Gene expression data classification method based on similarity order preservation

Abstract

The present invention discloses a gene expression data classification method based on similarity order preservation. The main steps are: 1. Processing gene expression data using a modal strategy to construct a multi-view gene expression data set; 2. Constructing a cross-view similarity order preservation correlation analysis model; 3. Optimizing and solving the similarity order preservation cross-view correlation analysis model to obtain a projection matrix; 4. Using a parallel feature fusion strategy to perform feature fusion, selecting different amounts of gene expression data for training and testing, and calculating the average recognition rate. Compared with the prior art, the present invention can use the similarity between samples before and after projection to construct a stable sample structure relationship, thereby extracting more discriminative features and improving the accuracy of gene expression data classification.

Description

Technical Field

[0001] The invention belongs to the technical field of gene analysis and pattern recognition, and relates to a gene expression data classification method based on similarity order preservation. Background Art

[0002] DNA microarray technology can rapidly detect gene expression on a large scale to obtain gene expression data. By analyzing gene expression data, we can understand the current physiological state of cells and distinguish cancer cells from normal cells, so as to make an accurate diagnosis. The number of gene expression data samples is usually tens to hundreds, while the number of genes in each sample is tens of thousands. High-dimensional small samples, as a significant feature of gene expression data, pose a challenge to most statistical methods. Direct classification of gene samples will lead to the problem of dimensionality disaster, and it is often necessary to reduce the dimensionality of gene expression data. Feature extraction, as one of the most important dimensionality reduction methods, can obtain features with discriminative capabilities. Therefore, feature extraction of key effective genes has become a key issue in gene classification research.

[0003] Multi-view learning can not only make full use of the complementarity between perspectives, but also effectively eliminate the redundancy between perspectives, thereby extracting more discriminative feature representations. In the joint dimensionality reduction task, multi-view data can play a better recognition performance than single-view data. Various existing multi-view learning methods mainly project multi-view data into subspaces through different optimization criteria, thereby retaining the effective discriminative features of the original data. However, when using subspaces for learning, the similarity between samples before and after the projection is often ignored. Similarity order preservation is an important data property, which can use the similarity between samples to construct a stable sample structure. Therefore, the present invention proposes a similarity order preservation feature extraction method, namely Similarity Order Preserving Across-view Correlation Analysis (SOPACA). SOPACA can use high-dimensional training samples to learn a set of projection directions for each perspective, and obtain more discriminative similarity features by projecting the original high-dimensional gene samples into a similarity order-preserving subspace. Summary of the invention

[0004] Traditional multi-view learning methods based on subspace projection often ignore the similarity between samples before and after projection, which affects the multi-view learning performance. To address this problem, the present invention proposes a gene expression data classification method based on similarity order preservation. The core of the present invention is to construct a similarity order preservation distribution within a discriminatively sensitive perspective and constrain the similarity correlation between discriminatively sensitive perspectives, and to construct a similarity order preservation cross-perspective correlation analysis model, so as to extract features from gene expression data. The specific implementation steps of the present invention are as follows:

[0005] 1. Use the modality strategy to modalize the gene expression data, use wavelet transform to extract low-frequency components as different modal data, and construct a multi-view gene expression dataset: Where m is the number of viewing angles, n is the number of gene samples, d i is the dimension of the i-th group of features, i = 1, 2, …, m;

[0006] 2. Construct a similarity order-preserving cross-view correlation analysis model. The specific construction process is as follows:

[0007] (2a) Construct the similarity order-preserving scatter matrix of the i-th perspective. The specific construction method is as follows:

[0008] Calculate sample similarity matrix

[0009]

[0010] in Representation sample and Belong to the same category, Represents any two samples in the i-th group of gene data sets and The normalized similarity between them is specifically expressed as:

[0011] Construct the similarity order-preserving scatter matrix of the i-th perspective Where D (i) is a diagonal matrix with diagonal elements is the Laplace matrix;

[0012] (2b) Construct the similarity correlation matrix between the i-th and j-th perspectives. The specific construction method is as follows:

[0013] Calculate the weighted matrix of similarity between views

[0014]

[0015]

[0016] Construct the similarity correlation matrix between the i-th and j-th perspectives: Where D (ij) is a diagonal matrix with diagonal elements is the Laplace matrix, Operation Indicates the multiplication of corresponding elements of the matrix;

[0017] (2c) Constructing a cross-view similarity order-preserving correlation analysis model:

[0018] By maximizing the inter-view similarity correlation and minimizing the intra-view similarity order-preserving dispersion, a cross-view similarity order-preserving correlation analysis model is constructed.

