix A.

Project the gene expression level vector x _i of the i-th training sample onto the projection matrix A, and obtain the d-dimensional feature vector y _i = ^AT x _i of the i-th training sample and the training sample feature set Y=A ^T X=[ y _i |i=1,2,...,m], where ^AT represents the transpose of the projection matrix A.

Step 5, given the test sample gene expression dataset.

Given the expression data of p test samples on n genes, it is represented by an n×p-dimensional matrix U, the rows of matrix U represent genes, and the columns represent test samples: the element u _kj of matrix U represents the jth test sample The expression level on the kth gene, the jth column u _j of the matrix U represents the expression level vector of the jth test sample on the nth gene, j=1,2,...,p.

Step 6: Calculate the test sample feature set Q according to the test sample gene expression data U and the projection matrix A.

Project the gene expression level vector u _j of the jth test sample on the projection matrix A to obtain the d-dimensional feature vector q _j = A ^T u _j and the test sample feature set Q = A ^T U = [ q _j |j=1,2,...,p].

Step 7, according to the training sample feature set Y and the test sample feature set Q, use the nearest neighbor classifier to classify the test samples.

(7.1) Calculate the Euclidean distance L(q _j ,y _i ) from the feature vector of the test sample j to the feature vector of each training sample i, i=1,2,...,m, j=1,2,..., p;

(7.2) Take the category of the training sample with the closest Euclidean distance L(q _j ,y _i ) as the category of the test sample j.

The present invention will describe the solutions and effects of the present invention in more detail through the following experimental examples. These experimental examples are for illustrative purposes and are not intended to limit the scope of the invention.

Example 1: A classification experiment was performed on the first set of gene expression data.

This set of data is the gene expression data provided by the NCI of the American Cancer Institute. The dimension of the gene space is 2308, the number of samples is 64, and the sample category is 4. The details of the data are listed in Table 1.

Table 1 The first set of experimental data

dataset name number of genes Number of samples Number of sample categories The first set of gene expression data 2308 64 4

The steps to classify the data in Table 1 are as follows:

In the first step, the 64 samples are divided into training samples and test samples using the 5-fold cross-validation method, that is, the samples are divided into 5 parts, and one of them is used as a test sample in turn, and the rest are used as training samples; the test samples have p , then the number of training samples is m=64-p, the gene expression data matrix X of the training samples is 2308×m dimensional, and the gene expression data matrix U of the test sample is 2308×p dimensional.

In the second step, from the category information of m training samples and the 2308×m-dimensional gene expression data matrix X, the category-preserving projection method is used to obtain d discriminative feature vectors y' _l of training samples, l=1,2,..., d, the maximum feature dimension d is 49, that is, d=1,2,...,49.

The third step is to use the d discriminant feature vectors of the training samples and the gene expression data matrix X of the training samples, and use the regression optimization method to obtain a 2308×d-dimensional projection matrix A.

In the fourth step, according to the training sample gene expression data matrix X and the projection matrix A, a d×m-dimensional training sample feature set Y= ^AT X is obtained.

In the fifth step, according to the test sample gene expression data matrix U and the projection matrix A, a d×p-dimensional test sample feature set Q= ^AT U is obtained.

In the sixth step, according to the training sample feature set Y and the test sample feature set Q, calculate the Euclidean distance from its d-dimensional feature vector to all training samples’ d-dimensional feature vectors for each test sample, and the training sample with the closest Euclidean distance category as the category of this test sample.

For example, when d=3, the experimental results show that among the 64 samples, the classification results of 63 samples are consistent with their true categories, and the classification results of only 1 sample are inconsistent with the real category.

The seventh step is to compare the classification results of all samples on the d-dimensional feature with the true category of the sample, and count the number of correctly classified samples. d=1,2,...,49. For example, when d=3, out of 64 samples, 63 samples are correctly classified, and the classification correct recognition rate of samples reaches 98.44%.

The result of using the inventive method to classify the data in Table 1 is recorded as classification result 1; after adopting the CPP method to carry out feature extraction to the data in Table 1, then use the nearest neighbor classifier to realize sample classification, and obtain classification result 2, It is represented by "CPP+nearest neighbor"; compare the correct recognition rate of the sample classification of classification result 1 and classification result 2, and the comparison curve of the correct recognition rate of sample classification is shown in Figure 2, where the abscissa represents the feature dimension of the sample, and the ordinate represents The correct recognition rate of sample classification.

Example 2: A classification experiment was performed on the second set of gene expression data.

This set of data is the expression of 16063 gene fragments in tissue samples of 190 cases of different cancer types, including 14 cancer types. The details of the data are listed in Table 2.

Table 2 The second set of experimental data

dataset name number of genes Number of samples Number of sample categories Second set of gene expression data 16063 190 14

The steps to classify the data in Table 2 are the same as those in Example 1. The maximum feature dimension is 150.

