CN104268564B - It is a kind of based on the sparse Gene Expression Data Analysis method for blocking power - Google Patents

Abstract

The invention discloses a sparse gene expression data analysis method based on truncated power, which specifically includes: preprocessing the gene data set, including regularization processing, using the principal component analysis method to determine the number of principal components and combining local iterative search to determine the principal components. The cardinality of the components; feature extraction is performed on the genetic data in the genetic data set processed in step 1, reducing the interference of the data and improving the accuracy of clustering in the subsequent process; performing clustering processing on the genetic data whose data features are extracted; The clustering processing result obtained in step 3 is compared with the set clustering accuracy rate, and the tuning parameters of sparse dimensionality reduction are adjusted in feedback to achieve the best clustering accuracy. The invention solves the problem of sparse eigenvalue decomposition, and is used for sparse principal component analysis, which not only has strong interpretation ability of principal components, but also has fast operation speed, can well verify the sparse principal component method, and improves the efficiency and accuracy of gene data analysis.

Description

A truncated power-based method for sparse gene expression data analysis

technical field

The invention discloses a sparse gene expression data analysis method based on truncated power, and relates to the technical field of gene expression data analysis.

Background technique

With the rapid development of biomedicine, the wide application of DNA chip (DNA microarray) can quickly measure the expression level of genes. Since the analysis of genetic data can be used to identify cancer cells to predict the probability of a certain disease, it is of great significance to human life. Therefore, gene clustering has become a hot topic in current research.

The original collected genetic data has the characteristics of many attributes and few samples. The results of direct clustering analysis are often disturbed by a large amount of redundant data, and high-dimensional data is also a challenge to traditional clustering methods. In order to overcome these shortcomings, different dimensionality reduction principal feature extraction methods have been proposed one after another. Independent Component Analysis (ICA) can decompose multidimensional data sets into independent components (ICs), eliminating high-order dependencies. The Principal Component Analysis (PCA) method is a classic dimensionality reduction method, which can perform dimensionality reduction processing on high-dimensional data to extract its main feature data. Its goal is to maximize the variance, that is, the relationship between attributes. The largest relative change. However, due to its own linear combination defects, the principal components generated by it are not interpretable, that is, it is not known which specific genes determine a symptom in the genetic data. Therefore, by sparsely processing the loading factor on the basis of the principal component, the expression ability of the principal component and the sparsity of the loading factor (Loadings) can be considered in the process of extracting the principal component, so that the principal component has a small number of attributes. At the same time, the non-zero number of factor coefficients is less than or equal to the number of genes, but the expressive ability is more obvious than that of principal component analysis.

There are different methods for solving sparse PCA such as threshold, regression, energy, and planning. In contrast, the energy method is very good in the interpretability of principal components, the running time of the algorithm, and the accuracy of clustering. Stable, among which the truncated power iteration method is a typical algorithm, which can solve the problem of sparse eigenvalue decomposition very well. It is a good method for sparse principal component analysis, which not only has strong explanatory ability of principal components but also runs fast. feature extraction method.

Combining sparse principal component analysis with clustering algorithm is a more efficient and accurate analysis method for gene expression data. Clustering has become one of the main methods of gene expression data analysis, and the probability of disease occurrence can be quickly and accurately judged by category judgment. However, due to the characteristics of genetic data itself, there are many attributes and few samples, so that there will be a large amount of redundant data and interference information in high-dimensional data, and direct clustering analysis will lead to a low accuracy rate. Principal component analysis is a classic dimensionality reduction method that can map high-dimensional data to low-dimensional space, but its results do not have strong explanatory power.

Contents of the invention

The technical problem to be solved by the present invention is to provide a sparse gene expression data analysis method based on truncated powers for the defects of the prior art. Sparse principal component analysis-truncated power method was used to preprocess the data to extract the main expression data, and to ensure the strong expression ability of gene principal components while minimizing the non-zero number in the load factor. Through a typical gene data set experiment, the gene data after feature extraction are clustered using the K-means method.

