Cancer single cell type identification method based on optimal transmission subspace clustering

Abstract

According to the cancer single cell type identification method based on optimal transmission subspace clustering provided by the invention, a learning strategy guided by a local graph is adopted, and the common problem in depth subspace clustering is effectively solved, that is, a sub-optimal solution is easy to converge in a self-expression learning process, so that a relatively poor clustering result is caused. The strategy significantly improves the accuracy and robustness of the clustering process. Furthermore, a Wasserstein regularization self-expression learning method is introduced in the invention, and an optimal transmission algorithm is combined, so that the learning ability of the model for the sub-space structure in the cell clustering task is greatly improved, the model can obtain more stable and reliable sub-space representation, and the clustering quality is improved.

Description

Technical Field

[0001] The present application belongs to the technical field of cell clustering, and in particular, relates to a method for identifying single cancer cell types based on optimal transmission subspace clustering. Background Art

[0002] The development of single-cell RNA sequencing (scRNA-seq) technology has made it possible to analyze gene expression at the single-cell level in cancer. This advanced technology provides new insights into biological mechanisms such as tumor microenvironment analysis and personalized medicine. A key task in scRNA-seq data analysis is cell type identification, which involves grouping cells based on similar gene expression patterns. This can be effectively achieved through unsupervised clustering.

[0003] Several clustering methods have been proposed to identify cell types from scRNA-seq profiles. A common approach involves a sequential process: first, the gene expression matrix is ​​reduced in dimensionality, and then traditional clustering methods such as k-means, hierarchical clustering, and graph-based clustering methods are applied. For example, principal component analysis (PCA) is combined with hierarchical clustering to produce cell identification results. Also, a shared nearest neighbor (SNN) graph is constructed based on the principal components of the gene expression matrix to capture the similarities between cells, and the Louvain algorithm is used for clustering. In addition, some methods further enhance the clustering performance by using ensemble strategies. For example, SC3 combines the results of multiple clustering algorithms to achieve more stable and consistent results. Meanwhile, SIMLR adopts multiple kernel functions to capture different features and relationships in the data, thereby achieving more accurate cell type identification through clustering.

[0004] Recently, a variety of deep clustering methods have been successfully applied to scRNA-seq data for cell identification by leveraging the feature representation learning capabilities of deep learning. For example, by building a variational autoencoder to learn cell embeddings and cluster assignments, and simultaneously developing an adaptive cluster merging method to improve clustering results without estimating the number of clusters in advance. Also, a non-negative matrix factorization algorithm based on network structure learning is used to identify cell types in scRNA-seq data, converting the task into a constrained optimization problem. In another example, a deep embedding clustering method based on convolutional autoencoders and soft k-means clustering is introduced, and the high loss rate and noise problems are solved by simultaneously learning feature representations and performing clustering. In addition to traditional embedding learning, there are several methods that use graph neural networks to integrate structural relationships between cells to capture more reliable cell clustering representations. For example, by combining a ZINB-based autoencoder, a graph neural network module, and a mutual supervision module to effectively learn and cluster scRNA-seq data and capture the intrinsic properties of individual cells and their relationships. Similarly, there is also a method that builds a cell graph, refines it through network denoising, uses a graph attention autoencoder to learn cluster-friendly representations, and finally clusters cells using a self-optimization method. In addition, there is also a method that integrates a graph convolutional network (GCN) into a multi-autoencoder framework to improve cell clustering. It uses a feature autoencoder to build a cell graph, refines the cell representation through a GCN-based autoencoder, and applies k-means clustering to iteratively refine the cell representation through a cluster-specific autoencoder.

[0005] The key challenge of cell clustering is to accurately estimate cell relationships and obtain robust feature representations for cell type identification. Although some studies have demonstrated the effectiveness of clustering tasks, most existing methods still face severe challenges due to the inherent high loss rate and noise of scRNA-seq data. These intrinsic characteristics often lead to unstable clustering results, making cell type identification less reliable. Summary of the invention

[0006] In view of the limitations of existing methods, this application proposes a cancer single cell type identification method based on optimal transmission subspace clustering for cancer single cell type identification. Specifically, a self-expression Wasserstein distance is proposed, and it is further regularized to improve the quality of self-expression, which is an important component for capturing the relationship between samples and realizing clustering, and is ultimately used to guide the learning of the entire model. The Wasserstein regularized self-expression learning can be efficiently solved by the optimal transmission algorithm. In addition, a local structure-guided learning strategy is adopted to improve the reliability of the model by solving common problems in deep subspace clustering.