[0019]

[0020]

[0021] where α (i) , α (j) Respectively represent the projection directions of the i-th and j-th perspectives;

[0022] 3. Optimize and solve the similarity order-preserving cross-view correlation analysis model to obtain m projection matrices corresponding to m groups of data The specific solution process is as follows:

[0023] (3a) Construct the Lagrange multiplier function of the model:

[0024]

[0025] Where λ is the Lagrange multiplier, let have

[0026]

[0027] (3b) The above equation can be transformed into the following generalized eigenvalue problem:

[0028]

[0029] By solving the above formula, we can obtain the eigenvectors corresponding to the first d largest eigenvalues As the solution vector, we finally get m projection matrices corresponding to m groups of data.

[0030] 4. Using the projection matrix A of m sets of data i The low-dimensional projections of each group of training samples and test samples are calculated separately, and the parallel fusion strategy is used to fuse the features to obtain effective identification features. The features are identified by the nearest neighbor classifier to obtain the final classification recognition rate.

[0031] Compared with the prior art, the advantages and positive effects of the present invention are:

[0032] The present invention projects gene expression data onto a similar order-preserving subspace. The low-dimensional data in the subspace can have intra-class clustering and inter-class discreteness while maintaining the sample similarity before and after projection, thereby effectively enhancing the identification ability of low-dimensional data. While maintaining the sample structure relationship, it makes full use of the sample supervision information, thereby achieving better recognition effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a specific implementation flow chart of the present invention;

[0034] Figure 2 is a flow chart of the modality strategy used in the present invention for constructing a multi-view gene expression dataset;

[0035] Figure 3 It is a flow chart of constructing a similarity order preserving cross-view correlation analysis model adopted by the present invention. DETAILED DESCRIPTION

[0036] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific examples.

[0037] Figure 1 It is a specific implementation flow chart of the present invention, and its detailed steps are as follows:

[0038] Step 1: Modalize the gene expression data using modality strategies, such as Figure 2 As shown in the figure, three wavelet transforms, Coiflets, Daubechies and Symlets, are used to extract low-frequency components as different modal data to construct a multi-view gene expression dataset: Where m is the number of viewing angles, n is the number of gene samples, d i is the dimension of the i-th group of features, i = 1, 2, …, m;

[0039] Step 2: Construct a similarity order-preserving cross-view correlation analysis model, such as Figure 3 As shown, the specific construction process is as follows:

[0040] (2a) Construct the similarity order-preserving scatter matrix of the i-th perspective. The specific construction method is as follows:

[0041] Calculate sample similarity matrix

[0042]

[0043] in Representation sample and Belong to the same category, Represents any two samples in the i-th group of gene data sets and The normalized similarity between them is specifically expressed as:

[0044] Construct the similarity order-preserving scatter matrix of the i-th perspective Where D (i) is a diagonal matrix with diagonal elements is the Laplace matrix;

[0045] (2b) Construct the similarity correlation matrix between the i-th and j-th perspectives. The specific construction method is as follows:

[0046] Calculate the weighted matrix of similarity between views

[0047]

[0048]

[0049] Construct the similarity correlation matrix between the i-th and j-th perspectives: Where D (ij) is a diagonal matrix with diagonal elements is the Laplace matrix, Operation Indicates the multiplication of corresponding elements of the matrix;

[0050] (2c) Constructing a cross-view similarity order-preserving correlation analysis model:

[0051] By maximizing the inter-view similarity correlation and minimizing the intra-view similarity order-preserving dispersion, a cross-view similarity order-preserving correlation analysis model is constructed.