The present invention adopts the following technical schemes for solving the problems of the technologies described above:

A truncated power-based sparse gene expression data analysis method, the specific steps include:

Step 1. Preprocessing the genetic data set, including regularization, using principal component analysis to determine the number of principal components and combining local iterative search to determine the cardinality of principal components;

Step 2. Perform truncated power sparse dimensionality reduction and feature extraction on the genetic data determined by the sparse tuning parameters processed in step 1, to reduce the interference of data and improve the accuracy of subsequent process clustering;

Step 3, performing clustering processing on the genetic data whose data features are extracted;

Step 4: Compare the clustering processing result obtained in step 3 with the set clustering accuracy rate, and feedback and adjust the tuning parameters of sparse dimensionality reduction in step 1 to achieve the best clustering accuracy.

As a further preferred solution of the present invention, in step 1, the specific process of the pretreatment is:

Set a gene data set A, the number of samples is n, the number of genes is p, and n<<p is satisfied, the covariance matrix Σ is obtained after regularizing the data set A, and the solution of the principal components The model representation is as follows:

find x'＝arg max x ^T ∑x subject to x ^T x＝1

Among them, x is an independent variable, which corresponds to the coefficient of transforming high-dimensional data into low-dimensional data, which will be updated continuously during the optimization solution process, x'target coefficient, that is, the optimal load corresponding to the principal component after optimization solution, and T represents the conversion set operation.

As a further preferred solution of the present invention, the matrix eigenvalues in the solution model of the principal components are solved by using the power iteration method, and the iterative solution process is:

v ₁ =Sv ₀

v ₂ =Sv ₂ =S ² v ₀

·

·

·

v _t ＝Sv _t-1 ＝…＝S ^k v ₀

Among them, S is the matrix to be solved, v _i is the update vector in each iteration process, and its initial value is i is the number of iterations, and its initial value is 0. When the matrix converges, the value of i is t, and λ is the greatest common divisor of all variables in the v _t vector;

Assuming that v ^* is the eigenvector to be solved, then v ^* can be obtained by transforming v _i and extracting the common parameter λ.

As a further preferred solution of the present invention, in step 1, the sparse dimensionality reduction process needs to satisfy |x|| ₀ ≤ k, where k is the cardinal number of the main component.

As a further preferred solution of the present invention, the truncation method is used to control the sparsity, and combined with the power iteration method, the sparse principal component is solved. The specific process includes:

(501) setting truncation operator:

Among them, F is a set of k subscripts;

(502) Solve the sparse principal component according to the following formula:

λ _max (Σ,k) = max x ^T Σx

subject to||x|| ₂ ＝1,||x|| ₀ ≤k

The solution process specifically includes:

Step1: Initialize x ₀ and number of iterations t=1, set base k _i ;

Step2: Calculate x _t =∑x _t-1 /||∑x _t-1 ||, obtain k subscripts of x _t according to the absolute value and assign them to F _t ;

Step3: Calculate x _t '=Truncate(x _t , F _t ), normalize x _t =x _t '/||x _t '||, t←t+1;

Step4: When the calculation result of Step3 converges, stop the calculation; otherwise, repeat Step2 and Step3.

As a further preferred solution of the present invention, in step 3, K-means clustering algorithm is used for clustering processing.

Compared with the prior art, the present invention adopts the above technical scheme and has the following technical effects: the present invention can well verify the sparse principal component method, and improves the efficiency and accuracy of genetic data analysis.

Description of drawings

Fig. 1 is a schematic diagram of the genetic data processing flow chart of the present invention.

Figure 2 is a graph showing the relationship between the number of principal components and interpretability of genetic data.

Fig. 3 is a graph showing the relationship between the base number and explainability of leukemia data in an embodiment of the present invention.

Fig. 4 is a graph showing the relationship between lymphoma data base and interpretation in an embodiment of the present invention.

Fig. 5 is a three-dimensional visualization of leukemia data in an embodiment of the present invention.