The result of adopting the inventive method to classify the data in Table 2 is recorded as classification result 3; after adopting the CPP method to carry out feature extraction to the data in Table 2, realize sample classification with nearest neighbor classifier again, obtain classification result 4, It is represented by "CPP+Nearest Neighbor"; compare the correct recognition rate of the sample classification of the classification result 3 and the classification result 4, and the comparison curve of the correct recognition rate of the sample classification is shown in Figure 3, where the abscissa represents the feature dimension of the sample, and the ordinate represents The correct recognition rate of sample classification.

The following conclusions can be drawn from Figures 2 and 3:

a) The correct recognition rate of the classification of the present invention is obviously better than the correct recognition rate of the nearest neighbor classifier after the CPP feature extraction, and the correct recognition rate of the present invention is relatively stable, and it is a monotonous non-decreasing trend with the increase of the feature dimension, However, after the nearest neighbor classifier after CPP feature extraction reaches the highest recognition rate, the correct recognition rate drops significantly as the feature dimension increases.

b) For the first group of gene expression data, when the feature dimension is 3, the correct recognition rate of the present invention reaches the maximum value, reaching 98.44%, and the highest correct recognition rate from the nearest neighbor classification after CPP feature extraction is 96.88%.

c) For the second group of gene expression data, the nearest neighbor classifier after CPP feature extraction reached a maximum correct recognition rate of 62.63% when the feature dimension was 16, while the method of the present invention correctly identified The rate has reached 65.79%, and the highest correct recognition rate can reach 66.32%.

Claims (1)

1. A supervised gene expression data classification method is characterized by comprising the following steps:

(1) Setting the number of gene expressions in a training sampleData set X = { X _i L i =1,2, \8230 |, m }, where x _i Is an n-dimensional column vector which represents the expression level vector of the ith training sample on n genes, and m is the number of the training samples; let the ith training sample class be denoted as c _i ；

(2) Obtaining identification feature vector y 'of training sample by adopting category retention projection method' _l L =1,2, \ 8230, d is the number of identification feature vectors, d is more than or equal to 1<n：

(2.1) defining m x m dimensional homogeneous relation matrix W ¹ Value of (2)And m x m dimensions of heterogeneous relationship matrix W ² Value of (2)The following:

wherein, c _t Representing a category of the t-th training sample;

(2.2) calculating a diagonal matrix D of the same kind in dimensions of m x m ¹ Value of diagonal element ofAnd a heterogeneous diagonal matrix D of m x m dimensions ² Value of diagonal element of

Diagonal matrix of the same kind D ¹ And heterogeneous diagonal matrix D ² All the off-diagonal element values of (a) are 0;

(2.3) calculating an m x m-dimensional intra-class dispersion matrix L ¹ And m x m dimensional inter-class scatter matrix L ² ：

L ¹ ＝D ¹ -W ¹ ，

L ² ＝D ² -W ² ；

(2.4) defining generalized eigenequation L ¹ y'＝λL ² y ', λ are eigenvalues, y' is an m-dimensional eigenvector;

(2.5) solving feature vectors corresponding to the first d minimum feature values of the generalized feature equation to serve as d identification feature vectors y 'of the training sample' _l ，l＝1,2,…,d；

(3) Utilizing discriminative feature vector y' _l Obtaining a projection matrix A with dimensions of n multiplied by d by adopting a regression optimization method:

(3.1) setting a _l For the n-dimensional optimal projection vector, the following regression optimization equation is defined:

wherein alpha and beta are two regression coefficients with different values, and satisfy 0< alpha <1,0< beta <1, alpha ≠ beta;

(3.2) solving the regression optimization formula to obtain d n-dimensional projection vectors a _l L =1,2, \8230;, d, a projection matrix a = [ a ] constituting an n × d dimension ₁ ,a ₂ ,…,a _d ]；

(4) Gene expression level vector x of ith training sample _i Projected on the projection matrix A to obtain the eigenvector y of the ith training sample _i ＝A ^T x _i Wherein A is ^T Represents the transpose of the projection matrix a; training sample feature set Y = { Y = _i |i＝1,2,…,m}；

(5) Let test sample gene expression data set U = { U = { U _j L j =1,2, \8230;, p }, where u _j Is an n-dimensional column vector which represents the expression level vector of the jth test sample on n genes, and p is the number of the test samples;

(6) The gene expression level vector u of the jth test sample is expressed _j Projecting the test sample on a projection matrix A to obtain a feature vector q of a jth test sample _j ＝A ^T u _j Wherein A is ^T Represents the transpose of the projection matrix a; test sample feature set Q = { Q = { Q = _j |j＝1,2,…,p}；

(7) Classifying the test samples by adopting a nearest neighbor classifier, and calculating a characteristic vector q of the jth test sample _j To each training sample feature vector y _i The class of the training sample with the closest euclidean distance is used as the class of the jth test sample.