Single-cell multi-omics data integration method and model based on optimal transmission alignment

Abstract

This application relates to the field of artificial intelligence technology, and more particularly to a method and model for integrating single-cell multi-omics data based on optimal transport alignment. In each modality, high-order relationships between cells are modeled based on hypergraph structures. A shared hypergraph encoder learns the latent representations of cells, thus preserving structural information within a unified representation space. Subsequently, an optimal transport mechanism is introduced to establish cell-level soft correspondences between different modalities, characterizing cross-modal geometric consistency without assuming explicit one-to-one pairing. Based on this, the correspondence structures learned through optimal transport are used to align and correct cross-modal representations, enabling cells in different modalities to gradually converge in a unified latent space. The aim is to solve the problem of simultaneously achieving consistency of cross-modal distribution structures and fine-grained cell-level alignment in the latent space under unpaired and high-noise conditions.

Description

Technical Field

[0001] This application relates to the field of artificial intelligence technology, and in particular to a method and model for integrating single-cell multi-omics data based on optimal transport alignment. Background Technology

[0002] The goal of multimodal single-cell data integration is to map cell observations from different modalities to a unified latent representation space, enabling cells with similar biological properties to be correctly aggregated within this space while preserving biological heterogeneity among cells. Ideally, the integration should reduce cross-modal representation gaps while avoiding excessive smoothing of structural differences between different cell populations. However, in practical applications, multimodal single-cell data often originates from different measurement platforms, and there is usually a lack of strict one-to-one correspondence between modalities; that is, cell observations from different modalities are not perfectly paired.

[0003] Traditional multimodal single-cell data integration methods often employ fusion-based strategies, typically projecting heterogeneous modalities (such as RNA, protein expression, and chromatin accessibility) into a common embedding space through early feature splicing or linear mapping. However, this indiscriminate fusion approach is prone to characterization interference. Modality-specific noise and scale differences can distort the original geometric structure between cells, thereby weakening the portrayal of real biological relationships. This problem is particularly prominent in situations with a high imbalance in modality dimensions. For example, when tens of thousands of gene expression features coexist with only a few hundred surface protein measurements, the dominant modality often dominates the joint representation, causing weak modality information to be submerged or even lost.

[0004] Therefore, how to simultaneously achieve consistency of cross-modal distribution structures and fine alignment at the cell level in the latent space under unpaired and high-noise conditions has become the problem to be overcome by the single-cell multi-omics data integration method proposed in this application. Summary of the Invention

[0005] The main objective of this application is to provide a single-cell multi-omics data integration method based on optimal transport alignment, which aims to solve the problem of how to simultaneously achieve consistency of cross-modal distribution structures and fine alignment at the cell level in the latent space under unpaired and high-noise conditions.

[0006] To achieve the above objectives, this application provides a method for integrating single-cell multi-omics data based on optimal transport alignment, the method comprising:

[0007] S10, obtain the hypergraph structure corresponding to the first cell modality and the second cell modality, learn the hypergraph structure corresponding to the two modalities through the parameter-shared hypergraph encoder, and obtain the first cell latent representation and the second cell latent representation, thereby preserving the structural information within the modality in a unified representation space;

[0008] S20, determine the cross-modal cost matrix between the first cell latent representation and the second cell latent representation, determine the soft correspondence weights based on the cross-modal cost matrix, and determine the OT centroid of each cell in the first cell mode and the second cell mode according to the soft correspondence weights;

[0009] S30, the first cell latent representation and the second cell latent representation are mapped into student projection representations through the student projection head, and the OT centroid is mapped into teacher projection representation through the teacher projection head;

[0010] S40, Construct a target loss function based on the student projection representation and the teacher projection representation, and perform backpropagation training on the hypergraph encoder and the student projection head;

[0011] S50 generates a joint cell representation based on the trained hypergraph encoder and student projector head.

[0012] Optionally, in S10, the hypergraph structure uses an incidence matrix. express:

[0013]

[0014] in:

[0015]

[0016]

[0017]

[0018] In the formula, Represents a node its A set of nearest neighbors, Indicates the super edge. Denotes the set of superedges. This represents the total number of hyperedges in mode m. This represents the total number of nodes in mode m;

[0019] The elements of the correlation matrix are defined as follows:

[0020] .

[0021] Optionally, in S10, the hypergraph structure corresponding to the two modes is learned through a parameter-sharing hypergraph encoder, including:

[0022] S11, Modality-specific linear mapping is used to transform the input modal features Projecting to a unified dimension :

[0023]

[0024] In the formula, This represents the linear mapping parameter matrix corresponding to the m-th mode. This represents the bias term for the m-th mode;

[0025] S12, let and Let the node degree matrix and hyperedge degree matrix be respectively, and let the normalized hypergraph propagation operator be defined as:

[0026]

[0027] In the formula, The incidence matrix characterizing the hypergraph structure; Represents the transpose of the incidence matrix;

[0028] S13, based on propagation operator Determine one layer of hypergraph convolution:

[0029]

[0030] in, For the first The layer can learn parameters, and the same set of parameters is shared across all modes. , It is a non-linear activation function.

