Clustering methods for incomplete multi-omics cancer subtype data

Abstract

This invention proposes a clustering method for incomplete multi-omics cancer subtype data, belonging to the field of machine learning. The method includes: using a variational autoencoder to generate a shared latent representation and an omics-specific latent representation for each sample, capturing omics-specific biological features, and regularizing the representation distribution through reconstruction loss and KL divergence; employing a diffusion model framework to fuse the shared latent representation and omics-specific latent representation of multiple omics, generating a comprehensive representation that effectively handles incomplete data and enhances the comprehensive extraction of multi-omics information; optimizing the comprehensive representation and enhancing its consistency through two-level contrastive learning; jointly optimizing the clustering input by jointly optimizing the clustering loss, reconstruction loss, and semantic contrastive loss to generate a high-quality latent representation; and using an improved K-means clustering algorithm to analyze the multi-omics data based on the jointly optimized clustering input to obtain the final cancer subtype clustering results. This invention can improve the accuracy and robustness of cancer subtype identification.

Description

Technical Field

[0001] This invention belongs to the field of machine learning, and in particular relates to a clustering method for incomplete multi-omics cancer subtype data. Background Technology

[0002] Cancer is a highly heterogeneous disease, with patients responding to clinical treatment in significantly different ways. Studies have shown that molecular characteristics profoundly influence disease prognosis in tumors that are difficult to distinguish through histopathology. Therefore, to achieve personalized treatment, cancer subtype classification has become a research hotspot, precisely stratifying patients through molecular or phenotypic characteristics.

[0003] With advancements in biotechnology, the acquisition of multi-omics data has become increasingly convenient. Early methods relied on single-omics data, applying traditional clustering algorithms to predict cancer subtypes. However, single-omics data only partially characterize molecular features and often face the problem of incomplete data, such as missing mRNA, miRNA, and DNA methylation data in some samples, limiting the comprehensiveness and accuracy of the analysis. Integrating multi-omics data can provide a more comprehensive perspective, revealing potential patterns in cancer subtypes and deepening our understanding of the complex multi-level interactions between biomolecules, especially in scenarios with incomplete data. Multi-omics integration is crucial in subtype identification, but traditional clustering methods struggle to cope with the complexity of high-dimensional, heterogeneous, and incomplete data, requiring innovative methods to improve the accuracy and robustness of clustering. Variational autoencoders effectively capture specific omics features by generating probabilistic latent representations, utilize a diffusion model framework to fuse the latent distributions of incomplete omics, generate robust comprehensive representations, and combine contrastive learning to optimize multi-omics consistency and sample discriminability, providing an efficient solution for cancer subtype clustering with incomplete multi-omics data. Summary of the Invention

[0004] The purpose of this invention is to propose a clustering method for incomplete multi-omics cancer subtype data, which can effectively process incomplete multi-omics data and improve the accuracy and robustness of cancer subtype identification.

[0005] To achieve the above objectives, the technical solution of the present invention is: a clustering method for incomplete multi-omics cancer subtype data, specifically comprising:

[0006] S1. Omics encoding based on variational autoencoder framework: For non-missing omics data of each sample in incomplete multi-omics cancer subtype data, the shared encoder extracts shared features across omics and generates shared latent representations, and the omics-specific encoder extracts specific features of each omics and generates omics-specific latent representations.

[0007] S2. Information aggregation based on multi-omics diffusion model framework: The generated shared latent representation and omics-specific latent representation are used as the initial latent representation. During the forward diffusion process, noise is added to capture cross-omics shared biological features and omics-specific variations of the data. During the reverse denoising process, the hidden links between omics are integrated through a bidirectional cross-attention mechanism to generate a joint distribution. Finally, starting from the noise distribution, the data is repeatedly sampled and a comprehensive representation is generated through the reverse denoising process.

[0008] S3. Using the generated comprehensive representation as input, information aggregation and optimization are performed through a two-level contrastive learning framework: the two-level contrastive loss is composed of high-level contrastive loss and semantic-level contrastive loss, and two-level contrastive learning is performed to generate optimized representation;

[0009] S4. Joint Optimization and Clustering: Based on the extension of the K-means algorithm, cancer subtype data are clustered by using the optimized representation as the initial clustering input through an iterative optimization algorithm. At the same time, the clustering input is jointly optimized by clustering loss, reconstruction loss and semantic contrast loss to improve clustering performance and finally output the clustering results.