Fig. 6 is a three-dimensional visualization of lymphoma data in an embodiment of the present invention.

detailed description

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

The schematic diagram of the processing flow of the present invention is shown in Figure 1. The whole process includes data preprocessing, feature extraction and clustering. Since the sparsity of the sparse method needs to be manually specified, there is a feedback loop in the middle to better adjust the accuracy of clustering. The relationship between rate and sparseness, the specific steps are as follows:

Step 1. Preprocessing the genetic data set, including regularization, using principal component analysis to determine the number of principal components and combining local iterative search to determine the cardinality of principal components;

Step 2. Perform truncated power sparse dimensionality reduction and feature extraction on the genetic data determined by the sparse tuning parameters processed in step 1, to reduce the interference of data and improve the accuracy of subsequent process clustering;

Step 3, performing clustering processing on the genetic data whose data features are extracted;

Step 4: Compare the clustering processing result obtained in step 3 with the set clustering accuracy rate, and feedback and adjust the tuning parameters of sparse dimensionality reduction in step 1 to achieve the best clustering accuracy.

The preprocessing process is specifically as follows: given a gene data set A, its number of samples is n, and the number of genes is p, where n<<p, after performing regularization preprocessing on the data set, its correlation is obtained. The variance matrix ∑, the solution model of the principal components can be expressed as follows:

find x'＝arg max x ^T ∑x subject to x ^T x＝1

Among them, x is an independent variable, which corresponds to the coefficient of converting high-dimensional data into low-dimensional data, which is continuously updated during the optimization solution process, x'target coefficient, that is, the optimal load corresponding to the principal component after optimization solution, and T represents the special transformation set operation.

There are two ways to solve the principal components: Singular value decomposition A=UDV is performed on the data set A, D is the singular value matrix of the data matrix, and its size determines the extraction order of the principal components, just like the eigenvalues of the matrix, U is the value of the data matrix left singular value vector. V is the right singular value vector of the data matrix, that is, the corresponding coefficient matrix, and the new principal component Z=UD; the other is the eigenvalue decomposition, which obtains the covariance matrix of the attribute variable and performs eigendecomposition on it, according to the eigenvalue The size selects the corresponding eigenvector as the load factor.

Compared with the traditional eigenvalue decomposition method, the power iteration method is another efficient method to solve the eigenvalue of the matrix. When a matrix S is given and iterated repeatedly through v _i+1 =Sv _i , the theory proves that when it converges, v ^* is its eigenvector, v ^* is transformed by extracting public parameter λ from v _i , and v _i is the update vector in each iteration process, the initial value is Its iterative process is as follows:

v ₁ =Sv ₀

v ₂ =Sv ₂ =S ² v ₀

·

·

·

v _t ＝Sv _t-1 ＝…＝S ^k v ₀

Among them, i is the number of iterations, and the initial value is 0. When it converges, the value of i is t, and λ is the greatest common divisor of all variables in the v _t vector.

Due to the defects of the principal components of PCA (Principal components analysis, principal component analysis), the extracted principal components are linear combinations of the original attributes, so the results are not interpretable. Therefore, on the basis of the original formula model, the load factor is sparsely processed, so that |x|| ₀ ≤ k, and k is the base of the main component.

The present invention uses the truncation method to control the sparsity, and combines the power iteration method to efficiently solve the sparse principal component. It is necessary to first define a truncation operator, as follows:

Among them, F is a set of k subscripts, then the formula model of power iteration and truncation to solve sparse principal components is as follows:

λ _max (Σ,k) = max x ^T Σx

subject to||x|| ₂ ＝1,||x|| ₀ ≤k

Among them, x is the factor coefficient corresponding to the corresponding principal component, and its solution process is as follows:

Step1: Initialize x ₀ and number of iterations t=1, set base k _i ;

Step2: Calculate x _t =∑x _t-1 /||∑x _t-1 ||, obtain k subscripts of x _t according to the absolute value and assign them to F _t ;

Step3: Calculate x _t '=Truncate(x _t , F _t ), normalize x _t =x _t '/||x _t '||, t←t+1;

Step4: When the calculation result of Step3 converges, stop the calculation; otherwise, repeat Step2 and Step3.