[0007] To achieve the above objectives, the present application provides a method for identifying single cancer cell types based on optimal transmission subspace clustering, which specifically includes:

[0008] S1: Use reconstruction loss to pre-train the autoencoder and obtain the initial representation as the starting point for self-expression learning;

[0009] S2: Combine the deep subspace clustering model with Wasserstein self-representation learning and use the standard ADMM optimization method to alternately update the deep subspace clustering parameters;

[0010] S3: Compute the optimal transmission plan using the Sinkhorn-Knopp algorithm γ * , and feed it into the self-expression loss for refinement;

[0011] S4: Affinity Matrix It is applied to the spectral clustering algorithm to obtain the final clustering results for cell type identification.

[0012] The step S1 specifically includes:

[0013] Define the reconstruction loss L recon , the formula is:

[0014]

[0015] In the formula, X=[X 1 , X 2 , ..., X n ]∈R D×N represents a cancer single-cell sequencing dataset, where D represents the number of genes and N represents the number of cells; To reconstruct the original data from the latent representation using the corresponding decoder network, where D(·) represents the decoder network, θ d is the decoder parameter, Z is the potential representation of the original data learned by the autoencoder network, Z = E(X, Θ e ), where E(·) represents the encoder function, Θ e Represents encoder parameters.

[0016] Where, X = XC;

[0017]

[0018] stX = XC, diag(C) = 0;

[0019] where C is the self-expression coefficient matrix.

[0020] The step S2 further includes:

[0021] The deep subspace clustering model is described as follows:

[0022]

[0023] in, The reconstruction error of the latent representation is measured using the self-expression matrix C, is a regularization term that controls the complexity of C.

[0024] The step S4 further includes:

[0025] Define the self-expression matrix C and define the cost matrix as G = 1-C;

[0026] The self-expression based on the inter-cell distance is calculated based on γ* using the optimal transmission distance, as follows:

[0027]

[0028] Among them, the Sinkhorn-Knopp algorithm is used to solve the optimal transmission plan γ * , γ * Represents the optimal cell-to-cell relationship matching matrix.

[0029] The step S4 further includes:

[0030] According to the optimal transmission distance based on γ * Re-statement of self-representation learning as:

[0031]

[0032] The step S4 further includes:

[0033] The total loss function is defined as:

[0034] L total =L train +λL self ;

[0035] where λ is a parameter that balances the reconstruction and self-expression losses.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] (1) Self-expressive learning mechanism using Wasserstein regularization: This mechanism is implemented through the optimal transfer algorithm and can effectively improve the robustness in the clustering process.

[0038] (2) Local graph-guided deep subspace clustering model: This strategy can effectively avoid the problem of convergence to suboptimal solutions that is prone to occur in traditional clustering processes, thereby improving clustering quality and accuracy.

[0039] (3) Application in cell type identification: The specific application area of ​​this technology is cell type identification. Through the subspace clustering method, different types of cells can be identified more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a schematic diagram of a method for identifying single cancer cell types based on optimal transmission subspace clustering in one embodiment of the present application.

[0041] Figure 2 for Figure 1 Process diagram of a cancer single cell type identification method based on optimal transmission subspace clustering.

[0042] Figure 3 for Figure 1 The effect diagram of a cancer single cell type identification method based on optimal transmission subspace clustering. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme will be clearly and completely described below in conjunction with the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0044] Embodiment 1:

[0045] As attached Figure 1-3 As shown, in order to solve the above technical problems, the present application provides a method for identifying single cancer cell types based on optimal transmission subspace clustering, which specifically includes:

[0046] S1: Use reconstruction loss to pre-train the autoencoder and obtain the initial representation as the starting point for self-expression learning;

[0047] Among them, the autoencoder is an unsupervised learning neural network, which consists of two parts: the encoder and the decoder. The encoder compresses the input data into a low-dimensional potential representation, and the decoder reconstructs this representation back to the original input. By training the autoencoder, you can learn the potential representation that is helpful for clustering.

[0048] Preferably, before performing step S1, data collection and data preprocessing are required, and then the encoder and decoder structures are designed according to the required complexity. Then, the reconstruction loss function is used as the optimization target.

[0049] Let X = [X 1 , X 2 , ..., X n ]∈RN×D represents a cancer single-cell sequencing dataset, where N represents the number of cells and D represents the number of genes.

[0050] For subspace clustering, we assume that the data points of X are drawn from K different multilinear subspaces. The central concept is self-expressiveness: each sample can be expressed as a linear combination of other samples.