[0052]

[0053]

[0054] where α (i) , α (j) Respectively represent the projection directions of the i-th and j-th perspectives;

[0055] Step 3: Optimize and solve the similarity order-preserving cross-view correlation analysis model to obtain m projection matrices corresponding to m groups of data The specific solution process is as follows:

[0056] (3a) Construct the Lagrange multiplier function of the model:

[0057]

[0058] Where λ is the Lagrange multiplier, let have

[0059]

[0060] (3b) The above equation can be transformed into the following generalized eigenvalue problem:

[0061]

[0062] By solving the above formula, we can obtain the eigenvectors corresponding to the first d largest eigenvalues As the solution vector, we finally get m projection matrices corresponding to m groups of data.

[0063] Step 4: Use the projection matrix A of m sets of data i The low-dimensional projection of each group of training samples and test samples is calculated separately, and the parallel fusion strategy is used to fuse the features to obtain effective identification features. The nearest neighbor classifier is used to identify the features to obtain the final classification recognition rate.

[0064] The present invention is described below in conjunction with a specific example: The present invention is a gene feature extraction method based on Similarity Order Preserving Across-view Correlation Analysis (SOPACA). In order to evaluate the effectiveness of the present invention, an experiment is designed on a lung cancer gene expression dataset, and compared with multi-view canonical correlation analysis (MCCA), discriminative MCCA (DMCCA), label-based MCCA (LMCCA), and graph regularized MCCA (GrMCCs) methods. In the experiment, a lung cancer gene expression dataset was obtained from the GEO gene expression database, containing 107 samples, each of which contained expression data of 22,283 genes, including 58 cancer samples and 49 normal samples. Randomly extract t (t = 5, 10, 15, 20, 25) samples of each class to construct a training set, and the remaining samples are used as test sets. Each experiment is run independently 10 times.

[0065] Step 1: Use the modal strategy to modalize the gene expression data. Use three wavelet transforms, Coiflets, Daubechies, and Symlets, to extract low-frequency components as three modal data to construct a multi-view gene expression dataset: n is the number of gene samples, d iis the dimension of the i-th group of features;

[0066] Step 2: Construct a similarity order-preserving cross-view correlation analysis model, such as Figure 3 As shown, the specific construction process is as follows:

[0067] (2a) Construct the similarity order-preserving scatter matrix of the i-th perspective. The specific construction method is as follows:

[0068] Calculate sample similarity matrix

[0069]

[0070] in Representation sample and Belong to the same category, Represents any two samples in the i-th group of gene data sets and The normalized similarity between them is specifically expressed as:

[0071] Construct the similarity order-preserving scatter matrix of the i-th perspective Where D (i) is a diagonal matrix with diagonal elements is the Laplace matrix;

[0072] (2b) Construct the similarity correlation matrix between the i-th and j-th perspectives. The specific construction method is as follows:

[0073] Calculate the weighted matrix of similarity between views

[0074]

[0075]

[0076] Construct the similarity correlation matrix between the i-th and j-th perspectives: Where D (ij) is a diagonal matrix with diagonal elements is the Laplace matrix, Operation Indicates the multiplication of corresponding elements of the matrix;

[0077] (2c) Constructing a cross-view similarity order-preserving correlation analysis model:

[0078] By maximizing the inter-view similarity correlation and minimizing the intra-view similarity order-preserving dispersion, a cross-view similarity order-preserving correlation analysis model is constructed.

[0079]

[0080]

[0081] where α (i) , α (j) Respectively represent the projection directions of the i-th and j-th perspectives;

[0082] Step 3: Optimize and solve the similarity order-preserving cross-view correlation analysis model to obtain m projection matrices corresponding to m groups of data The specific solution process is as follows:

[0083] (3a) Construct the Lagrange multiplier function of the model:

[0084]

[0085] Where λ is the Lagrange multiplier, let have

[0086]

[0087] (3b) The above equation can be transformed into the following generalized eigenvalue problem:

[0088]

[0089] By solving the above formula, we can obtain the eigenvectors corresponding to the first d largest eigenvalues As the solution vector, we finally get three projection matrices corresponding to three sets of data

[0090] Step 4: Use the projection matrix A of the three sets of data i The low-dimensional projections of each group of training samples and test samples were calculated respectively, and the parallel fusion strategy was used to fuse the features to obtain effective identification features. The nearest neighbor classifier was used to identify the features to obtain the average recognition rate and corresponding standard deviation of each algorithm on the lung cancer gene expression dataset as shown in Table 1.