[0010] Preferably, the step of extracting shared features across omics and generating shared latent representations through a shared encoder, and extracting specific features of each omics and generating omics-specific latent representations through an omics-specific encoder, is as follows:

[0011] S1.1, using non-missing omics data from each sample in incomplete multi-omics cancer subtype data. As input; where: It is the first The first sample omics data, and To use the data after min-max normalization, Indicates sample The non-missing omics set, , For the set of real numbers, It is the feature dimension;

[0012] S1.2. Map the non-missing omics of each sample to the latent space through a shared encoder and an omics-specific encoder to generate Gaussian distribution parameters:

[0013]

[0014]

[0015] in: For the first Omics-specific encoders; , Representing data As an omics-specific encoder The mean and standard deviation of the approximate posterior distribution generated from the input; For shared encoders; , Representing data As a shared encoder The mean and standard deviation of the approximate posterior distribution of the input; , Omics-specific encoders and shared encoder Parameters;

[0016] The approximate posterior distribution is expressed as:

[0017]

[0018] in, This indicates that it is generated by an omics-specific encoder. Output the defined approximate posterior distribution. Indicates shared encoder Output the defined approximate posterior distribution; Indicates a Gaussian distribution; Represents a diagonal matrix; and They represent the samples respectively The parameters obtained by averaging the shared Gaussian distribution parameters of all non-missing omics:

[0019] ,

[0020] , Samples No. Omics-specific and shared latent representations for each omics are generated using reparameterization techniques:

[0021]

[0022] in, This represents element-wise multiplication. It follows a standard normal distribution. is a random vector, where I is the identity matrix.

[0023] Preferably, the lower bound of evidence is optimized through variational inference:

[0024]

[0025] in: Indicates sample No. Omics-specific variational autoencoder loss It is the KL divergence weight. Denotes KL divergence, and Let these represent the prior distributions set to capture the omics-specific latent representation distribution and the shared latent representation distribution, respectively. Indicates sample No. omics-specific reconstruction loss:

[0026] Reconstructing data from omics-specific latent representations and shared latent representations using omics-specific decoders :

[0027]

[0028] in, For omics Specific decoder, For decoder Parameters;

[0029] By decoder Output defined reconstruction distribution Represented as:

[0030]

[0031] in, To fix the hyperparameters;

[0032] The loss function is then expressed as:

[0033]

[0034] in: Indicates the approximate posterior distribution The expectations below Indicates the approximate posterior distribution The following expectations; Represents the omics-specific log-likelihood. Represents the shared log-likelihood, and the log-likelihood term. and and reconstructed distribution The optimization objectives ELBO of the variational autoencoder are interconnected.

[0035] Preferably, step S2 is implemented as follows:

[0036] S2.1, Share the latent representation of each sample generated in step S1. and omics-specific potential representations The initial latent representation is obtained by splicing. And used as input data, initial latent representation The dimension is , Each sample shares a latent representation and a feature dimension resulting from the concatenation of the omics-specific latent representation. , Shared latent representation for each sample Feature dimensions, Specific latent representations for each sample omics Feature dimensions;

[0037] S2.2, Gaussian noise is gradually added during the forward diffusion process:

[0038] , ;

[0039] in: These represent the latent representations at time step t in the forward diffusion process or the reverse denoising process, respectively. In the forward diffusion process... That is, the initial latent representation In the reverse denoising process For the initial latent representation of the prediction, This represents the total number of time steps in the forward diffusion process or the reverse denoising process. In the forward diffusion process, given a latent representation at time step t... Under what conditions is the latent representation The probability distribution, It follows a Gaussian distribution; This represents the noise scheduling coefficient at time step t during the forward diffusion process;

[0040] S2.3 The reverse denoising process uses the U-Net architecture and employs a bidirectional cross-attention mechanism to fuse features in the intermediate layer, learn the denoising distribution, and optimize parameters by minimizing the variational lower bound.

[0041]

[0042] in: For the inverse denoising process, given a latent representation at time step t Under what conditions is the latent representation The probability distribution is learned from the U-Net architecture, and the parameters of the U-Net architecture are... ; It is determined by the parameter as The U-Net architecture with potential representation The mean function is used as the input at time step t; It is determined by the parameter as The U-Net architecture with potential representation The covariance function is taken as input at time step t;

[0043] S2.4, From the perspective of noise distribution Initially, through the reverse denoising process Step sampling to generate a comprehensive representation Noise distribution Follows a standard normal distribution The sampling update formula in the reverse denoising process is:

[0044] , ,

[0045] in: Noise scheduling coefficient The cumulative product term, It is the index of time step t. It is the standard deviation parameter of time step t in the reverse denoising process;

[0046] Repeat the sampling process S times and take the average value to obtain the comprehensive representation. And project back Dimension;

[0047]

[0048] in, Let represent the initial latent representation of the prediction for the s'th sampling.

[0049] Preferably, by minimizing the variational lower bound Parameter optimization is performed, specifically expressed as:

[0050]

[0051] in: This represents the expectation of the probability distribution of the forward diffusion process. The initial latent representation of the model prediction The probability distribution, through optimization This makes the model predict A data distribution that approximates the true value, i.e., the initial latent representation. ; Denotes KL divergence, This indicates that the forward diffusion process is at the final time step. Time-latent representation probability distribution Represents a predefined prior distribution; This indicates that during the forward diffusion process, given the initial potential representation... and potential representation Under what conditions is the latent representation The probability distribution.