The feature extraction and clustering specifically include: gene expression data analysis can be used to identify gene categories through clustering. Traditional clustering methods are not very accurate and efficient when dealing with high-dimensional sample sets such as gene data. Although the gene expression data has a high dimensionality, its main data information can be represented by only 1-3 principal components. Therefore, feature extraction of the data can reduce the interference of the data and improve the accuracy of subsequent clustering. When x _i is obtained by the TPower method, the gene feature data z ^* = AX, where X = x ₁ ... x _m , m is the number of extracted principal components. After the data feature is extracted, the present invention adopts classic K-means clustering algorithm, although the deficiency of this method needs to specify the number of clusters, but the purpose of clustering is to verify whether the data extracted by the truncated power method can Better to achieve the clustering effect, therefore, in the follow-up experiments, the classic gene data sets are used, and their categories can be specified in advance.

In a specific embodiment of the present invention, two gene data sets of leukemia (Leukemia) and lymphoma (Lymphoma) are used as examples. In the field of biomedicine, both diseases seriously affect people's lives. Due to the rapid development of medical technology, the collection of genetic data is not difficult, and it has broad significance for the classification and clustering of genetic data, so the number of samples is not unique. In order to verify the efficiency of sparse principal component analysis, the two gene data used in the experiment are typical data sets: leukemia and lymphoma.

Leukemia originates from the abnormal proliferation or damage of hematopoietic stem cells that affects the functions of other tissues and organs. Leukemia is usually divided into acute lymphoblastic leukemia (Acute lymphoblastic Leukemia ALL) and acute myelogenous leukemia (AML). According to the classification of diseased cells, lymphocytes can be divided into T cells and B cells. Therefore, the leukemia data set It can be roughly divided into two categories: ALL and AML. If subdivided, it can be divided into three categories: ALL_T, ALL_B and AML. In the experiment, the leukemia data set contains 38 samples and 5000 genes, including 27 cases of ALL (19 cases of ALL_B, 8 cases of ALL_T), and 11 cases of AML.

Lymphoma, also known as lymphoma, is a malignant tumor of the lymphatic hematopoietic system. Once the disease is diagnosed, lymphoma will be distributed throughout the body. The incidence of non-Hodgkin's lymphoma (NHL) is much higher than that of Hodgkin's lymphoma (HL). . Diffuse Large B-Cell lymphoma (DLBCL) and follicular lymphoma (Follicular Lymphoma FL) are common NHL with a high incidence; Chronic Lymhocytic Lymphoma CLL (Chronic Lymhocytic Lymphoma CLL) comes from Although the malignant tumor of hematopoietic tissue develops slowly, it will be difficult to cure if it is not treated in time. The lymphoma data set used in the experiment has a total of 62 samples and 4026 genes, including 42 cases of DLBCL, 9 cases of FL and 11 cases of CLL.

The experiment of gene expression data starts with principal component analysis, and the number of principal components is roughly determined according to the interpretability of the principal components; then, the regularized data is truncated and sparse by the truncation power method, and the expression ability of the extracted genes is analyzed; Finally, the feature extraction is carried out through the product of the load factor, and the high-dimensional genetic data is transformed into the main feature components of the data, and the clustering algorithm is used for clustering analysis, and the analysis of the clustering accuracy is used to adjust the degree of sparsity. The experiment will be compared with the results of principal component analysis to verify that the sparseness of the principal component coefficients can better analyze gene expression data.

When implementing principal component analysis to determine the number of principal components, the relationship between the number of principal components and the interpretability of genetic data is shown in Figure 2. As the number of principal components increases, the interpretability of the principal components decreases. , when the number of principal components exceeds 25, the value of PEV is almost 0. Therefore, in the follow-up application of sparse principal component analysis to extract feature data, the number of principal components of leukemia data and lymphoma data is set to 10 and 15, and their total interpretability is 81.7% and 66.8%, respectively.

Once the number of extracted principal components is determined, in order to adjust the non-zero number of load factors, the base values in the truncated power method are set in sequence, and the sparsity of the factor coefficients is determined based on the difference of the PEV value. As shown in Figure 3 and Figure 4, the adjustment of the non-zero numbers of the first three principal components of the two genetic data sets is basically on the rise. When a certain base is reached, the value of PEV is basically unchanged, which is the principal component The determination of the number of nonzeros in the coefficients provides a good basis.