[0091] Table 1. Recognition rate change results on lung cancer gene expression dataset

[0092] SOPACA DMCCA MCCA GrMCCs LMCCA 5Train 98.66±0.85 97.11±1.52 96.08±2.37 94.64±3.10 97.01±1.41 10Train 99.08±0.91 98.28±1.12 98.16±1.11 96.55±2.82 98.28±1.12 15Train 98.70±1.22 98.18±1.40 97.92±1.40 98.05±2.31 98.18±1.40 20Train 98.81±0.94 98.51±1.00 97.61±1.00 97.61±2.01 98.36±1.10 25Train 99.65±0.74 99.30±0.91 99.30±1.11 98.60±1.38 99.30±0.91

[0093] A±B: A represents the average recognition rate (%), B represents the corresponding recognition rate standard deviation

[0094] As the number of samples increases, the SOPACA method always maintains the optimal recognition rate. When the number of samples is small, the SOPACA method shows its superiority over other algorithms, which is particularly important for gene expression data with high-dimensional small sample characteristics. The standard deviation can reflect the fluctuation of the recognition rate. The larger the standard deviation, the stronger the data volatility. Compared with other methods, the SOPACA method has a smaller standard deviation, indicating that the recognition rate changes smoothly, indicating that the proposed method has good robustness. The experimental results on the lung cancer gene expression data set show that the present invention is an effective gene feature extraction method.

[0095] In summary, the present invention has intra-class aggregation and inter-class discreteness while maintaining the similarity of samples before and after projection, effectively enhancing the identification ability of low-dimensional data, and making full use of sample supervision information while maintaining the sample structure relationship, thereby achieving better recognition effect.

Claims

1. A gene expression data classification method based on similarity order preservation, comprising the following steps: (1) Modal strategies are used to modalize gene expression data, and wavelet transform is used to extract low-frequency components as different modal data to construct a multi-view gene expression dataset: Where m is the number of viewing angles, n is the number of gene samples, d i is the dimension of the i-th group of features, i = 1, 2, …, m; (2) Construct a similarity order-preserving cross-view correlation analysis model. The model is constructed in the following steps: (2a) Construct the similarity order-preserving scatter matrix of the i-th perspective. The specific construction method is as follows: Calculate sample similarity matrix in Representation sample and Belong to the same category, Represents any two samples in the i-th group of gene data sets and The normalized similarity between them is specifically expressed as: Construct the similarity order-preserving scatter matrix of the i-th perspective Where D (i) is a diagonal matrix with diagonal elements is the Laplace matrix; (2b) Construct the similarity correlation matrix between the i-th and j-th perspectives. The specific construction method is as follows: Calculate the weighted matrix of similarity between views Construct the similarity correlation matrix between the i-th and j-th perspectives: Where D (ij) is a diagonal matrix with diagonal elements is the Laplace matrix, Operation Indicates the multiplication of corresponding elements of the matrix; (2c) Constructing a cross-view similarity order-preserving correlation analysis model: By maximizing the inter-view similarity correlation and minimizing the intra-view similarity order-preserving dispersion, a cross-view similarity order-preserving correlation analysis model is constructed. where α (i) , α (j) Respectively represent the projection directions of the i-th and j-th perspectives; (3) Optimize and solve the similarity order-preserving cross-view correlation analysis model to obtain m projection matrices corresponding to m groups of data (4) Using the projection matrix A of m sets of data i The low-dimensional projections of each group of training samples and test samples are calculated separately, and the parallel fusion strategy is used to fuse the features to obtain effective identification features. The features are identified by the nearest neighbor classifier to obtain the final classification recognition rate.

2. The gene expression data classification method based on similarity order preservation according to claim 1, characterized in that: The similarity order-preserving cross-view correlation analysis model described in step (3) is optimized and solved to obtain m projection matrices corresponding to m groups of data. Proceed as follows: (3a) Construct the Lagrange multiplier function of the model: Where λ is the Lagrange multiplier, let have (3b) The above equation can be transformed into the following generalized eigenvalue problem: By solving the above formula, we can obtain the eigenvectors corresponding to the first d largest eigenvalues As the solution vector, we finally get m projection matrices corresponding to m groups of data.

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