[0052] Preferably, step S3 is implemented as follows:

[0053] S3.1 Data Augmentation:

[0054] For comprehensive representation The row vector corresponding to each sample in the data Add random perturbations to generate enhanced representations :

[0055] ,

[0056] in This indicates a random perturbation. , The standard deviation is the preset value.

[0057] For comprehensive representation The row vector corresponding to each sample in the data Randomly select column index To perform feature permutation and generate enhanced representations , ;

[0058] S3.2 Extract the augmented representation corresponding to each sample using a multilayer perceptron (MLP). Advanced features and enhancement representation Advanced features And calculate the high-level contrast loss. :

[0059]

[0060] in: To control the similarity distribution using temperature parameters, This is a high-level positive sample pair similarity matrix. , This is the high-level negative sample pair similarity matrix. , Cosine similarity:

[0061] ,

[0062] in: for transpose, It is an L2 norm;

[0063] S3.3 Extracting high-level features through cluster head mapping semantic representation and advanced features semantic representation And calculate semantic-level contrastive loss. :

[0064]

[0065] in This is a semantic-level similarity matrix of positive sample pairs. , This is a semantic-level similarity matrix of negative sample pairs. :

[0066] ,

[0067] in for transpose;

[0068] S3.4, Compare losses based on higher levels Loss compared to semantic level Obtain contrast loss :

[0069]

[0070] in To control the semantic loss weights;

[0071] Calculate contrast loss gradient And perform iterative updates to the parameters:

[0072]

[0073]

[0074] in This is a set of parameters, including the weight matrix of the multilayer perceptron and the weight matrix of the clustering head; The learning rate;

[0075] Complete parameter set After iterative updates, the synthesized representation is adjusted through backpropagation. To optimize representation .

[0076] Preferably, the enhanced representation corresponding to each sample is extracted using a multilayer perceptron (MLP). Advanced features and enhancement representation Advanced features The details are as follows:

[0077]

[0078]

[0079] and Let represent the weight matrices of the first and second layer transformations of the multilayer perceptron, respectively. , , For the first hidden layer dimension, For the second hidden layer dimension, This is the ReLU activation function.

[0080] Preferably, the extraction of high-level features through cluster head mapping is... semantic representation and advanced features semantic representation The details are as follows:

[0081]

[0082]

[0083] in: This is the weight matrix in the clustering head used for feature mapping and clustering decisions. , The number of clusters, This is the Softmax activation function.

[0084] Preferably, step S4 is implemented as follows:

[0085] S4.1. Expand the optimized representation using the K-means algorithm. Select An initial cluster center To optimize the initial cluster distribution, where c'=1,..., c' represents the cluster index;

[0086] S4.2 Iterative optimization:

[0087] S4.2.1, in optimized form As the initial clustering input, it is used to optimize the representation. The row vector corresponding to each sample in the data Calculate row vectors With all cluster centers The Euclidean distance between them, and the row vectors Assign to the cluster with the smallest distance: , This represents the cluster label of the i-th sample. It is a row vector To the cluster center The square of the distance;

[0088] S4.2.2, Update Cluster Center : ,in, This indicates that for all clusters... row vectors Perform a summation operation. For clusters The number of samples;

[0089] S4.2.3, using clustering loss Reconstruction loss and semantic contrast loss The clustering input is jointly optimized, and the clustering results are obtained again based on the jointly optimized clustering input; total loss Represented as:

[0090]

[0091] in , Represents reconstruction loss Weighting and semantic contrast loss Weight;

[0092] S4.3 After the iteration termination condition is met, the clustering results are output, including the final cluster label for each sample. And ultimately, the cluster center of each cluster. .

[0093] Preferred clustering loss Reconstruction loss and semantic contrast loss The specific calculations are as follows:

[0094] Clustering loss:

[0095]

[0096] Reconstruction loss:

[0097]

[0098] in, It is the original i-th sample data. The decoder in step S1 is used to process the row vector. The result of the reconstruction ;

[0099] Semantic contrast loss:

[0100]

[0101] in, and The row vectors are obtained through the data augmentation method in step S3.1, the advanced feature extraction method in step S3.2, and the semantic representation extraction method in step S3.3, respectively. Two semantic representations of .

[0102] Compared with the prior art, the present invention has the following beneficial effects:

[0103] 1. Robust handling of incomplete data: By dynamically fusing incomplete omics cyclic distributions within a multi-omics diffusion model framework, this invention can effectively address the challenge of missing omics in multi-omics data, thereby significantly improving the robustness and reliability of data compared to traditional data imputation methods.