[0031] S14, after the... Modes are obtained after layer propagation The cell's potential representation:

[0032]

[0033] Where m = 1, 2; This represents the potential representation of the first cell. This indicates the potential representation of the second cell.

[0034] Optionally, in S20, the expression for the centroid of OT is:

[0035]

[0036]

[0037] In the formula, Represents the first cell mode in the first cell mode individual cells The centroid of OT under the second cell modality distribution; This represents the j-th cell in the second cell modality. The centroid of OT under the first cell modality distribution; Indicating the first cell mode, the first individual cells , and the second cell modality individual cells The matching strength at the distribution level, i.e., the soft correspondence weight.

[0038] Optionally, the expression for the soft corresponding weight is:

[0039]

[0040] In the formula, This represents the Sinkhorn–Knopp algorithm; C represents the cross-modal cost matrix; , These represent the edge distributions of the first and second cell modalities, respectively. is the regularization coefficient.

[0041] Optionally, the expression for the cross-modal cost matrix C is:

[0042]

[0043] in:

[0044]

[0045]

[0046]

[0047] In the formula, In mode 1, the first... The cell and the first in mode 2 The distance between individual cells in the embedded space; This indicates the number of cells in the first cell mode; Indicates the number of cells in the second cell modality; This represents the potential representation of the first cell. This indicates the potential representation of the second cell.

[0048] Optionally, in step S30, the student projection head and the teacher projection head satisfy the following loss function constraints during the mapping process:

[0049]

[0050] In the formula, This represents the distribution-level OT alignment loss corresponding to the first cell mode; This represents the distribution-level OT alignment loss corresponding to the second cell modality;

[0051] in:

[0052]

[0053]

[0054] In the formula, and These represent the outputs of the student projection head and the teacher projection head in the cell mode, respectively, with m=1 and 2; Indicates cosine similarity; This is the temperature coefficient.

[0055] Optionally, the expression for the target loss function is:

[0056]

[0057] In the formula, This represents the distributed OT alignment loss. This represents the instance-level OT-weighted comparison loss;

[0058] in:

[0059]

[0060]

[0061] In the formula, This represents the distribution-level OT alignment loss corresponding to the first cell mode; This represents the distribution-level OT alignment loss corresponding to the second cell modality; This represents the instance-level OT-weighted contrast loss corresponding to the first cell modality; This represents the instance-level OT-weighted contrast loss corresponding to the second cell modality;

[0062] in,

[0063]

[0064]

[0065]

[0066]

[0067] In the formula, and These represent the outputs of the student projection head and the teacher projection head in the cell mode, respectively, with m=1 and 2; Indicates cosine similarity; , All are temperature coefficients.

[0068] Furthermore, to achieve the above objectives, this application also provides a single-cell multi-omics data integration model based on optimal transport alignment, the single-cell multi-omics data integration model comprising:

[0069] The hypergraph encoder module is used to obtain the hypergraph structure corresponding to the first cell modality and the second cell modality. By learning the hypergraph structure corresponding to the two modalities through the parameter-shared hypergraph encoder, the potential representation of the first cell and the potential representation of the second cell are obtained, thereby preserving the structural information within the modality in a unified representation space.

[0070] Distribution-level optimal transport alignment is used to determine the cross-modal cost matrix between the first and second cell latent representations. Based on the cross-modal cost matrix, soft correspondence weights are determined, and the OT centroids of each cell in the first and second cell modes are determined according to the soft correspondence weights.

[0071] An instance-level OT weighted contrast learning module is used to map the first cell latent representation and the second cell latent representation into student projected representations through a student projector head, and to map the OT centroid into a teacher projected representation through a teacher projector head.

[0072] The training module is used to construct a target loss function based on the student projection representation and the teacher projection representation, and to perform backpropagation training on the hypergraph encoder and the student projection head; based on the hypergraph encoder and student projection head obtained after training, a joint cell representation is generated.

[0073] This application has at least the following beneficial effects:

[0074] 1. Instead of relying on the explicit one-to-one cell correspondence assumption between modalities, this model learns a soft-matching transfer matrix between cross-modal cells in a shared hypergraph embedding space based on Sinkhorn regularized optimal transfer. This transfer matrix is ​​simultaneously used to construct the OT-weighted distribution-level centroid representation and instance-level soft positive sample weights, thereby achieving implicit modeling of cross-modal cell correspondences without requiring known pairing relationships. This allows the model to be uniformly applied to both paired and unpaired multimodal single-cell data scenarios.

[0075] 2. By employing a modality-shared hypergraph encoder, higher-order population structures among cells are explicitly modeled within each modality, avoiding the structural information loss caused by relying solely on pairwise similarity. Building upon this, distribution-level operational alignment (OT) centroid alignment is introduced to constrain the consistency of embeddings across different modalities in the global geometric distribution. Furthermore, instance-level OT weighted contrastive learning is used to finely correct the local representation shifts of the same cell in different modalities. This joint mechanism of structural prior and OT geometric alignment enables the model to maintain the stability of higher-order structures within a modality while achieving consistent semantic and geometric embeddings across modalities.

