Cancer Single-Cell Type Identification Method Based on Optimal Transport Subspace Clustering

Abstract

This invention proposes a cancer single-cell type identification method based on optimal transport subspace clustering. By employing a local graph-guided learning strategy, this invention effectively addresses a common problem in deep subspace clustering: the tendency to converge to suboptimal solutions during self-expression learning, leading to poor clustering results. This strategy significantly improves the accuracy and robustness of the clustering process. Furthermore, this invention introduces the Wasserstein regularized self-expression learning method, combined with the optimal transport algorithm, greatly enhancing the model's ability to learn subspace structures in cell clustering tasks. This enables the model to obtain more robust and reliable subspace representations, thereby improving clustering quality.

Description

Technical Field

[0001] This application belongs to the field of cell clustering technology, and in particular relates to a method for identifying single-cell cancer types based on optimal transport subspace clustering. Background Technology

[0002] The development of single-cell RNA sequencing (scRNA-seq) technology has enabled gene expression analysis at the single-cell level in cancer research. 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 efficiently 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, dimensionality reduction of the gene expression matrix is ​​performed, followed by the application of traditional clustering methods such as k-means, hierarchical clustering, and graph-based clustering. For example, combining principal component analysis (PCA) with hierarchical clustering yields cell identification results. Additionally, a shared nearest neighbor (SNN) graph is constructed based on the principal components of the gene expression matrix to capture similarities between cells, and clustering is performed using the Louvain algorithm. Furthermore, some methods further enhance clustering performance by using ensemble strategies. For instance, SC3 combines the results of multiple clustering algorithms to achieve more stable and consistent results. Meanwhile, SIMLR employs multiple kernel functions to capture different features and relationships in the data, thereby achieving more accurate cell type identification through clustering.

[0004] Recently, leveraging the feature representation learning capabilities of deep learning, various deep clustering methods have been successfully applied to scRNA-seq data for cell identification. For example, by constructing a variational autoencoder to learn unit embeddings and cluster assignments, and simultaneously developing an adaptive cluster merging method, the clustering results are improved without prior estimation of the number of clusters. Furthermore, a nonnegative matrix factorization algorithm based on network structure learning is employed to identify cell types in scRNA-seq data, transforming the task into a constrained optimization problem. Another example is the introduction of a deep embedding clustering method based on a convolutional autoencoder and soft k-means clustering, addressing high loss rates and noise issues by simultaneously learning feature representations and performing clustering. Beyond traditional embedding learning, several methods utilize graph neural networks to integrate structural relationships between cells to capture more reliable cell clustering representations. For instance, by combining a ZINB-based autoencoder, graph neural network modules, and mutual supervision modules, scRNA-seq data can be effectively learned and clustered, capturing the intrinsic characteristics of individual cells and their relationships. Similarly, there are approaches that construct a cell map, refine it using network denoising, learn cluster-friendly representations using a graph attention autoencoder, and finally cluster cells using a self-optimizing method. Furthermore, there are methods that integrate graph convolutional networks (GCNs) into a multi-autoencoder framework to improve cell clustering. This approach uses a feature autoencoder to construct a cell map, refines the cell representations using a GCN-based autoencoder, applies k-means clustering, and iteratively refines the cell representations using a cluster-specific autoencoder.

[0005] A key challenge in cell clustering lies in accurately estimating cell relationships and obtaining robust feature representations for cell type identification. While some studies have demonstrated the effectiveness of clustering tasks, most existing methods still face significant challenges due to the inherently high loss rate and noise in scRNA-seq data. These inherent characteristics often lead to unstable clustering results, making cell type identification less reliable. Summary of the Invention

[0006] To address the limitations of existing methods, this application proposes a cancer single-cell type identification method based on optimal transport subspace clustering. Specifically, a self-expressed Wasserstein distance is proposed and further regularized to improve the quality of the self-expression, which is a crucial component for capturing relationships between samples and achieving clustering, ultimately guiding the learning of the entire model. This Wasserstein-regularized self-expression learning can be efficiently solved using the optimal transport algorithm. Furthermore, a local structure-guided learning strategy is employed to improve model reliability by addressing common problems in deep subspace clustering.

[0007] To achieve the above objectives, this application provides a method for cancer single-cell type identification based on optimal transport subspace clustering, specifically including:

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

[0009] S2: Deep subspace clustering parameters are alternately updated by combining a deep subspace clustering model with Wasserstein self-representation learning and using the standard ADMM optimization method.