[0104] 2. Efficient probabilistic feature extraction: Variational autoencoders, by generating probabilistic potential representations and combining reconstruction and KL divergence regularization, can capture omics-specific biological features in omics data more accurately than traditional feature extraction methods.

[0105] 3. Multi-omics information fusion optimization: The multi-omics diffusion model framework integrates multi-omics information to generate efficient comprehensive representations. Combined with contrastive learning optimization, it surpasses traditional multi-omics methods and can extract shared information more effectively, making it suitable for complex data scenarios.

[0106] 4. Improved clustering accuracy: Based on the comprehensive representation optimized by contrastive learning and combined with the K-means algorithm, this invention can accurately identify cancer subtypes, and thus significantly improve the accuracy and biological significance of clustering results compared to traditional methods.

[0107] 5. Improved ability to process complex data: By combining variational autoencoders, multi-omics diffusion model frameworks and two-level contrastive learning, this invention can better process high-dimensional, satisfied and incomplete multi-omics data, enhance the understanding and analysis of complex molecular exchanges, and is suitable for large-scale omics analysis and clinical applications. Attached Figure Description

[0108] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0109] The following is in conjunction with the appendix Figure 1 The technical solution of the present invention will be described in detail below.

[0110] This invention proposes a clustering method for incomplete multi-omics cancer subtype data, specifically including:

[0111] S1. Omics encoding based on variational autoencoder framework: For non-missing omics data of each sample in incomplete multi-omics cancer subtype data, the shared encoder extracts shared features across omics and generates shared latent representations, and the omics-specific encoder extracts specific features of each omics and generates omics-specific latent representations.

[0112] The variational autoencoder combines a shared encoder and an omics-specific encoder to generate probabilistic latent representations for each omics student, replacing the traditional deterministic encoder; through variational inference and reparameterization techniques, it generates robust latent representations, enhancing the model's adaptability to noise, incomplete data, and data heterogeneity;

[0113] S2. Information aggregation based on multi-omics diffusion model framework: The generated shared latent representation and omics-specific latent representation are used as the initial latent representation. During the forward diffusion process, noise is added to capture cross-omics shared biological features and omics-specific variations of the data. During the reverse denoising process, the hidden links between omics are integrated through a bidirectional cross-attention mechanism to generate a joint distribution. Finally, starting from the noise distribution, the data is repeatedly sampled and a comprehensive representation is generated through the reverse denoising process.

[0114] Two-way cross attention Integrating links between omics, among which These are the query matrix, key matrix, and value matrix, respectively. and These are the initial latent representation and the updated representation after processing by the bidirectional cross-attention mechanism, respectively.

[0115] S3. Using the generated comprehensive representation as input, information aggregation and optimization are performed through a two-level contrastive learning framework: the two-level contrastive loss is composed of high-level contrastive loss and semantic-level contrastive loss, and two-level contrastive learning is performed to generate optimized representation;

[0116] S4. Joint Optimization and Clustering: Based on the extension of the K-means algorithm, cancer subtype data are clustered by using the optimized representation as the initial clustering input through an iterative optimization algorithm. At the same time, the clustering input is jointly optimized by clustering loss, reconstruction loss and semantic contrast loss to improve clustering performance and finally output the clustering results.

[0117] In this embodiment, the process of extracting shared features across omics and generating shared latent representations using a shared encoder, and extracting specific features of each omics and generating omics-specific latent representations using an omics-specific encoder, is as follows:

[0118] S1.1, using non-missing omics data from each sample in incomplete multi-omics cancer subtype data. As input; where: It is the first The first sample omics data, and To use the data after min-max normalization, Indicates sample The non-missing omics set, , For the set of real numbers, It is the feature dimension;

[0119] S1.2. Map the non-missing omics of each sample to the latent space through a shared encoder and an omics-specific encoder to generate Gaussian distribution parameters:

[0120]

[0121]

[0122] in: For the first Omics-specific encoders; , Representing data As an omics-specific encoder The mean and standard deviation of the approximate posterior distribution generated from the input; For shared encoders; , Representing data As a shared encoder The mean and standard deviation of the approximate posterior distribution of the input; , Omics-specific encoders and shared encoder Parameters;

[0123] The approximate posterior distribution is expressed as:

[0124]

[0125] in, This indicates that it is generated by an omics-specific encoder. Output the defined approximate posterior distribution. Indicates shared encoder Output the defined approximate posterior distribution; Indicates a Gaussian distribution; Represents a diagonal matrix; and They represent the samples respectively The parameters obtained by averaging the shared Gaussian distribution parameters of all non-missing omics are used to ensure that the shared representation integrates cross-omics shared information.

[0126] ,

[0127] , Samples No. Omics-specific and shared latent representations for each omics are generated using reparameterization techniques for subsequent multi-omics factor analysis frameworks and contrastive learning.