[0076] 3. Experimental results on various paired and unpaired multimodal single-cell datasets show that the model proposed based on the method involved in this application achieves significant and stable performance improvements in both integration and matching tasks. Attached Figure Description

[0077] Figure 1 This is a flowchart illustrating the single-cell multi-omics data integration method based on optimal transmission alignment involved in the embodiments of this application;

[0078] Figure 2 This is a diagram of the HyOT-Align framework involved in the embodiments of this application;

[0079] Figure 3 This is a UMAP visualization of RNA modalities on the CITE dataset involved in the embodiments of this application, based on the original integration results.

[0080] Figure 4 This is a UMAP visualization of the Protein modalities on the CITE dataset involved in the embodiments of this application, based on the original integration results.

[0081] Figure 5 This is a umap visualization of the joint embedding space of RNA and Protein modalities after HyOT-Align integration on the CITE dataset, as described in the embodiments of this application.

[0082] Figure 6 This is a UMAP visualization of RNA modalities on the Multiome dataset involved in the embodiments of this application, based on the original integration results.

[0083] Figure 7 This is a UMAP visualization of the ATAC modalities on the Multiome dataset involved in the embodiments of this application, based on the original integration results.

[0084] Figure 8 This is a umap visualization of the joint embedding space of RNA and ATAC modalities after HyOT-Align integration on the Multiome dataset involved in the embodiments of this application.

[0085] Figure 9 This is a visualization of umap integrated on the MEBC dataset, as described in the embodiments of this application.

[0086] Figure 10 The image shows the ablation experiment results on the CITE dataset involved in the embodiments of this application;

[0087] Figure 11 The image shows the ablation experiment results on the Multiome dataset involved in the embodiments of this application.

[0088] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0089] To better understand the above technical solutions, exemplary embodiments of this disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of this disclosure to those skilled in the art.

[0090] First Embodiment

[0091] Suppose we have observational data from two single-cell omics modalities, denoted as ...

[0092]

[0093] in and This indicates the number of cells in the two modalities. and This corresponds to the feature dimension. This embodiment does not require... It does not assume a known one-to-one correspondence between cells in the two modalities, thus uniformly covering paired and unpaired multimodal single-cell data settings.

[0094] The goal of this embodiment is to learn a cross-modal consistent joint embedding space between two modalities to characterize the shared biological states of cells at different omics levels.

[0095] In this joint embedding space, the model is expected to simultaneously satisfy the following properties:

[0096] 1. Cells from different modalities but with similar biological semantics approach each other in geometric space;

[0097] 2. Local structures and cellular heterogeneity within each modality are preserved;

[0098] 3. The model does not rely on pairing assumptions and can work uniformly in both paired and unpaired data scenarios.

[0099] Based on the above problem definition, referring to Figure 1 This embodiment provides a method for integrating single-cell multi-omics data based on optimal transport alignment. The model architecture involved in this method is described in [reference needed]. Figure 2 , Figure 2HyOT-Align, the framework for single-cell multi-omics data integration based on optimal transport alignment in this embodiment, performs the following steps based on this architecture:

[0100] S10, obtain the hypergraph structure corresponding to the first cell modality and the second cell modality, learn the hypergraph structure corresponding to the two modalities through the parameter-shared hypergraph encoder, and obtain the first cell latent representation and the second cell latent representation, thereby preserving the structural information within the modality in a unified representation space;

[0101] The first-stage goal of HyOT-Align is to extract structure-enhanced cellular representations from each modality, enabling the embeddings to not only reflect the original feature similarity but also explicitly encode higher-order relationships at the cell population level. To this end, the model independently constructs a hypergraph structure within each modality and maps different modalities to a unified latent space through a parameter-shared hypergraph convolutional encoder, providing a stable geometric basis for subsequent cross-modal OT alignment.

[0102] Let the mode The set of cell nodes is In modal In the feature space, for each node Search its A set of nearest neighbors And form a hyperedge with this node and its nearest neighbors. The set of all hyperedges is composed of hyperedges. Thus, modality-specific hypergraphs are obtained. Hypergraph structures use an incidence matrix. It means that among them Its elements are defined as:

[0103]

[0104] Considering the differences in feature dimensions and scales across different modalities, the model first employs a modality-specific linear mapping to project the input onto a unified dimension. : Subsequently, HyOT-Align uses a parameter-shared hypergraph convolutional encoder to learn representations for each modality. Let... and These are the node degree matrix and the hyperedge degree matrix, respectively. The normalized hypergraph propagation operator used in this embodiment is defined as follows:

[0105]

[0106] Based on this propagation operator, a single-layer hypergraph convolution can be written as:

[0107]

[0108] in, For the first The layer can learn parameters, and the same set of parameters is shared across all modes. , is a non-linear activation function. After the ... Modes are obtained after layer propagation Structural enhancement embedding .

[0109] S20, determine the cross-modal cost matrix between the first cell latent representation and the second cell latent representation, determine the soft correspondence weights based on the cross-modal cost matrix, and determine the OT centroid of each cell in the first cell mode and the second cell mode according to the soft correspondence weights;

[0110] After S10, the internal structure of each modality is learned using a hypergraph structure. and After that, with , As input, cross-modal correspondences are characterized in the embedding space through optimal transmission, and the geometry of different modalities is aligned at both the distribution and instance levels.

