Biological data visualization and batch correction system based on deep manifold learning

Abstract

The application discloses a biological data visualization and batch correction system based on deep manifold learning, which embeds a given data set into a two-dimensional or three-dimensional visualization space based on Euclidean manifold or hyperbolic manifold under the premise of considering specific task types, corresponding to biological data of the type "time fixed" or "time evolution" respectively. Specifically, the system learns the relationship between data points based on the local scale shrinkage technique through end-to-end training, converts the data to the visualization space while preserving the data geometric structure, and corrects the batch effect. The application has better effects in discovering complex biological data relationships, revealing time trajectories and processing complex batch factors.

Description

Technical Field

[0001] This invention relates to the field of high-dimensional bioinformatics data visualization, specifically to a biological data visualization and batch correction system based on deep manifold learning. Background Technology

[0002] Existing products lack a unified framework to address various application scenarios (data clustering, developmental trajectory inference, etc.) and a range of technical requirements (structure preservation, batch correction, etc.). They often require multiple separate methods for downstream analysis of biological data, preventing products from flexibly selecting effective algorithms based on the inherent properties of the data. This is typically manifested in independent batch correction algorithms (e.g., Harmony and scVI), independent "time-fixed" or "time-evolutionary" visualization algorithms (e.g., t-SNE, UMAP, IVIS, and PHATE), visualization algorithms suitable for small datasets, and fast visualization algorithms suitable for new datasets. Dimensionality reduction and visualization play crucial roles in biological data analysis, such as the biological interpretation of single-cell transcriptome data. In practical applications, there is an urgent need for a visualization method that is applicable to various application scenarios, including clustering and developmental trajectory inference, while also meeting multiple technical requirements, particularly the ability to preserve the inherent structure of the data and perform batch correction. Summary of the Invention

[0003] This invention integrates biological data visualization and batch correction tasks into a unified framework, proposing a biological data visualization and batch correction system based on deep manifold learning. It addresses issues such as batch effects, low-distortion embedding, and "data crowding" or "data distortion" in large-scale datasets. Furthermore, it attempts to develop a scalable pre-trained model to embed new homogeneous or heterogeneous data. This system achieves batch correction while preserving structure and can be used as a pre-trained model to embed new data.

[0004] A biological data visualization and batch correction system based on deep manifold learning, comprising a semantic module and a visualization module;

[0005] The semantic module is used to extract semantic information from the original data, thereby constructing an accurate data semantic embedding graph structure; the semantic module includes a data augmentation unit, a batch label augmentation unit, and a local scale shrinkage unit;

[0006] The data enhancement unit is used to generate new data, thereby expanding the data.

[0007] The batch label enhancement unit is used to generate batch labels for the enhanced new data;

[0008] The local scale shrinking unit is used to compress the Euclidean distance between the semantic embeddings corresponding to the original data and its augmented data, so as to better estimate the local geometry of the potential topological manifold and more accurately describe the relationship between the data.

[0009] The visualization module is used for data visualization embedding, constructing a visualization embedding graph structure, and preserving the semantic structure of the data; the visualization module includes a geometric structure preservation loss unit, a manifold embedding unit, and a batch structure graph unit.

[0010] The geometric structure preservation loss unit maps high-dimensional data to a low-dimensional embedding space while preserving the data's geometric structure.

[0011] The manifold embedding unit is used to adapt to the inherent characteristics of the data and provide a suitable embedding space for the data, so that clusters of similar types of "time-fixed" data are close to each other in the visualization space, and clusters of different types are far apart; so that "time-evolutionary" data can show a continuous differentiation trajectory at different differentiation stages.

[0012] The batch structure graph unit constructs a batch structure graph based on batch labels, thereby maintaining the structure while removing batch effects.

[0013] Furthermore, it also includes a preprocessing module for reducing potential noise in the data; the preprocessing module includes a normalization and logarithmic processing unit, a data standardization unit, and a principal component analysis unit.

[0014] Furthermore, it also includes a heterogeneity correction module, which is used to unify the number of dimensions and dimensional attributes of heterogeneous new data and model input data.