[0010] S3: Calculate the optimal transmission plan γ using the Sinkhorn-Knopp algorithm. * This is then fed back into the self-expression loss for further refinement;

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

[0012] Step S1 specifically includes:

[0013] Define reconstruction loss L recon The formula is:

[0014]

[0015] In the formula, X = [X1, X2, ..., X...] n ]∈R D×N This 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 These are the decoder parameters, where Z is the latent representation of the original data learned by the autoencoder network, Z = E(X, Θ). e ), where E(·) represents the encoder function, Θ e This indicates encoder parameters.

[0016] Where X = XC;

[0017]

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

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

[0020] 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. It is a regularization term that controls the complexity of C.

[0024] Step S4 further includes:

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

[0026] Self-expression based on intercellular distance is calculated using the optimal transport distance based on γ*, as follows:

[0027]

[0028] The Sinkhorn-Knopp algorithm is used to solve for the optimal transmission plan γ. * γ * This represents the optimal inter-cell relationship matching matrix.

[0029] Step S4 further includes:

[0030] Based on the optimal transmission distance γ * Self-representation learning can be rephrased as:

[0031]

[0032] 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 reconstruction and self-expression loss.

[0036] Compared with the prior art, the advantages of this application are as follows:

[0037] (1) Self-expressive learning mechanism using Wasserstein regularization: This mechanism is implemented through the optimal transfer algorithm and can effectively improve 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 easy to occur in traditional clustering, thereby improving the quality and accuracy of clustering.

[0039] (3) Application in cell type identification: The specific application area of ​​this technology is cell type identification. By using subspace clustering, it is possible to more accurately identify different types of cells. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a cancer single-cell type identification method based on optimal transport subspace clustering in one embodiment of this application.

[0041] Figure 2 for Figure 1 A flowchart illustrating the process of a cancer single-cell type identification method based on optimal transport subspace clustering.

[0042] Figure 3 for Figure 1 A rendering of a cancer single-cell type identification method based on optimal transport subspace clustering. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions will be clearly and completely described below in conjunction with the embodiments of this application. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0044] Example 1:

[0045] As attached Figure 1-3 As shown, in order to solve the above-mentioned technical problems, this application provides a method for cancer single-cell type identification based on optimal transport subspace clustering, specifically including:

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

[0047] An autoencoder is an unsupervised learning neural network consisting of an encoder and a decoder. The encoder compresses the input data into a low-dimensional latent representation, while the decoder reconstructs this representation back to the original input. By training the autoencoder, a latent representation that facilitates clustering can be learned.

[0048] Preferably, before proceeding to step S1, data collection and preprocessing are required; then, the encoder and decoder structures are designed according to the complexity of the requirements. Finally, a reconstruction loss function is used as the optimization objective.

[0049] Let X = [X1, X2, ..., Xn] n ]∈R N×DThis represents a single-cell sequencing dataset for cancer, where N represents the number of cells and D represents the number of genes.

[0050] For subspace clustering, suppose the data points of X are drawn from K distinct multilinear subspaces, and the central concept is self-representation: each sample can be represented as a linear combination of the other samples.

[0051] Mathematically, this is represented as X = XC, where C is the self-expression coefficient matrix. Ideally, if X... i and X j If they are located in the same subspace, then C ij ≠0, otherwise C ij =0. This causes 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 Equation 1 below:

[0052]

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

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

[0055] Formula 2: Z = E(X, Θ) e );

[0056] Where E(·) represents the encoder function, Θ e This represents the encoder parameters. The original data is then reconstructed from the latent representation using the corresponding decoder network.

[0057] Formula 3:

[0058] Where D(·) represents the decoder network, θ d These are decoder parameters. Reconstruction loss L recon This is used to learn a more discriminative data representation by quantifying the differences between the input data and the 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 this representation is used to obtain the self-expression matrix C in equation (1). Based on this, the clustering module of the self-expression loss can be restated as follows:

[0061] Formula 5:

[0062] The first term uses the self-representation matrix C to measure the reconstruction error of the latent representation, 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 is combined with Wasserstein distance regularization self-expression learning, and the deep subspace clustering parameters are alternately updated using the standard ADMM optimization method;

[0064] This application introduces an optimal transmission strategy to improve the relationship between self-captured samples through Wasserstein distance.