[0051] Mathematically, this is expressed as X = XC, where C is the self-expression coefficient matrix. Ideally, if X i and X j are in the same subspace, then C ij ≠0, otherwise C ij = 0. This forces C to exhibit a block diagonal structure, where the number of blocks corresponds to the number of subspaces. This structure can be implemented by minimizing an appropriate norm of C based on the assumption of independent subspaces, which can be expressed as follows in Formula 1:

[0052]

[0053] stX = XC, diag(C) = 0;

[0054] In deep subspace clustering, the autoencoder network can be used as an unsupervised model to project the original features into a lower-dimensional latent representation space. Specifically, the encoder network is used to learn the latent representation Z of the original data:

[0055] Formula 2: Z = E(X, θ e );

[0056] where E(·) represents the encoder function, Θ e represents the encoder parameters. The corresponding decoder network is then used to reconstruct the original data from the latent representation:

[0057] Formula 3:

[0058] where D(·) represents the decoder network, θ d is the decoder parameter. The reconstruction loss L recon Used to learn more discriminative data representation by quantifying the difference between input data and reconstructed data. The loss is defined as follows:

[0059] Formula 4:

[0060] Furthermore, the latent representation Z learned through the autoencoder network is utilized and used to obtain the self-expressive matrix C in equation (1). Based on this, the clustering module of the self-expressive loss can be reformulated as follows:

[0061] Formula 5:

[0062] The first term measures the reconstruction error of the latent representation using the self-expression matrix C, and the second term is a regularization term that controls the complexity of C. The regularization parameter λ balances the reconstruction accuracy and the sparsity of C.

[0063] S2: Deep subspace clustering combined with Wasserstein distance regularization self-expression learning, and the standard ADMM optimization method is used to alternately update the deep subspace clustering parameters;

[0064] In this application, an optimal transfer strategy is introduced to better capture the relationship between samples by improving the Wasserstein distance.

[0065] Traditionally, optimal transportation determines the transportation plan that minimizes the cost or distance between two probability distributions. Given probability distributions x and y, move the mass from x to i Transfer to y j The cost is given by the cost matrix G and G ij =Γ(x i ,y j ), the associated optimal transmission distance can be defined as:

[0066] Formula 6:

[0067] st∫γ(x,y)dy=μ(x), ∫γ(x,y)dx=v(y);

[0068] For the discrete case, use and Represents point x i and j The probability mass at , the optimal transmission distance (OT) is defined as:

[0069] Formula 7:

[0070]

[0071] In order to solve the optimal transmission distance problem, the model uses ADMM (alternating direction multiplier method, an algorithm commonly used to solve constrained optimization problems). It decomposes the original problem into multiple sub-problems for alternating optimization, which is suitable for solving Wasserstein regularized self-expression models. By constructing an augmented Lagrangian function to solve γ and G, the algorithm stops when γ and G converge or the maximum number of iterations is reached.

[0072] S3: Compute the optimal transmission plan using the Sinkhorn-Knopp algorithm γ * , and feed it into the self-expression loss for refinement;

[0073] In this application, optimal transfer is applied to redefine the self-expressive learning of C, aiming to better capture the relationship between samples and guide model learning.

[0074] For this self-expressive learning, the cost matrix is ​​defined as G = 1-C, reflecting the relationship between samples in the latent space. Then the optimal transmission distance is used based on γ * Calculate the self-expression based on the distance between cells:

[0075] Formula 8:

[0076] The resulting optimization can be solved using the Sinkhorn-Knopp algorithm to obtain the optimal transmission schedule γ * , represents the optimal cell-to-cell relationship matching matrix, which is introduced into the self-expression loss function to improve the learning ability of the model.

[0077] The specific implementation process is as follows:

[0078] Input: cost matrix G, row vector and r and column vector and c, maximum number of iterations K, regularization term λ;

[0079] Output: optimal transmission matrix γ * ;

[0080] Initialization: α = ones(n), β = ones(m);

[0081]

[0082] By incorporating this optimal transmission plan γ * To further rephrase self-representation learning:

[0083] Formula 9:

[0084] Therefore, the reformulated self-expressive learning incorporates the learned optimal transmission plan, making it more effective in guiding the entire model learning process.

[0085] In general, the total loss function of the proposed model can be defined as:

[0086] Formula 10: L total =L train +λL self .

[0087] S4: Affinity Matrix It is applied to the spectral clustering algorithm to obtain the final clustering results for cancer single cell type identification.