[0128]

[0129] in, This represents element-wise multiplication. It follows a standard normal distribution. is a random vector, where I is the identity matrix.

[0130] In this embodiment, the lower bound of the optimized evidence is obtained through variational inference:

[0131]

[0132] in: Indicates sample No. Omics-specific variational autoencoder loss It is the KL divergence weight. Denotes KL divergence, and Let these represent the prior distributions set to capture the omics-specific latent representation distribution and the shared latent representation distribution, respectively. Indicates sample No. omics-specific reconstruction loss:

[0133] Reconstructing data from omics-specific latent representations and shared latent representations using omics-specific decoders :

[0134]

[0135] in, For omics Specific decoder, For decoder Parameters;

[0136] By decoder Output defined reconstruction distribution Represented as:

[0137]

[0138] in, To fix the hyperparameters;

[0139] The loss function is then expressed as:

[0140]

[0141] in: Indicates the approximate posterior distribution The expectations below Indicates the approximate posterior distribution The following expectations; Represents the omics-specific log-likelihood. Represents the shared log-likelihood, and the log-likelihood term. and and reconstructed distribution The optimization objectives ELBO of the variational autoencoder are interconnected.

[0142] In this embodiment, step S2 is implemented as follows:

[0143] S2.1, Share the latent representation of each sample generated in step S1. and omics-specific potential representations The initial latent representation is obtained by splicing. And used as input data, initial latent representation The dimension is , Each sample shares a latent representation and a feature dimension resulting from the concatenation of the omics-specific latent representation. , Shared latent representation for each sample Feature dimensions, Specific latent representations for each sample omics Feature dimensions;

[0144] S2.2, Gaussian noise is gradually added during the forward diffusion process:

[0145] , ;

[0146] in: These represent the latent representations at time step t in the forward diffusion process or the reverse denoising process, respectively. In the forward diffusion process... That is, the initial latent representation In the reverse denoising process For the initial latent representation of the prediction, This refers to the total number of time steps in the forward diffusion process or the reverse denoising process (in this embodiment, ...). ); In the forward diffusion process, given a latent representation at time step t... Under what conditions is the latent representation The probability distribution, It follows a Gaussian distribution; This represents the noise scheduling coefficient at time step t during the forward diffusion process;

[0147] S2.3 The reverse denoising process uses the U-Net architecture and employs a bidirectional cross-attention mechanism to fuse features in the intermediate layer, learn the denoising distribution, and optimize parameters by minimizing the variational lower bound.

[0148]

[0149] in: For the inverse denoising process, given a latent representation at time step t Under what conditions is the latent representation The probability distribution is learned from the U-Net architecture, and the parameters of the U-Net architecture are... ; It is determined by the parameter as The U-Net architecture with potential representation The mean function is used as the input at time step t; It is determined by the parameter as The U-Net architecture with potential representation The covariance function is taken as input at time step t;

[0150] S2.4, From the perspective of noise distribution Initially, through the reverse denoising process Step sampling to generate a comprehensive representation Noise distribution Follows a standard normal distribution The sampling update formula in the reverse denoising process is:

[0151] , ,

[0152] in: Noise scheduling coefficient The cumulative product term, It is the index of time step t. It is the standard deviation parameter of time step t in the reverse denoising process;

[0153] Repeat the sampling process S times and take the average value to obtain the comprehensive representation. And project back Dimension;

[0154]

[0155] in, Let represent the initial latent representation of the prediction for the s'th sampling.

[0156] In this embodiment, by minimizing the variational lower bound Parameter optimization is performed, specifically expressed as:

[0157]

[0158] in: This represents the expectation of the probability distribution of the forward diffusion process. The initial latent representation of the model prediction The probability distribution, through optimization This makes the model predict A data distribution that approximates the true value, i.e., the initial latent representation. ; Denotes KL divergence, This indicates that the forward diffusion process is at the final time step. Time-latent representation probability distribution Represents a predefined prior distribution; This indicates that during the forward diffusion process, given the initial potential representation... and potential representation Under what conditions is the latent representation The probability distribution; this embodiment uses the Adam optimizer with a learning rate of 1e-4 and a batch size of 32.