[0015] Furthermore, the data augmentation unit performs data augmentation through the following interpolation method:

[0016]

[0017] in, For the enhanced data; N(x) is the representation vector of data i; d is the number of features; N(x) is the number of features. i The data point x is defined. i A list of k nearest neighbors; combined parameter r u ~U(0, p U ) is generated by a uniform distribution, where p U It is a hyperparameter and is set to 1.

[0018] Furthermore, the batch label enhancement unit enhances batch labels using the following interpolation method:

[0019]

[0020] in, For enhanced batch labels; y i It is the batch label for data i.

[0021] Furthermore, the similarity between semantic embeddings in the local scale shrinking unit. for:

[0022]

[0023] Where γ is the local scale contraction coefficient; Represents the original data x i Corresponding semantic embedding Represents the original data x i Augmented data The corresponding semantic embedding v is the degree of freedom of the student's t-distribution; C v It is the normalization function of v; the Euclidean distance between semantic embeddings. Defined as:

[0024]

[0025] Furthermore, the geometry preservation loss is defined as:

[0026]

[0027] Where b is the batch size; It is a semantic embedding based on semantic component learning. and Calculate the undirected similarity; It is a visual embedding based on visual module learning. and Calculate the undirected similarity; undirected similarity u ij Defined as:

[0028] u ij =u i|j +u j|i -2u i|j u j|i

[0029] Among them, u j|i Defined as directed similarity, it is obtained by transforming the distance measure using the Student t-distribution.

[0030] The student t-distribution is represented as:

[0031]

[0032] Where v is the degree of freedom of the student t-distribution; v inse Set to 100; v in vi Set as a hyperparameter. C v It is the normalization function of v, defined as:

[0033]

[0034] Furthermore, the manifold embedding unit includes an Euclidean manifold embedding unit adapted to "time-fixed" data and a hyperbolic manifold embedding unit adapted to "time-evolving" data; the hyperbolic manifold embedding unit includes two embedding models: the Poincaré model and the Lorentz model.

[0035] For any point Exponential mapping operation of the Poincaré model Mapping the embedding from the tangent space to the hyperbolic space, it is represented as:

[0036]

[0037] in, It is an opening sphere, d is the dimension of the visualization space; the negative constant -K is the curvature of the hyperbolic manifold, K>0; conformal factor It's a Möbius strip; the tangent vector v is not equal to 0. For any point... It is represented as:

[0038]

[0039] For any point Exponential mapping operation of the Lorentz model Mapping the embedding from the tangent space to the hyperbolic space, it is represented as:

[0040]

[0041] in

[0042] Furthermore, the similarity between the visualization embeddings in the visualization module Redefining:

[0043]

[0044] Where β represents the batch structure diagram G batch Importance; v is the degrees of freedom of the student's t-distribution; C v It is the normalization function of v; Choose an appropriate distance metric based on the type of biological data; for example, use Euclidean distance for "time-fixed" data and hyperbolic distance for "time-evolutionary" data; and consider the edge weights of the batch structure graph. Defined as:

[0045]

[0046] The beneficial effects of this invention are as follows:

[0047] (1) The neural network visualization analysis system with structure preservation and batch correction proposed in this invention is a parameterized, end-to-end model with multiple functions and can save data information in the form of parameters.

[0048] (2) This invention is adapted to the visualization analysis of biological data with "fixed time" and "time evolution".

[0049] (3) The present invention has the function of simultaneously realizing batch correction and visualization.

[0050] (4) This invention can be used as a pre-trained model to realize the visualization analysis and label annotation analysis of homogeneous or heterogeneous data. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the neural network visualization analysis system for structure preservation and batch correction according to the present invention, including a semantic module and a visualization module.

[0052] Figure 2 This is a schematic diagram of the graph structure of the neural network visualization analysis system for structure preservation and batch correction of the present invention, including a semantic embedding graph, a visualization embedding graph, and a batch structure graph.

[0053] Figure 3 This is a flowchart illustrating the application of the heterogeneous correction module, preprocessing module, and pre-trained model when embedding new data in this invention.

[0054] Figure 4 This is a visualization result of the invention on single-cell transcriptome data of mouse retinal neurons (RGCs).