[0111] Specifically, the model has obtained two modalities of structure-enhanced embedding representations. , This step further aligns the overall distribution structure of different modalities in the embedding space. Considering the systematic differences in noise levels and feature statistics of multimodal single-cell data, relying solely on a shared encoder is insufficient to guarantee the consistency of different modal embeddings in the global geometric structure. Therefore, HyOT-Align introduces a distribution-level alignment mechanism based on optimal transmission and efficiently estimates cross-modal transmission relationships during actual training using the Sinkhorn–Knopp algorithm.

[0112] First, a cross-modal cost matrix is ​​constructed in the embedding space to characterize the geometric differences between cell distributions of different modalities. , The cost matrix is ​​defined as:

[0113]

[0114] in This represents the first cell mode (hereinafter referred to as mode 1) in which the first cell mode is... The first cell and the second cell modality (hereinafter referred to as modality 2) The distance between cells in the embedding space. Based on this, HyOT-Alig does not directly solve for the theoretical optimization form of optimal transmission, but instead uses the Sinkhorn–Knopp algorithm to calculate the entropy-regularized optimal transmission plan. Specifically, the cross-modal transmission matrix is ​​defined as:

[0115]

[0116] in , The edge distribution is for two modes (uniform distribution is used in this embodiment). is the regularization coefficient. The soft correspondence weights between the two modes are given, and their elements are... Reflects the first mode in mode 1 The cell and mode 2 in the second The matching strength of each cell at the distribution level. The Sinkhorn algorithm depends only on the arrangement of the cost matrix and the edge distribution. If the order of the two modalities and the edge distribution are interchanged, the corresponding transfer matrix satisfies To avoid symbol confusion, this embodiment uses a uniform notation. As a notation for a cross-modal transmission matrix.

[0117] Based on the transmission matrix HyOT-Align further constructs cross-modal OT centroid representations as semantic targets for distribution-level alignment. For the first digit in modality 1... The centroid of the OT of the cell in mode 2 distribution is the same as that of the cell in mode 2. The centroids of OT for each of the 1 cells in modality 1 distribution are as follows:

[0118]

[0119] This centroid can be understood as the “alignment position” of a cell in modality 1 or 2 in the embedding space of another modality. Its construction process is entirely adaptively determined by the optimal transport plan, thereby encoding cross-modal geometric consistency at the distribution level.

[0120] S30, the first cell latent representation and the second cell latent representation are mapped into student projection representations through the student projection head, and the OT centroid is mapped into teacher projection representation through the teacher projection head;

[0121] After determining the OT centroid, in the distribution-level alignment phase of S30, HyOT-Align employs a momentum teacher mechanism to stabilize the cross-modal semantic signal provided by the OT centroid. Specifically, HyOT-Align introduces a lightweight multilayer perceptron (MLP) student projector after the supergraph encoder, mapping the modal embeddings output by the encoder to the student projection space. For modalities... The student projection representation is defined as the unified representation space used for cross-modal alignment and joint optimization in the model. The teacher network contains a teacher projection head with the same structure as the student projection head. Its parameters are updated using an exponential moving average of the student projection head parameters, and its input is an OT centroid representation constructed based on optimal transmission. And generate teacher projection representations for distribution-level alignment targets. The teacher network does not participate in backpropagation; its parameters are updated via an exponential moving average of the student projector head parameters, thus providing a stable alignment target during training.

[0122] Building upon this, HyOT-Align employs a distributed-level contrastive learning loss. In the student projection space, it treats the student projection representation of the current modality and its corresponding OT centroid teacher projection representation as positive sample pairs, while considering the teacher targets of other samples in the same modality as negative samples. Taking modality 1 as an example, its distributed-level OT alignment loss is defined as:

[0123]

[0124] in and These represent the outputs of the student projector and the teacher projector, respectively. Represents cosine similarity. This is the temperature coefficient. Similarly, the distributed-level OT alignment loss for mode 2 can be defined. The final distribution-level alignment loss is obtained by averaging the corresponding losses of the two modes:

[0125]

[0126] Through the aforementioned distribution-level optimal transmission alignment mechanism, HyOT-Align aligns the overall distribution structure of different modal embeddings without relying on explicit cell pairing relationships, and provides a stable and semantically consistent global reference for subsequent instance-level OT weighted contrastive learning.

[0127] S40, Construct a target loss function based on the student projection representation and the teacher projection representation, and perform backpropagation training on the hypergraph encoder and the student projection head;

[0128] In this step, the distribution-level optimal transport alignment in S30 aligns the geometry of different modal embeddings at the global level. However, this constraint mainly acts at the distribution level and may still be insufficient to characterize the fine-grained cross-modal correspondences between cells. To further enhance the alignment accuracy of cross-modal representations at the cell level, HyOT-Align introduces an instance-level optimal transport weighted contrastive learning mechanism on the basis of distribution-level alignment to perform fine-grained modeling of cross-modal instance relationships.