[0159] In this embodiment, step S3 is implemented as follows:

[0160] S3.1 Data Augmentation:

[0161] For comprehensive representation The row vector corresponding to each sample in the data Add random perturbations to generate enhanced representations :

[0162] ,

[0163] in This indicates a random perturbation. , , The preset standard deviation (in this embodiment) );

[0164] For comprehensive representation The row vector corresponding to each sample in the data Randomly select column index To perform feature permutation and generate enhanced representations , ;

[0165] S3.2 Extract the augmented representation corresponding to each sample using a multilayer perceptron (MLP). Advanced features and enhancement representation Advanced features And calculate the high-level contrast loss. :

[0166]

[0167] in: To control the similarity distribution for temperature parameters (in this embodiment, ), This is a high-level positive sample pair similarity matrix. , This is the high-level negative sample pair similarity matrix. , Cosine similarity:

[0168] ,

[0169] in: for transpose, It is an L2 norm;

[0170] S3.3 Extracting high-level features through cluster head mapping semantic representation and advanced features semantic representation And calculate semantic-level contrastive loss. :

[0171]

[0172] in This is a semantic-level similarity matrix of positive sample pairs. , This is a semantic-level similarity matrix of negative sample pairs. :

[0173] ,

[0174] in for transpose;

[0175] S3.4, Compare losses based on higher levels Loss compared to semantic level Obtain contrast loss :

[0176]

[0177] in To control the semantic loss weights (in this embodiment, );

[0178] Calculate contrast loss gradient And perform iterative updates to the parameters:

[0179]

[0180]

[0181] in The parameter set includes the weight matrix of the multilayer perceptron and the weight matrix of the clustering head (the weight matrix of the first layer transformation of the MLP). The weight matrix of the second layer transformation and And the weight matrix in the clustering head used to implement feature mapping and clustering decisions. ); The learning rate (in this embodiment, Train for 100 epochs until convergence;

[0182] Complete parameter set After iterative updates, the synthesized representation is adjusted through backpropagation. To optimize representation .

[0183] In this embodiment, the enhanced representation corresponding to each sample is extracted using a multilayer perceptron (MLP). Advanced features and enhancement representation Advanced features The details are as follows:

[0184]

[0185]

[0186] and Let represent the weight matrices of the first and second layer transformations of the multilayer perceptron, respectively. , , For the first hidden layer dimension, For the second hidden layer dimension, This is the ReLU activation function.

[0187] In this embodiment, the extraction of high-level features through cluster head mapping is described. semantic representation and advanced features semantic representation The details are as follows:

[0188]

[0189]

[0190] in: This is the weight matrix in the clustering head used for feature mapping and clustering decisions. , The number of clusters, This is the Softmax activation function.

[0191] In this embodiment, step S4 is specifically implemented as follows:

[0192] S4.1. The K-means algorithm (i.e., K-means++ algorithm) is used to expand the optimized representation. Select An initial cluster center To optimize the initial cluster distribution, where c'=1,..., c' represents the cluster index;

[0193] S4.2 Iterative optimization:

[0194] S4.2.1, in optimized form As the initial clustering input, it is used to optimize the representation. The row vector corresponding to each sample in the data Calculate row vectors With all cluster centers The Euclidean distance between them, and the row vectors Assign to the cluster with the smallest distance: , This represents the cluster label of the i-th sample. It is a row vector To the cluster center The square of the distance;

[0195] S4.2.2, Update Cluster Center : ,in, This indicates that for all clusters... row vectors Perform a summation operation. For clusters The number of samples;

[0196] S4.2.3, using clustering loss Reconstruction loss and semantic contrast loss The clustering input is jointly optimized, and the clustering results are obtained again based on the jointly optimized clustering input; total loss Represented as:

[0197]

[0198] in , Represents reconstruction loss Weighting and semantic contrast loss Weight;

[0199] S4.3 After the iteration termination condition is met, the clustering results are output, including the final cluster label for each sample. And ultimately, the cluster center of each cluster. .

[0200] In this embodiment, clustering loss Reconstruction loss and semantic contrast loss The specific calculations are as follows:

[0201] Clustering loss:

[0202]

[0203] Reconstruction loss:

[0204]

[0205] in, It is the original i-th sample data. The decoder in step S1 is used to process the row vector. The result of the reconstruction ;

[0206] Semantic contrast loss:

[0207]

[0208] in, and The row vectors are obtained through the data augmentation method in step S3.1, the advanced feature extraction method in step S3.2, and the semantic representation extraction method in step S3.3, respectively. Two semantic representations of .