[0055] Figure 5 This is a visualization result of the present invention on single-cell transcriptome data of human cellular landscape cells (HCL).

[0056] Figure 6 This is the evaluation result of the geometric structure preservation effect of the present invention on single-cell transcriptome data of RGC and HCL.

[0057] Figure 7 This is the batch correction and visualization result of the present invention on multiple batches of "time-evolution" single-cell transcriptome data.

[0058] Figure 8 This invention preserves the geometric structure of multiple batches of "time-evolution" single-cell transcriptome data. Detailed Implementation

[0059] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0060] The present invention provides a biological data visualization and batch correction system (DV) based on deep manifold learning, which has the ability to maintain the inherent structure of the data and handle batch effects. It is applicable to a variety of datasets from different application domains and data sizes. The system includes a semantic module and a visualization module, as well as a preprocessing module and a heterogeneous correction module adapted to tasks involving embedding heterogeneous new data.

[0061] In the data preprocessing stage, the preprocessing module employs a series of key preprocessing operations to remove potential noise from the data, including normalization and logarithmic operations, a data standardization module (scaling the test data using the mean and standard deviation learned from the training data when embedding new data), and a principal component analysis module (mapping the test data into multiple principal components using the principal component analysis model learned from the training data when embedding new data). To address heterogeneity (where training and test data have different feature names and numbers), a heterogeneity correction module is used before performing preprocessing operations to overcome the heterogeneity problem in the test data. This involves selecting identical features present in both the training and test data, maintaining the original values ​​for identical features in the test data, setting missing features to 0, and removing redundant features.

[0062] This invention's biological data visualization and batch correction system based on deep manifold learning uses a six-layer neural network, comprising two main components: a semantic module (input data dimension -500-300-100) and a visualization module (100-300-100-3 / 2). The number of neurons can also be flexibly set. The visualization embedding layer is typically set to 2 or 3 dimensions, but can also be flexibly set to other dimensions to learn the data's embedding representation. The neural network uses the Adam stochastic gradient descent optimization algorithm and is trained for 300 epochs. In experimental testing, the model typically only needs to be trained for 50 epochs to achieve good visualization results. The neural network uses the Leaky Rectified Linear Unit (LeakyReLU) activation function to process the hidden layers because the LeakyReLU activation function can calculate gradients even where the input is less than zero, avoiding uneven gradient directions. Simultaneously, batch normalization (BN) is uniformly performed on the hidden layers, ensuring that the input to each layer of the neural network maintains the same distribution.

[0063] The two main components of the system are described below:

[0064] Component A: Semantic Module

[0065] The semantic module is used to extract semantic information from the raw data, thereby constructing an accurate data semantic embedding graph structure. It includes a data augmentation unit and a batch label augmentation unit. The neural network corresponding to this semantic module is defined as follows:

[0066] z se =m θ (x) (5)

[0067] Where x represents the original data and θ represents the parameters that the semantic components need to be optimized.

[0068] (I) Unit A-1, Data Augmentation Unit

[0069] The data augmentation unit generates new data to supplement the original data and improve the model's generalization ability by combining data within the neighborhood, interpolating, or using mixups. This embodiment uses linear interpolation to achieve data augmentation.

[0070]

[0071] in, Let d be the feature vector of data i, and d be the number of features. N(x) i The data point x is defined. i A list of k nearest neighbors; combined parameter r u ~U(0, p U ) is generated by a uniform distribution, where p U This is a hyperparameter set to 1. This allows us to obtain a new dataset. It includes raw data and augmented data

[0072] (II) Unit A-2, Batch Label Enhancement Unit

[0073] Considering that unit A-1 has undergone data augmentation, this component uses a similar method to obtain batch labels for the augmented data.

[0074]

[0075] Among them, y i It is the batch label of data i, and the new dataset is defined as

[0076] (III) Unit A-3, Local Scale Contraction Unit

[0077] Local scale shrinking units are used to compress the original data x. i and its enhanced data Corresponding semantic embedding and Euclidean distance between To better estimate the local geometry of the underlying topological manifold and more accurately describe the relationships between data.