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

[0066] Formula 6:

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

[0068] For discrete cases, use and Representing point x i and y j The probabilistic quality at a given location, the optimal transmission distance (OT), is defined as:

[0069] Formula 7:

[0070]

[0071] To solve the optimal transmission distance problem, the model employs ADMM (Alternating Direction Multiplier Method, an algorithm commonly used to solve constrained optimization problems). It decomposes the original problem into multiple subproblems that are alternately optimized, making it suitable for solving Wasserstein regularized self-expressive models. An augmented Lagrangian function is constructed to solve for γ and G, and the process stops when γ and G converge or the maximum number of iterations is reached.

[0072] S3: Calculate the optimal transmission plan γ using the Sinkhorn-Knopp algorithm. * This is then fed back into the self-expression loss for further refinement;

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

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

[0075] Formula 8:

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

[0077] The specific implementation process is as follows:

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

[0079] Output: Optimal transfer matrix γ * ;

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

[0081]

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

[0083] Formula 9:

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

[0085] In summary, 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 from the sklearn library is used as the input. The cancer single-cell feature matrix obtained through training is input, and the affinity matrix is ​​used to replace the similarity matrix required in the spectral clustering algorithm. Finally, the final result of the cancer single-cell type is obtained. 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 previously calculated self-expression matrix C 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] Clustering is performed using the SpectralClustering method from the sklearn library. The affinity matrix is ​​taken as input and converted into a Laplacian matrix. Then, eigenvalue decomposition is performed to obtain a low-dimensional representation of the samples. Finally, the K-means algorithm is used for clustering.

[0093] To further verify the effectiveness of the cancer single-cell type identification method based on optimal transport subspace clustering proposed in this application, such as... Figure 3 As shown in the figure, the clustering results of the model on the four public datasets Zeisel, Human_ESC, Splen and Human_pancres are 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] This application, by employing a local graph-guided learning strategy, effectively addresses a common problem in deep subspace clustering: the tendency for self-expression learning to converge to suboptimal solutions, leading to poor clustering results. This strategy significantly improves the accuracy and robustness of the clustering process. Furthermore, this application introduces Wasserstein regularized self-expression learning and combines it with the optimal transfer algorithm, greatly enhancing the model's ability to learn subspace structures in cell clustering tasks. This enables the model to obtain more robust and reliable subspace representations, thereby improving clustering quality.

[0095] In the several embodiments provided in this application, it will be understood that each block in the flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the figures. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved.

[0096] If the aforementioned functions are implemented as software functional 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 this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0097] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application for those skilled in the art.

Claims

1. A method for identifying single-cell cancer types based on optimal transport subspace clustering, characterized in that, The method includes the following steps: S1: Pre-train the autoencoder using reconstruction loss and obtain the initial representation as the starting point for self-expression learning; S2: Deep subspace clustering parameters are alternately updated by combining a deep subspace clustering model with Wasserstein self-representation learning and using the standard ADMM optimization method. S3: Calculate the optimal transmission plan γ using the Sinkhorn-Knopp algorithm. * This is then fed back into the self-expression loss for further refinement; S4: Affinity matrix This is applied to the spectral clustering algorithm to obtain the final clustering results for cell type identification; among which, Step S1 specifically includes: Define reconstruction loss L recon The formula is: In the formula, X = [X1, X2, ..., X... n ]∈R D×N This 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 These are the decoder parameters, where Z is the latent representation of the original data learned by the autoencoder network, Z = E(X, Θ). e ), where E(·) represents the encoder function, Θ e Indicates encoder parameters; 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. It is a regularization term that controls the complexity of d; Step S4 further includes: Define a self-expression matrix C, and define the cost matrix as G = 1 - C; Using optimal transmission distance based on γ * The formula for calculating self-expression based on intercellular distance is as follows: The Sinkhorn-Knopp algorithm is used to solve for the optimal transmission plan γ. * γ * This represents the optimal inter-cell relationship matching matrix. Step S4 further includes: The total loss function is defined as: L total =L train +λ Lself ; Where λ is a parameter that balances reconstruction and self-expression loss.

2. The cancer single-cell type identification method based on optimal transport subspace clustering according to claim 1, characterized in that, Also includes: X = XC; stX = XC, diag(C) = 0; Where C is the self-expression matrix.

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