[0209] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A clustering method for incomplete multi-omics cancer subtype data, characterized in that, Specifically, it includes: S1. Omics encoding based on variational autoencoder framework: For non-missing omics data of each sample in incomplete multi-omics cancer subtype data, the shared encoder extracts shared features across omics and generates shared latent representations, and the omics-specific encoder extracts specific features of each omics and generates omics-specific latent representations. S2. Information aggregation based on multi-omics diffusion model framework: The generated shared latent representation and omics-specific latent representation are used as the initial latent representation. During the forward diffusion process, noise is added to capture cross-omics shared biological features and omics-specific variations of the data. During the reverse denoising process, the hidden links between omics are integrated through a bidirectional cross-attention mechanism to generate a joint distribution. Finally, starting from the noise distribution, the data is repeatedly sampled and a comprehensive representation is generated through the reverse denoising process. S3. Using the generated comprehensive representation as input, information aggregation and optimization are performed through a two-level contrastive learning framework: the two-level contrastive loss is composed of high-level contrastive loss and semantic-level contrastive loss, and two-level contrastive learning is performed to generate optimized representation; S4. Joint Optimization and Clustering: Based on the extension of the K-means algorithm, cancer subtype data are clustered by using the optimized representation as the initial clustering input through an iterative optimization algorithm. At the same time, the clustering input is jointly optimized by clustering loss, reconstruction loss and semantic contrast loss to improve clustering performance and finally output the clustering results. The specific implementation method of step S2 is as follows: S2.1, Share the latent representation of each sample generated in step S1. and omics-specific potential representations The initial latent representation is obtained by splicing. And used as input data, initial latent representation The dimension is , Each sample shares a latent representation and a feature dimension resulting from the concatenation of the omics-specific latent representation. , Shared latent representation for each sample Feature dimensions, Specific latent representations for each sample omics Feature dimensions; S2.2, Gaussian noise is gradually added during the forward diffusion process: ， ； in: These represent the latent representations at time step t in the forward diffusion process or the reverse denoising process, respectively. In the forward diffusion process... That is, the initial latent representation In the reverse denoising process For the initial latent representation of the prediction, This represents the total number of time steps in the forward diffusion process or the reverse denoising process. In the forward diffusion process, given a latent representation at time step t... Under what conditions is the latent representation The probability distribution, It follows a Gaussian distribution; This represents the noise scheduling coefficient at time step t during the forward diffusion process; S2.3 The reverse denoising process uses the U-Net architecture and employs a bidirectional cross-attention mechanism to fuse features in the intermediate layer, learn the denoising distribution, and optimize parameters by minimizing the variational lower bound. in: For the inverse denoising process, given a latent representation at time step t Under what conditions is the latent representation The probability distribution is learned from the U-Net architecture, and the parameters of the U-Net architecture are... ; It is determined by the parameter as The U-Net architecture with potential representation The mean function is used as the input at time step t; It is determined by the parameter as The U-Net architecture with potential representation The covariance function is taken as input at time step t; S2.4, From the perspective of noise distribution Initially, through the reverse denoising process Step sampling to generate a comprehensive representation Noise distribution Follows a standard normal distribution The sampling update formula in the reverse denoising process is: ， ， in: Noise scheduling coefficient The cumulative product term, It is the index of time step t. It is the standard deviation parameter of time step t in the reverse denoising process; Repeat the sampling process S times and take the average value to obtain the comprehensive representation. And project back Dimension; in, Let represent the initial latent representation predicted by the s'th sampling; The specific implementation method of step S3 is as follows: S3.1 Data Augmentation: For comprehensive representation The row vector corresponding to each sample in the data Add random perturbations to generate enhanced representations : ， in This indicates a random perturbation. , The standard deviation is the preset value. For comprehensive representation The row vector corresponding to each sample in the data Randomly select column index To perform feature permutation and generate enhanced representations , ; S3.2 Extract the augmented representation corresponding to each sample using a multilayer perceptron (MLP). Advanced features and enhancement representation Advanced features And calculate the high-level contrast loss. : in: To control the similarity distribution using temperature parameters, This is a high-level positive sample pair similarity matrix. , This is the high-level negative sample pair similarity matrix. , Cosine similarity: ， in: for transpose, It is an L2 norm; S3.3 Extracting high-level features through cluster head mapping semantic representation and advanced features semantic representation And calculate semantic-level contrastive loss. : in This is a semantic-level similarity matrix of positive sample pairs. , This is a semantic-level similarity matrix of negative sample pairs. : ， in for transpose; S3.4, Compare losses based on higher levels Loss compared to semantic level Obtain contrast loss : in To control the semantic loss weights; Calculate contrast loss gradient And perform iterative updates to the parameters: in This is a set of parameters, including the weight matrix of the multilayer perceptron and the weight matrix of the clustering head; The learning rate; Complete parameter set After iterative updates, the synthesized representation is adjusted through backpropagation. To optimize representation .

2. The incomplete multi-omics cancer subtype data clustering method according to claim 1, characterized in that, The process involves extracting shared features across omics using a shared encoder and generating shared latent representations, and extracting omics-specific features using an omics-specific encoder and generating omics-specific latent representations, as detailed below: S1.1, using non-missing omics data from each sample in incomplete multi-omics cancer subtype data. As input; where: It is the first The first sample omics data, and To use the data after min-max normalization, Indicates sample The non-missing omics set, , For the set of real numbers, It is the feature dimension; S1.