[0078] Therefore, the original data x i and its enhanced data Similarity between corresponding semantic embeddings Redefining:

[0079]

[0080] Where γ is the local scale contraction coefficient, and Euclidean distance between semantic embeddings. Defined as:

[0081]

[0082] II. Component B: Visualization Module

[0083] The visualization module is used to learn data visualization embeddings and construct the visualization embedding graph structure G. vi To preserve the semantic structure of the data, the neural network corresponding to this module is defined as follows:

[0084] z vi =m φ (z se (10)

[0085] Among them, z se For semantic embedding, z vi For visual embedding, φ is the parameter that the visual component needs to be optimized.

[0086] (I) Element B-1, geometrically preserved loss element

[0087] Geometric structure preserving loss units preserve the geometric structure of data while mapping high-dimensional data to a low-dimensional (2 or 3-dimensional) embedding space, which helps humans intuitively understand the true structure and distribution of data.

[0088] L as defined in this invention GSP The loss function is expressed as:

[0089]

[0090] Where b is the batch size (number of data items). It is a semantic embedding based on semantic module learning. and Calculate the undirected similarity (edge ​​weights in graph structures). It is a visual embedding based on visual module learning. and Calculate the undirected similarity. Undirected similarity u ij Defined as:

[0091] u ij =u i|j +u j|i -2u i|j u j|i (12)

[0092] Among them, u j|i Defined as directed similarity, it is obtained by transforming the distance measure using the Student t-distribution.

[0093] The t-student distribution defined in this invention is expressed as:

[0094]

[0095] Where v is the degrees of freedom of the student's t-distribution. v in se Set to 100, v in vi Set as a hyperparameter. C v It is the normalization function of v, defined as:

[0096]

[0097] (ii) Unit B-2, manifold embedded unit

[0098] The manifold embedding units include Euclidean manifold embedding units adapted for "time-fixed" data and hyperbolic manifold embedding units adapted for "time-evolutionary" data. In the visualization space, different types of data in "time-fixed" data should be clustered separately, with clusters of similar types close to each other and clusters of different types far apart; data at different differentiation stages in "time-evolutionary" data should show continuous differentiation trajectories.

[0099] A Euclidean manifold is a manifold with zero curvature. Applied to the DV_Eu model, its metric is defined as... The length of a geodesic is a straight line in Euclidean space, and the distance between two points is defined as:

[0100]

[0101] A hyperbolic manifold is a Riemannian manifold with a negative constant curvature of -K (K > 0). This invention employs two manifold models to implement hyperbolic embedding:

[0102] (1) Poincaré model

[0103] The Poincaré model corresponds to the Riemannian manifold. Applied to the DV_Poin model, where It's a kickoff, the standard Conform factor The distance between two points is defined as:

[0104]

[0105] For any embedding point Exponential mapping operations Mapping the embedding from the tangent space to the hyperbolic space, it is represented as:

[0106]

[0107] in, It is a Möbius stripe, where the tangent vector v is not equal to 0, for any embedding point. It is represented as:

[0108]

[0109] (2) Lorentz Model

[0110] The Lorentz model corresponds to the Riemannian manifold. Applied to the DV_Lor model, where Measurement The distance between two points is defined as:

[0111]

[0112] Exponential mapping operations Mapping the embedding from the tangent space to the hyperbolic space, it is represented as:

[0113]

[0114] in,

[0115] The Lorentz model avoids the numerical instability that may occur in the Poincaré distance. The Lorentz inner product is defined as:

[0116]

[0117] (III) Unit B-3, Batch Structure Diagram Unit

[0118] The batch structure graph unit constructs a batch structure graph based on batch labels (edge ​​weights use Euclidean distance) and integrates it with the visualized embedded graph structure, thereby removing the batch effect problem while preserving the structure.

[0119] Therefore, visualizing the similarity between embeddings Redefining:

[0120]

[0121] Here, β represents the importance of the batch structure diagram. Choose an appropriate distance metric based on the type of biological data; for example, use Euclidean distance for "time-fixed" data and hyperbolic distance for "time-evolutionary" data, and consider the edge weights of batch structure graphs. Defined as:

[0122]

[0123] This invention integrates semantic component A and visualization component B into a unified framework to achieve unified loss function optimization, including several epochs, each epoch containing several batches, calculating the loss function based on each batch, and updating the model parameters θ and φ with the help of the backpropagation algorithm.