[0129] Instance-level alignment directly operates on the student projection space, sharing the same student projector head with distribution-level OT alignment, thus ensuring the consistency of the joint optimization objective. This student projection space serves as the core representation space for cross-modal joint optimization in HyOT-Align, and is constrained by both distribution-level and instance-level alignment losses. Specifically, instance-level alignment uses the cross-modal transfer matrix obtained at the distribution-level stage. Based on this, the transfer matrix characterizes the soft correspondence weights between cells of different modalities and can be regarded as a continuous estimate of cross-modal instance similarity. Unlike the strategy based on hard positive and negative sample partitioning in traditional contrastive learning, HyOT-Align utilizes... Cross-modal sample pairs are weighted to highlight high-confidence correspondences during optimization and naturally suppress the interference of unreliable matches on model training. Taking modality 1 as an example, the instance-level OT weighted contrastive loss to modality 2 is defined as:

[0130]

[0131] in The instance representation in the student projection space is used. This loss weights cross-modal sample pairs with optimal transport weights, allowing cell pairs with higher transport probabilities to have a greater impact on model parameter updates during training. To avoid instance-level alignment introducing bias in a single direction, HyOT-Align applies instance-level OT weighted contrast constraints symmetrically to the two modalities. Similarly, an instance-level loss from modality 2 to modality 1 can be defined. The final instance-level OT-weighted contrastive loss is obtained by averaging the losses from the two directions:

[0132]

[0133] Combining the aforementioned distribution-level and instance-level cross-modal alignment mechanisms, HyOT-Align learns a cross-modal consistent joint representation space by jointly optimizing multiple alignment objectives. During training, the model simultaneously applies a distribution-level optimal transport alignment loss and an instance-level OT-weighted contrastive loss, thereby collaboratively constraining the consistency of cross-modal representations at both the global distribution level and the local instance level. Specifically, the overall training objective of the model is defined as:

[0134]

[0135] in This represents the optimal transmission alignment loss at the distribution level, used to align the overall distribution structure of different modal embeddings; This represents instance-level OT-weighted contrastive loss, used to enhance the correspondence between cells across modalities at the local level; Hyperparameters are used to balance the two types of losses and control the relative importance of instance-level alignment in the overall optimization process.

[0136] In HyOT-Align, cross-modal joint representations are not constructed through explicit feature splicing or fusion operators, but rather by mapping cells from different modalities to the same Student projection space and imposing alignment constraints. Specifically, for modalities... Student projection display There is a cross-modal joint representation space as This means that cells from different modalities are mapped to the same student projection space, sharing a unified geometric coordinate system. This space serves as the final joint representation of the model and can be directly used for cross-modal clustering, visualization, and overall structure analysis of multimodal data.

[0137] S50 generates a joint cell representation based on the trained hypergraph encoder and student projector head.

[0138] During the inference phase of S50, HyOT-Align no longer introduces a teacher network, retaining only the hypergraph encoder and student projector heads to generate cross-modal joint representations. For paired multimodal data, the model can directly perform multi-omics integration analysis based on the joint representations; for unpaired multimodal data, the model can further utilize the optimal transfer matrix for cross-modal matching, or adopt a unified "match first, then integrate" process, thereby flexibly adapting to different types of multimodal single-cell data analysis tasks within the same framework.

[0139] In the technical solution provided in this embodiment, high-order relationships between cells are modeled based on hypergraph structures in each modality. The latent representation of cells is learned through a shared hypergraph encoder, thereby preserving structural information within the modality in a unified representation space. Subsequently, an optimal transfer mechanism is introduced to establish cell-level soft correspondences between different modalities, characterizing the geometric consistency between modalities without assuming explicit one-to-one pairing. Based on this, the corresponding structures learned by the optimal transfer are used to align and correct the cross-modal representations, enabling cells in different modalities to gradually converge in a unified latent space.

[0140] Verification of Examples

[0141] Based on the first embodiment, this embodiment selects three representative multi-omics datasets to conduct experiments on the HyOT-Align model obtained by the single-cell multi-omics data integration method based on optimal transmission alignment, and verifies its applicability and robustness in paired and unpaired multimodal single-cell data scenarios.

[0142] (1) Dataset preparation and preprocessing

[0143] (1.1) Paired multimodal dataset

[0144] This embodiment uses the dataset GSE194122 from the GEO database. This dataset originates from human bone marrow mononuclear cells (BMMCs). BMMCs are a heterogeneous cell population found in bone marrow, primarily composed of lymphocytes, monocytes, hematopoietic stem cells, and progenitor cells. They are an important model system for studying hematopoietic processes, immune function, and various hematological diseases. This dataset jointly measures gene expression and surface protein expression of the same cell (hereinafter referred to as the CITE dataset) and gene expression and chromatin accessibility (hereinafter referred to as the Multiome dataset), which naturally have a one-to-one correspondence at the cellular level. The data version used in this embodiment is provided by the official NeurIPS 2021 Multimodal Single-Cell Data Integration Challenge. The data has undergone preprocessing steps such as quality control, double cell removal, normalization, and cell type annotation according to the competition's unified process. This embodiment directly uses the processed data for modeling and experiments without introducing additional data cleaning or manual screening operations to ensure the reproducibility and fairness of the experimental results.