2. Map the non-missing omics of each sample to the latent space through a shared encoder and an omics-specific encoder to generate Gaussian distribution parameters: in: For the first Omics-specific encoders; , Representing data As an omics-specific encoder The mean and standard deviation of the approximate posterior distribution generated from the input; For shared encoders; , Representing data As a shared encoder The mean and standard deviation of the approximate posterior distribution of the input; , Omics-specific encoders and shared encoder Parameters; The approximate posterior distribution is expressed as: in, This indicates that it is generated by an omics-specific encoder. Output the defined approximate posterior distribution. Indicates shared encoder Output the defined approximate posterior distribution; Indicates a Gaussian distribution; Represents a diagonal matrix; and They represent the samples respectively The parameters obtained by averaging the shared Gaussian distribution parameters of all non-missing omics: ， , Samples No. Omics-specific and shared latent representations for each omics are generated using reparameterization techniques: in, This represents element-wise multiplication. It follows a standard normal distribution. is a random vector, where I is the identity matrix.

3. The incomplete multi-omics cancer subtype data clustering method according to claim 2, characterized in that, Optimize the lower bound of evidence through variational inference: in: Indicates sample No. Omics-specific variational autoencoder loss It is the KL divergence weight. Denotes KL divergence, and Let these represent the prior distributions set to capture the omics-specific latent representation distribution and the shared latent representation distribution, respectively. Indicates sample No. omics-specific reconstruction loss: Reconstructing data from omics-specific latent representations and shared latent representations using omics-specific decoders : in, For omics Specific decoder, For decoder Parameters; By decoder Output defined reconstruction distribution Represented as: in, To fix the hyperparameters; The loss function is then expressed as: in: Indicates the approximate posterior distribution The expectations below Indicates the approximate posterior distribution The following expectations; Represents the omics-specific log-likelihood. Represents the shared log-likelihood, and the log-likelihood term. and and reconstructed distribution The optimization objectives ELBO of the variational autoencoder are interconnected.

4. The incomplete multi-omics cancer subtype data clustering method according to claim 1, characterized in that, By minimizing the variational lower bound Parameter optimization is performed, specifically expressed as: in: This represents the expectation of the probability distribution of the forward diffusion process. The initial latent representation of the model prediction The probability distribution, through optimization This makes the model predict A data distribution that approximates the true value, i.e., the initial latent representation. ; Denotes KL divergence, This indicates that the forward diffusion process is at the final time step. Time-latent representation probability distribution Represents a predefined prior distribution; This indicates that during the forward diffusion process, given the initial potential representation... and potential representation Under what conditions is the latent representation The probability distribution.

5. The incomplete multi-omics cancer subtype data clustering method according to claim 1, characterized in that, The augmented representation corresponding to each sample is extracted using a multilayer perceptron (MLP). Advanced features and enhancement representation Advanced features The details are as follows: and Let represent the weight matrices of the first and second layer transformations of the multilayer perceptron, respectively. , , For the first hidden layer dimension, For the second hidden layer dimension, This is the ReLU activation function.

6. The method for clustering incomplete multi-omics cancer subtype data according to claim 1, characterized in that, The high-level features are extracted through cluster head mapping. semantic representation and advanced features semantic representation The details are as follows: in: This is the weight matrix in the clustering head used for feature mapping and clustering decisions. , The number of clusters, This is the Softmax activation function.

7. The incomplete multi-omics cancer subtype data clustering method according to claim 6, characterized in that, Step S4 is implemented as follows: S4.

1. Expand the optimized representation using the K-means algorithm. Select An initial cluster center To optimize the initial cluster distribution, where c'=1,..., c' represents the cluster index; S4.2 Iterative optimization: S4.2.1, in optimized form As the initial clustering input, it is used to optimize the representation. The row vector corresponding to each sample in the data Calculate row vectors With all cluster centers The Euclidean distance between them, and the row vectors Assign to the cluster with the smallest distance: , This represents the cluster label of the i-th sample. It is a row vector To the cluster center The square of the distance; S4.2.2, Update Cluster Center : ,in, This indicates that for all clusters... row vectors Perform a summation operation. For clusters The number of samples; S4.2.3, using clustering loss Reconstruction loss and semantic contrast loss The clustering input is jointly optimized, and the clustering results are obtained again based on the jointly optimized clustering input; total loss Represented as: in , Represents reconstruction loss Weighting and semantic contrast loss Weight; S4.3 After the iteration termination condition is met, the clustering results are output, including the final cluster label for each sample. And ultimately, the cluster center of each cluster. .

8. The incomplete multi-omics cancer subtype data clustering method according to claim 7, characterized in that, Clustering loss Reconstruction loss and semantic contrast loss The specific calculations are as follows: Clustering loss: Reconstruction loss: in, It is the original i-th sample data. The decoder in step S1 is used to process the row vector. The result of the reconstruction ; Semantic contrast loss: in, and The row vectors are obtained through the data augmentation method in step S3.1, the advanced feature extraction method in step S3.2, and the semantic representation extraction method in step S3.3, respectively. Two semantic representations of .

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