[0088] In this application, the SpectralClustering method in the sklearn library is applied to input the cancer single cell feature matrix obtained through training, and the affinity matrix is ​​used instead of the similarity matrix required in the spectral clustering algorithm to finally obtain the final result of the cancer single cell type. The specific implementation process is as follows:

[0089] The affinity matrix is ​​used to represent the similarity or affinity between samples. In this embodiment, the self-expression matrix C calculated previously is used as the affinity matrix. Specifically, the affinity matrix A can be derived from C:

[0090]

[0091] This ensures that the row sums are 1, which meets the requirements of the similarity matrix in the spectral clustering algorithm.

[0092] The SpectralClustering method in the sklearn library is used for clustering. The affinity matrix is ​​taken as input and converted into a Laplacian matrix. Then, eigendecomposition is performed to obtain a low-dimensional representation of the sample. Finally, the K-means algorithm is used for clustering.

[0093] In order to further verify the effectiveness of the cancer single cell type identification method based on optimal transmission subspace clustering in this application, Figure 3 As shown in the figure, the clustering effect of the model on the four public data sets of Zeisel, Human_ESC, Spleen and HUman_pancres is shown in the figure. It can be seen from the figure that the clustering effect of this model is very good, and the ARI index (ARI index is used to evaluate the clustering effect, the higher the better) is at a high level.

[0094] By adopting a local graph-guided learning strategy, the present invention effectively solves a common problem in deep subspace clustering, that is, the self-expression learning process is prone to converge to a suboptimal solution, which leads to poor clustering results. This strategy significantly improves the accuracy and robustness of the clustering process. Furthermore, the present application also introduces Wasserstein regularized self-expression learning, and combines it with the optimal transfer algorithm, which greatly improves the model's ability to learn the subspace structure in the cell clustering task, allowing the model to obtain a more robust and reliable subspace representation, thereby improving the clustering quality.

[0095] In several embodiments provided in the present application, it is understood that each box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, a program segment or a part of a code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved.

[0096] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device to perform all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0097] The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the scope of protection of the present application. It is particularly pointed out that for those skilled in the art, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of protection of the present application.

Claims

1. A method for identifying single cancer cell types based on optimal transmission subspace clustering, characterized in that: The method comprises the following steps: S1: Use reconstruction loss to pre-train the autoencoder and obtain the initial representation as the starting point for self-expression learning; S2: Combine the deep subspace clustering model with Wasserstein self-representation learning and use the standard ADMM optimization method to alternately update the deep subspace clustering parameters; S3: Compute the optimal transmission plan using the Sinkhorn-Knopp algorithm γ * , and feed it into the self-expression loss for refinement; S4: Affinity Matrix It is applied to the spectral clustering algorithm to obtain the final clustering results for cell type identification.

2. The method for identifying single cancer cell types based on optimal transmission subspace clustering according to claim 1, characterized in that: The step S1 specifically includes: Define the reconstruction loss L recon , the formula is: Where X=[X1,X2,...,X n ]∈R D×N represents a cancer single-cell sequencing dataset, where D represents the number of genes and N represents the number of cells; To reconstruct the original data from the latent representation using the corresponding decoder network, where D(·) represents the decoder network, θ d is the decoder parameter, Z is the potential representation of the original data learned by the autoencoder network, Z = E(X, Θ e ), where E(·) represents the encoder function, Θ e Represents encoder parameters.

3. The method for identifying single cancer cell types based on optimal transmission subspace clustering according to claim 2, characterized in that: Also includes: X = XC; stX=XC,diag(C)=0; where C is the self-expression coefficient matrix.

4. The method for identifying single cancer cell types based on optimal transmission subspace clustering according to claim 1, characterized in that: The step S2 further includes: The deep subspace clustering model is described as follows: in, The reconstruction error of the latent representation is measured using the self-expression matrix C, is a regularization term that controls the complexity of C.

5. The method for identifying single cancer cell types based on optimal transmission subspace clustering according to claim 4, characterized in that: The step S4 further includes: Define the self-expression matrix C and define the cost matrix as G = 1-C; Use the optimal transmission distance based on γ * The self-expression based on the distance between cells was calculated as: Among them, the Sinkhorn-Knopp algorithm is used to solve the optimal transmission plan γ * , γ * Represents the optimal cell-to-cell relationship matching matrix.

6. The method for identifying single cancer cell types based on optimal transmission subspace clustering according to claim 4, characterized in that: The step S4 further includes: According to the optimal transmission distance based on γ * Re-statement of self-expressive learning is:

7. The method for identifying single cancer cell types based on optimal transmission subspace clustering according to claim 4, characterized in that: The step S4 further includes: The total loss function is defined as: THE total =l train +λL self ; where λ is a parameter that balances the reconstruction and self-expression losses.

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