[0145] (1.2) Unpaired datasets

[0146] To verify the cross-modal alignment capability of HyOT-Align under conditions lacking explicit cell pairing information, this embodiment further selected the mouse embryonic and adult brain cortex (MEBC) multimodal dataset constructed by Chen et al. based on SNARE-seq technology, data number GSE126074. SNARE-seq is a pioneering single-cell sequencing technology that can simultaneously acquire scRNA-seq and scATAC-seq data from the same cell at the experimental level. In this embodiment, the preprocessed version provided by Tang et al. was used, which has completed standard quality control, feature filtering, and normalization operations.

[0147] It should be noted that although the dataset provides cell-level pairing information at the raw sequencing level, this embodiment does not use these real pairing relationships in the experimental setup. Instead, following the setup of Tang et al., a non-paired multimodal dataset is artificially constructed by shuffling the cell correspondence between RNA and ATAC modalities.

[0148] The details of the three datasets are shown in Table 1 below:

[0149] Table 1. Single-cell multi-omics datasets

[0150]

[0151] (2) Experimental design

[0152] To verify the performance of the HyOT-Align method proposed in this application in the integration of single-cell multi-omics data, this embodiment describes the experimental setup from two aspects: the selection of baseline methods and the implementation of models and parameter settings, so as to ensure the fairness and reproducibility of the experimental results.

[0153] The five representative single-cell multi-omics data integration methods selected in this embodiment are:

[0154] • Seurat v3 is one of the most widely used single-cell multi-omics integration frameworks. This method is based on an anchor matching mechanism, which identifies corresponding cell pairs between different modalities and uses these anchors to correct and align the data, thereby achieving joint representation learning.

[0155] • MOJITOO is a multimodal single-cell integration method based on canonical correlation analysis. This method constructs a low-dimensional common representation space for cells by learning a set of shared canonical components across different modalities.

[0156] • MOFA+ is a statistical model that integrates single-cell multi-omics, aiming to obtain low-dimensional characterization of cells based on Bayesian group factor analysis.

[0157] • Schem uses a quadratic programming framework to reweight features from different modalities to achieve consistent integration of multimodal data while preserving the biological structure of the main modality.

[0158] • CVQVAE is a multimodal integration method based on deep generative models. It maps data from different omics to a unified latent space by cross-training variational autoencoders and introducing a vector quantization mechanism.

[0159] In all experiments of this embodiment, the model is trained based on the overall optimization objective defined by the target loss function in the first embodiment, that is, by jointly optimizing the distribution-level optimal transport alignment loss and the instance-level OT weighted contrastive learning loss to learn a cross-modal unified representation. The Adam optimizer is used for parameter updates during model training, with an initial learning rate set to 0.001. In the hypergraph encoder, the ReLU function is used as a non-linear activation function to enhance the model's expressive power.

[0160] In the hypergraph construction phase, this embodiment sets the number of hypergraph neighbors for each node to k = 50. In the distributed OT alignment module, the temperature parameter for contrastive learning is set to... = 0.1; In instance-level OT weighted contrastive learning, the temperature parameter is set to = 0.07. Furthermore, the loss weight coefficient λ used to balance the alignment objectives at the distribution and instance levels is set to 1, ensuring that both types of alignment objectives have equal importance in the overall optimization process.

[0161] (3) Comparison of experimental results and analysis

[0162] To evaluate the performance of HyOT-Align in the task of integrating single-cell multi-omics data, this embodiment compares it with several representative existing methods, focusing on the integration performance of the model on paired and unpaired multi-omics datasets.

[0163] The results of all methods on the CITE and Multiome datasets for ARI, NMI and ASW are shown in Tables 2 and 3:

[0164] Table 2. Performance comparison of various methods on the CITE dataset

[0165]

[0166] Table 3. Performance comparison of various methods on the Multiome dataset

[0167]

[0168] Overall, HyOT-Align achieved the best results across all three evaluation metrics, demonstrating its ability to learn a more consistent and structurally sound joint representation space in paired multimodal data scenarios. Regarding cluster consistency metrics, HyOT-Align achieved scores of 0.71 and 0.78 on ARI and NMI, respectively, showing improvements over Seurat v3, MOJITOO, MOFA+, Schema, and CVQVAE. The improvement in ARI was particularly significant, indicating that HyOT-Align can more accurately recover the true cell type structure within the joint embedding space. In terms of embedding space structure quality, HyOT-Align also achieved the highest ASW score (0.55), indicating that it better maintains intra-cell compactness and inter-cell separability while ensuring cross-modal alignment. In contrast, some comparative methods, while performing similarly on NMI or ARI, showed a slight decrease in ASW, suggesting that their joint representations still have some shortcomings in intra-class compactness or inter-class separability.