[0124] The following two specific embodiments illustrate the effectiveness of the neural network visualization analysis system with structure preservation and batch correction of the present invention.

[0125] In the first embodiment, Figure 4 and Figure 5 This invention demonstrates the visualization effect of the proposed DV method on time-fixed single-cell transcriptome data (where there is no batch effect problem). Figure 4 a and Figure 5 a employs the DV_Eu method based on Euclidean manifolds proposed in this invention. Figure 4 b and Figure 5 b employs the DV_Poin method based on Poincaré hyperbolic manifolds proposed in this invention. Figure 4 c and Figure 5 c employs the DV_Lor method based on the Lorentz hyperbolic manifold proposed in this invention. Furthermore, the proposed DV method is compared with a series of state-of-the-art baseline methods, such as principal component analysis (PCA). Figure 4 d and Figure 5 d) t-distributed random nearest neighbor embedding (t-SNE) Figure 4 g and Figure 5 g) Unified manifold approximation and projection (UMAP) Figure 4 h and Figure 5 h), IVIS ( Figure 4 e and Figure 5 e), PHATE Figure 4 f and Figure 5 f) and Poin_maps( Figure 4 i). Figure 6 The invention demonstrates the effectiveness of the proposed DV method and baseline method in terms of local and global geometry preservation metrics.

[0126] In datasets with large numbers of cell samples and cell clusters, such as mouse retinal neurons (RGCs), Figure 4 a~i) and human cellular landscape cells (HCL, Figure 5 Data sets a~h), DV( Figure 4 a~c and Figure 5 a~c) compared to the baseline method ( Figure 4 d~i and Figure 5 (d~h) shows significant advantages. Although DV, Poin_maps, UMAP, and t-SNE are all capable of distinguishing individual cell types in RGC and HCL, DV achieves superior local and global structural preservation performance. Figure 6 a, b). More importantly, the hyperbolic manifold-based DV_Poin and DV_Lor methods exhibit better global structure preservation performance in RGC cells than the Euclidean manifold-based DV_Eu method, especially the Poincaré model-based DV_Poin. Specifically, Cartpt-RGC clusters in DV_Poin ( Figure 4 b) and Poin_maps Figure 4 i) Cells are close to each other in hyperbolic visualization space, but separated in visualization spaces of other methods. This indicates that hyperbolic visualization space has a stronger ability to preserve the global hierarchical structure of cells. In HCL cells, there are mainly six cell populations (fetal stromal cells, fetal epithelial cells, adult endothelial cells, endothelial cells, adult stromal cells, and immune cells). In DV_Eu, these cell populations are close to each other. Figure 5 a), but more dispersed in the t-SNE latent space ( Figure 5 g). HCL cells contain two cell sources (adult cells and fetal cells), in DV_Eu( Figure 5 In a), their respective cell clusters are close to each other and there is good differentiation between the two cell sources, but in UMAP embedding there is more confusion. Figure 5 h). Theoretically, DV_Poin( Figure 5 b) and DV_Lor( Figure 5 c) It has a larger spatial capacity for structured storage, thus gaining greater power to push apart different clusters. This is helpful for the analysis of label-free (cell type) data, such as partitioned visualization analysis (e.g., the DV_Poin hyperbolic visualization space can be divided into six main regions). Compared to DV_Eu, some clusters belonging to adult endothelial cells (intestinal cells with immune function) are closer to immune cells (mainly B cells). Meanwhile, UMAP and t-SNE are generally not effective at visualizing large cell samples. For example, the "cell crowding" problem in t-SNE (… Figure 5In g), different clusters are evenly distributed in the embedding space, making it difficult to effectively identify the main clusters and effectively mine different cell types. This is the "cell distortion" problem in UMAP. Figure 5 h), different clusters are distorted and mixed. DV overcomes the above problems because it learns a more reliable semantic graph based on a nonlinear deep neural network and uses batch training, while t-SNE and UMAP use all data for training. Their hyperparameters (e.g., "perplexity" in t-SNE) must be adapted to a larger number of cells, but increasing "perplexity" will significantly increase the computational cost of t-SNE. DV can naturally handle a large number of cell samples, and its time complexity is linearly related to the number of input cells. In addition, PCA ( Figure 4 d and Figure 5 d), IVIS ( Figure 4 e and Figure 5 e) and PHATE Figure 4 f and Figure 5 f) It performs poorly on these large single-cell transcriptome datasets, which are mainly “time-fixed”.