After the number of principal components and the cardinality of loads are determined, the K-means method can be used to evaluate the effectiveness of the feature extraction of the sparse principal component analysis according to the clustering accuracy. In order to highlight that the extracted principal components can be used for better clustering, as shown in Figure 5 and Figure 6, in the three-dimensional space of three sparse principal components, the genetic data is drawn according to the true category of the genetic samples The three-dimensional visualization of the data shows that the gene categories can be clearly distinguished after the data is sparsely processed.

The clustering experiment result of above-mentioned embodiment can participate in following table:

Clustering experiment results

The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and can also be made without departing from the gist of the present invention within the scope of knowledge possessed by those of ordinary skill in the art. Variations.

Claims (3)

1. It is 1. a kind of based on the sparse Gene Expression Data Analysis method for blocking power, it is characterised in that specific steps include：

   Step 1: pre-processed to gene data collection, including regularization, determined using PCA principal component number, The radix for determining principal component is searched for reference to local iteration；

   Step 2: the sparse tuning parameter of the determination after step 1 is handled is carried out blocking power sparse dimension reduction to gene data With feature extraction, reduce the interference of data and improve the accuracy of subsequent process cluster；

   Step 3: the gene data being extracted to data characteristics carries out clustering method processing, carried out using K-means clustering algorithms Clustering method processing；

   Step 4: the clustering processing result that step 3 obtains is compared with the cluster accurate rate set, and feedback regulation is dilute The tuning parameter of dimensionality reduction is dredged to reach optimal clustering precision；

   In step 1, the detailed process of the pretreatment is：

   A gene data collection A is set, its number of samples is n, and gene number is p, and meets n ＜ ＜ p, and data set A is carried out Its covariance matrix ∑ is drawn after Regularization, the solving model of principal component is represented as follows：

   Find x'=arg max x^T∑x subject to x^TX=1

   Wherein, x is independent variable, and the coefficient of low-dimensional data is converted to corresponding to high dimensional data, will not during Optimization Solution Disconnected to update, optimal load corresponding to principal component after x' target factors, i.e. Optimization Solution, T represents transposition computing；

   The matrix exgenvalue in the solving model of principal component is solved using power iteration method, its iterative process is：

   V1=Sv₀

   V2=Sv₂=S²v₀

   ·

   ·

   ·

   v_t=Sv_t-1=...=S^kv₀

   Wherein, S is matrix to be solved, v_iFor the renewal vector in each iterative process, its initial value isI is iterations, Its initial value is 0, and when matrix is restrained, i value is t, λ v_tThe greatest common divisor of all variables in vector；

   Set v^*For characteristic vector to be solved, then v^*Via v_iDrawn by extracting common parameter λ-conversion.
2. It is 2. as claimed in claim 1 a kind of based on the sparse Gene Expression Data Analysis method for blocking power, it is characterised in that step In rapid one, the sparse dimension reduction processing needs to meet | | x | |₀≤ k, wherein, k is the radix of principal component.
3. It is 3. as claimed in claim 2 a kind of based on the sparse Gene Expression Data Analysis method for blocking power, it is characterised in that to adopt Degree of rarefication is controlled with intercept method, and combines power iteration method, carries out the solution of sparse principal component, detailed process includes：

   (501) interruption operator is set：

   <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>T</mi> <mi>r</mi> <mi>u</mi> <mi>n</mi> <mi>c</mi> <mi>a</mi> <mi>t</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>F</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>j</mi> </msub> </mtd> <mtd> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <mi>F</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

   Wherein, F is k lower target set；

   (502) sparse principal component is solved according to equation below：

   λ_max(Σ, k)=max x^TΣx

   subject to||x||₂=1, | | x | |₀≤k

   Solution procedure specifically includes：

   Step1:Initialize x₀With iterations t=1, radix k is set_i；

   Step2:Calculate x_t=∑ x_t-1/||∑x_t-1| |, obtain k x by order of magnitude_tSubscript be assigned to F_t；

   Step3:Calculate x_t'=Truncate (x_t,F_t), normalize x_t=x_t'/||x_t' | |, t ← t+1；

   Step4：When Step3 numerical convergences, stop calculating；Otherwise, Step2 and Step3 steps are repeated.