[0169] In addition, to further intuitively evaluate the integration effect of different modalities in the joint representation space, this embodiment performs UMAP visualization analysis on the original modal representations and the integrated joint embeddings on a paired multimodal dataset. Figures 3 to 5This demonstrates the two-dimensional embedding distribution of the CITE dataset under different modalities and fusion results. For example... Figure 3 and Figure 4 As shown, for the CITE-seq dataset, RNA and Protein modalities exhibit a mixed distribution in their respective original feature spaces. Different cell types lack clear clustering structures in low-dimensional embeddings, demonstrating significant modal noise and structural disorder. In contrast, as... Figure 5 As shown, in the joint embedding space after HyOT-Align integration, different cell types can form relatively compact and continuous cluster structures, and cells from different modalities achieve good overlap on the same cell type, which significantly improves the interpretability of the embedding space.

[0170] like Figures 6 to 8 This paper presents the two-dimensional embedding distribution of the Multiome dataset under different modalities and fusion results, with all UMAP plots colored according to cell type. Figure 6 and Figure 7 As shown in the Multiome dataset, both RNA and ATAC modalities struggle to clearly represent cell type boundaries in the original embedding space, especially in the ATAC data, where different cell types highly overlap in the low-dimensional space, resulting in poor structural consistency. Figure 8 As shown, after joint representation learning using HyOT-Align, the RNA and ATAC modalities achieved relatively consistent alignment in the embedding space. Different cell types exhibited clearer separation structures in the joint embedding, indicating that the model can effectively alleviate modality differences and recover potential cell type-related structures. The visualization results of both paired multimodal datasets show that HyOT-Align can still learn a structurally clear and modality-independent joint embedding space even when the original modality representation structure is relatively chaotic, which is consistent with the results reflected by the aforementioned quantitative evaluation metrics.

[0171] To further evaluate HyOT-Align's cross-modal alignment capability in unpaired multimodal data scenarios, this embodiment performs UMAP visualization analysis on the joint embedding results on the MEBC dataset. Figure 9The results of two-dimensional embedding on the unpaired MEBC dataset are presented, with the left column colored by modality (RNA / ATAC) and the right column colored by cell type. The modality-based coloring results show that after HyOT-Align integration, the RNA and ATAC modalities do not form a significant modality separation structure in the joint embedding space. Cells of different modalities exhibit a highly overlapping distribution in the low-dimensional space, indicating that the model can effectively mitigate systematic shifts between modalities and achieve cross-modal alignment even in the absence of explicit cell pairing information. The cell type-based coloring results show that different cell types form relatively clear and continuous cluster structures in the joint embedding space, indicating that the representation learned by HyOT-Align not only maintains consistency at the modality level but also preserves biological structural information related to cell type.

[0172] (4) Ablation test

[0173] To analyze the roles of key modules in HyOT-Align in the multimodal integration task, this embodiment conducts ablation experiments on two paired multimodal datasets (CITE-seq and Multiome). In the ablation settings, the same data preprocessing procedures, model structure size, and training hyperparameters are maintained; only specific components in the model are removed or replaced to ensure fairness in the experimental comparison. Specifically, this includes: removing the distribution-level optimal transport alignment module (w / o Dist-OT), removing the instance-level OT-weighted contrastive learning module (w / o Inst-OT), retaining instance-level contrastive learning but not using OT weights (Inst-CL), and replacing the hypergraph encoder (MLP-Encoder) with a multilayer perceptron, with the full model used as a control.

[0174] Ablation test results as follows Figure 10 and Figure 11As shown in the figure, the full model achieves the best results on both datasets in terms of ARI, NMI, and ASW. Removing distribution-level OT alignment significantly degrades the overall performance of the model on both datasets, indicating that the lack of global distribution constraints significantly weakens the cross-modal alignment effect. In contrast, removing instance-level OT weighted contrastive learning results in relatively smaller performance degradation, but the ASW index drops more significantly, suggesting that the instance-level OT mechanism plays an important role in improving intra-class compactness and local structural consistency. The Inst-CL variant outperforms w / o Inst-OT on both datasets, but still falls short of the full model, indicating that instance-level contrastive learning itself can improve representation quality, while OT weights further enhance the reliability of cross-modal positive samples. Replacing the hypergraph encoder with an MLP encoder results in the most significant performance degradation on both datasets, indicating that the lack of high-order structural modeling capabilities has a significant negative impact on multimodal representation learning.

[0175] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0176] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for integrating single-cell multi-omics data based on optimal transport alignment, characterized in that, The method includes the following steps: S10, obtain the hypergraph structure corresponding to the first cell modality and the second cell modality, learn the hypergraph structure corresponding to the two modalities through the parameter-shared hypergraph encoder, and obtain the first cell latent representation and the second cell latent representation, thereby preserving the structural information within the modality in a unified representation space; S20, determine the cross-modal cost matrix between the first cell latent representation and the second cell latent representation, determine the soft correspondence weights based on the cross-modal cost matrix, and determine the OT centroid of each cell in the first cell mode and the second cell mode according to the soft correspondence weights; S30, the first cell latent representation and the second cell latent representation are mapped into student projection representations through the student projection head, and the OT centroid is mapped into teacher projection representation through the teacher projection head; S40, Construct a target loss function based on the student projection representation and the teacher projection representation, and perform backpropagation training on the hypergraph encoder and the student projection head; S50 generates a joint cell representation based on the trained hypergraph encoder and student projector.