[0127] In the second embodiment, Figure 7 This paper demonstrates the visualization effect of the proposed DV method on "time-evolutionary" single-cell transcriptome data (which suffers from batch effect problems). Figure 7 a employs the DV_Eu method based on Euclidean manifolds proposed in this invention. Figure 7 b employs the DV_Poin method based on Poincaré hyperbolic manifolds proposed in this invention. Figure 7 c employs the DV_Lor method based on the Lorentz hyperbolic manifold proposed in this invention. Furthermore, the proposed DV method is compared with a series of state-of-the-art baseline methods, such as t-SNE ( Figure 7 g), UMAP Figure 7 h), IVIS ( Figure 7 d) PHATE Figure 7 e) scPhere based on Euclidean manifolds Figure 7 f) and scPhere_wn (based on hyperbolic manifold) Figure 7 i). Figure 8 The paper demonstrates the performance of the proposed DV method and baseline methods on local and global geometry preservation metrics across all batches. Due to the complex multi-batch dataset, the geometry preservation metrics are presented using box plots. Furthermore, Figure 8Effects analysis was conducted for different dimensions of the embedding space (with a focus on 2D or 3D visualization space). For example, Harmony_UMAP_2 represents the geometric structure preservation effect of using the Harmony batch correction method and the UMAP visualization method in the 2D visualization space; scVI_IVIS_2 represents the geometric structure preservation effect of using the scVI batch correction method and the IVIS visualization method in the 2D visualization space; and DV_Eu_20 represents the geometric structure preservation effect of using the DV_Eu batch correction and visualization method in the 20D embedding space.

[0128] Specifically, compared to the baseline method, DV_Poin( Figure 7 b) and DV_Lor( Figure 7 c) More intuitive visualizations and more competitive performance were achieved on the "Time Evolution" dataset, such as epithelial cells (batch information for disease origin, disease state, and location factors from 30 patients). In epithelial cells, the developmental sequence from intestinal stem cells to terminally differentiated cells within the Poincaré disc was easily discernible. Figure 7 (b, c) The center of the disk is a stem cell, which helps to visually explain cell differentiation: one trajectory is from stem cells to secretory TA cells, to immature goblet cells, to goblet cells; the other trajectory is from stem cells to TA2 cells, to immature intestinal cells, and then to intestinal cells. Conversely, when cells are embedded in an Euclidean manifold, the developmental trajectory is less obvious. Figure 7 f). t-SNE( Figure 7 g), UMAP Figure 7 h), DV_Eu( Figure 7 a) IVIS Figure 7 d) PHATE Figure 7 e) and scPhere_wn( Figure 7 The two-dimensional visualization of i) is reasonable, although there are some small spurious clusters in the t-SNE embeddings, a spurious cluster of goblet cells near intestinal cells exists in the DV_Eu, IVIS, and scPhere_wn embeddings, and multiple cell types are merged in the PHATE embedding (e.g., m cells and TA2 cells). Developmental trajectories are not obvious when cell types in the DV_Eu and scPhere_wn embeddings are missing. Furthermore, DV_Poin and DV_Lor have significant local (i) characteristics compared to the baseline approach for Euclidean manifolds. Figure 8 a) and global ( Figure 8 b) The geometric structure retains its advantages, and these advantages increase significantly with the increase of the dimension of the embedding space.