2. The single-cell multi-omics data integration method based on optimal transport alignment as described in claim 1, characterized in that, In S10, the hypergraph structure uses the incidence matrix. express: ； in: ； ； ； In the formula, Represents a node its A set of nearest neighbors, Indicates the super edge. Denotes the set of superedges. This represents the total number of hyperedges in mode m. This represents the total number of nodes in mode m; The elements of the correlation matrix are defined as follows: 。 3. The single-cell multi-omics data integration method based on optimal transport alignment as described in claim 1 or 2, characterized in that, In S10, the hypergraph structure corresponding to two modes is learned through a parameter-sharing hypergraph encoder, including: S11, Modality-specific linear mapping is used to transform the input modal features Projecting to a unified dimension : ； In the formula, This represents the linear mapping parameter matrix corresponding to the m-th mode. This represents the bias term for the m-th mode; S12, let and Let the node degree matrix and hyperedge degree matrix be respectively, and let the normalized hypergraph propagation operator be defined as: ； In the formula, The incidence matrix characterizing the hypergraph structure; This represents the transpose of the incidence matrix; S13, based on propagation operator Determine one layer of hypergraph convolution: ； in, For the first The layer can learn parameters, and the same set of parameters is shared across all modes. , It is a non-linear activation function. 4.S14, after the first Modes are obtained after layer propagation The cell's potential representation: ； in, m=1, 2; This represents the potential representation of the first cell. This indicates the potential representation of the second cell.

5. The single-cell multi-omics data integration method based on optimal transport alignment as described in claim 1, characterized in that, In S20, the expression for the centroid of OT is: ； ； In the formula, Represents the first cell mode in the first cell mode individual cells The centroid of OT in the second cell modality distribution; This represents the j-th cell in the second cell modality. The centroid of OT under the first cell modality distribution; Indicating the first cell mode, the first individual cells , and the second cell modality individual cells The matching strength at the distribution level, i.e., the soft correspondence weight.

6. The single-cell multi-omics data integration method based on optimal transport alignment as described in claim 4, characterized in that, The expression for the soft corresponding weight is: ； In the formula, This represents the Sinkhorn–Knopp algorithm; C represents the cross-modal cost matrix; , These represent the edge distributions of the first and second cell modalities, respectively. is the regularization coefficient.

7. The single-cell multi-omics data integration method based on optimal transport alignment as described in claim 5, characterized in that, The expression for the cross-modal cost matrix C is: ； in: ； ； ； In the formula, Indicating the first mode in mode 1 The cell and the first in mode 2 The distance between individual cells in the embedded space; This indicates the number of cells in the first cell mode; Indicates the number of cells in the second cell modality; This represents the potential representation of the first cell. This indicates the potential representation of the second cell.

8. The method for integrating single-cell multi-omics data based on optimal transport alignment as described in any one of claims 4 to 6, characterized in that, In step S30, the student projection head and the teacher projection head satisfy the following loss function constraints during the mapping process: ； In the formula, This represents the distribution-level OT alignment loss corresponding to the first cell mode; This represents the distribution-level OT alignment loss corresponding to the second cell modality; in: ； ； In the formula, and These represent the outputs of the student projection head and the teacher projection head in the cell mode, respectively, with m=1 and 2; Indicates cosine similarity; This is the temperature coefficient.

9. The method for integrating single-cell multi-omics data based on optimal transport alignment as described in claim 1, characterized in that, The expression for the target loss function is: ； In the formula, This represents the distributed OT alignment loss. This represents the instance-level OT-weighted comparison loss; in: ； ； In the formula, This represents the distribution-level OT alignment loss corresponding to the first cell mode; This represents the distribution-level OT alignment loss corresponding to the second cell modality; This represents the instance-level OT-weighted contrast loss corresponding to the first cell modality; This represents the instance-level OT-weighted contrast loss corresponding to the second cell modality; in, ； ； ； ； In the formula, and These represent the outputs of the student projection head and the teacher projection head in the cell mode, respectively, with m=1 and 2; Indicates cosine similarity; , All are temperature coefficients.

10. A single-cell multi-omics data integration model based on optimal transport alignment, characterized in that, The single-cell multi-omics data integration model includes: The hypergraph encoder module is used to obtain the hypergraph structure corresponding to the first cell modality and the second cell modality. By learning the hypergraph structure corresponding to the two modalities through the parameter-shared hypergraph encoder, the potential representation of the first cell and the potential representation of the second cell are obtained, thereby preserving the structural information within the modality in a unified representation space. Distribution-level optimal transport alignment is used to determine the cross-modal cost matrix between the first and second cell latent representations. Based on the cross-modal cost matrix, soft correspondence weights are determined, and the OT centroids of each cell in the first and second cell modes are determined according to the soft correspondence weights. An instance-level OT weighted contrast learning module is used to map the first cell latent representation and the second cell latent representation into student projected representations through a student projector head, and to map the OT centroid into a teacher projected representation through a teacher projector head. A joint cell representation module is used to generate a joint cell representation based on the trained hypergraph encoder and student projector head, wherein the student projector representation and the teacher projector representation are backpropagated and trained on the hypergraph encoder and the student projector head based on the constructed target loss function.

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