[0129] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A biological data visualization and batch correction system based on deep manifold learning, characterized in that, The system includes a semantic module and a visualization module; The semantic module is used to extract semantic information from the original data, thereby constructing an accurate data semantic embedding graph structure; the semantic module includes a data augmentation unit, a batch label augmentation unit, and a local scale shrinkage unit; The data enhancement unit is used to generate new data, thereby expanding the data. The batch label enhancement unit is used to generate batch labels for the enhanced new data; The local scale shrinking unit is used to compress the Euclidean distance between the semantic embeddings corresponding to the original data and its augmented data, so as to better estimate the local geometry of the potential topological manifold and more accurately describe the relationship between the data. The visualization module is used for data visualization embedding, constructing a visualization embedding graph structure, and preserving the semantic structure of the data; the visualization module includes a geometric structure preservation loss unit, a manifold embedding unit, and a batch structure graph unit. The geometric structure preservation loss unit maps high-dimensional data to a low-dimensional embedding space while preserving the data's geometric structure. The manifold embedding unit is used to adapt to the inherent characteristics of the data and provide a suitable embedding space for the data, so that clusters of similar types of "time-fixed" data are close to each other in the visualization space, and clusters of different types are far apart; so that "time-evolutionary" data can show a continuous differentiation trajectory at different differentiation stages. The batch structure graph unit constructs a batch structure graph based on batch labels, thereby maintaining the structure while removing batch effects.

2. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, It also includes a preprocessing module for reducing potential noise in the data; the preprocessing module includes a normalization and logarithmic processing unit, a data standardization unit, and a principal component analysis unit.

3. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, It also includes a heterogeneity correction module, which is used to unify the number of dimensions and dimensional attributes of heterogeneous new data and model input data.

4. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, The data augmentation unit performs data augmentation using the following interpolation method: ； in, For the enhanced data; It is data The representation vector; It is the number of features; Data points were defined. of A list of nearest neighbors; combined parameters It is generated by a uniform distribution, where It is a hyperparameter and is set to 1.

5. The biological data visualization and batch correction system based on deep manifold learning according to claim 4, characterized in that, The batch label enhancement unit enhances batch labels using the following interpolation method: ； in, For enhanced batch labels; It is data Batch labels.

6. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, The similarity between semantic embeddings in the local scale shrinking unit for: ； in, It is the local scale contraction coefficient; Represents raw data Corresponding semantic embedding ; Represents raw data Augmented data The corresponding semantic embedding ; Students Degrees of freedom of distribution; yes The normalization function; the Euclidean distance between semantic embeddings. Defined as: 。 7. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, The geometry preservation loss is defined as: ； in, It refers to the batch size; It is a semantic embedding based on semantic component learning. and Calculate the undirected similarity; It is a visual embedding based on visual module learning. and Calculate undirected similarity; undirected similarity Defined as: ； in, Defined as directed similarity, it uses student... Obtained by distribution transformation distance metric; The students The distribution is represented as: ； in, Students Degrees of freedom of distribution; In Set to 100; In Set as a hyperparameter; yes The normalization function is defined as: 。 8. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, The manifold embedding unit includes an Euclidean manifold embedding unit adapted to "time-fixed" data and a hyperbolic manifold embedding unit adapted to "time-evolving" data; the hyperbolic manifold embedding unit includes two embedding models: the Poincaré model and the Lorentz model; For any point Exponential mapping operation of the Poincaré model Mapping the embedding from the tangent space to the hyperbolic space, it is represented as: ； in, It's a kickoff. It is the dimension of the visualized space; a negative constant. It is the curvature of the hyperbolic manifold. Conform factor It is the Möbius strip; tangent vector Not equal to 0; For any point It is represented as: ； For any point Exponential mapping operation of the Lorentz model Mapping the embedding from the tangent space to the hyperbolic space, it is represented as: ； in ; .

9. The biological data visualization and batch correction system based on deep manifold learning according to claim 1, characterized in that, Similarity between visualization embeddings in the visualization module Redefining: ； in, Representative batch structure diagram The importance of; Students Degrees of freedom of distribution; yes The normalization function; Choose an appropriate distance metric based on the type of biological data: Euclidean distance is used for "time-fixed" data, and hyperbolic distance is used for "time-evolutionary" data; edge weights in batch structure graphs. Defined as: 。

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