Identification of microbe–disease signed associations via multi-scale variational graph autoencoder based on signed message propagation

Abstract

Background

Plenty of clinical and biomedical research has unequivocally highlighted the tremendous significance of the human microbiome in relation to human health. Identifying microbes associated with diseases is crucial for early disease diagnosis and advancing precision medicine.

Results

Considering that the information about changes in microbial quantities under fine-grained disease states helps to enhance a comprehensive understanding of the overall data distribution, this study introduces MSignVGAE, a framework for predicting microbe-disease sign associations using signed message propagation. MSignVGAE employs a graph variational autoencoder to model noisy signed association data and extends the multi-scale concept to enhance representation capabilities. A novel strategy for propagating signed message in signed networks addresses heterogeneity and consistency among nodes connected by signed edges. Additionally, we utilize the idea of denoising autoencoder to handle the noise in similarity feature information, which helps overcome biases in the fused similarity data. MSignVGAE represents microbe-disease associations as a heterogeneous graph using similarity information as node features. The multi-class classifier XGBoost is utilized to predict sign associations between diseases and microbes.

Conclusions

MSignVGAE achieves AUROC and AUPR values of 0.9742 and 0.9601, respectively. Case studies on three diseases demonstrate that MSignVGAE can effectively capture a comprehensive distribution of associations by leveraging signed information.

Background

Microbes are a class of microorganisms that typically exist as single cells or cell colonies [1]. Accumulated research has shown that microbial communities primarily consist of viruses, archaea, bacteria, and protozoa, and they have close interactions with human hosts [2, 3]. The majority of commensal microorganisms in humans are harmless and even have mutually beneficial relationships with their human hosts. Human microbiota can resist pathogen invasion, promote nutrient absorption, and enhance metabolic capabilities [4]. For example, probiotics can stimulate the host’s immune system by producing immune-modulatory signals, enhancing protection against pathogens [5]. Therefore, ecological imbalance or dysbiosis of microbial communities can lead to human diseases [6,7,8,9,10,11,12]. Furthermore, studies have shown that microbial metabolism can significantly influence clinical responses to drugs, and drug administration can also have specific effects on microbial communities [3, 13, 14]. For example, Panebianco et al. reported interactions between gut microbiota and anticancer drugs, affecting drug efficacy and side effects [15]. Maier et al. discovered that approximately 24% of drugs designed for the human body have inhibitory effects on microorganisms, particularly antipsychotic drugs [16]. Despite the growing body of research that uncovers the role of microorganisms in the development of human diseases, our understanding of how microorganisms residing in the human body impact human health and contribute to diseases remains limited. The identification of microbes associated with diseases and the prediction of trends in microbial population changes can not only deepen our understanding of potential disease mechanisms but also facilitate early diagnosis and advancements in precision medicine.

In recent years, there has been a proliferation of computational methods for identifying disease-related microbes [17]. These methods can be broadly categorized into four groups: network-based methods, matrix factorization methods, regularization methods, and neural network methods, as discussed by Wang et al. [18] and Wen et al. [19]. (1) Network-based methods: This category includes methods that leverage topological information from networks constructed using multiple databases. For instance, Lei et al. designed LGRSH, which applies the node2vec [20] algorithm to obtain low-dimensional representations and employs an improved rule-based inference method to predict disease-related microbes [21]. (2) Matrix factorization methods: The core idea of these methods is to factorize the input matrix into two lower-dimensional matrices while preserving the reconstructive property. For example, Peng et al. introduced RNMFMDA, which employs random walk with restart for reliable negative sampling. They then employ a neighborhood regularized logistic matrix factorization method to predict disease-related microbes [22]. (3) Regularization methods: These methods involve applying different forms of regularization to least square classifications. Xu et al. proposed MDAKRLS, which combines Kronecker regularized least square with hamming interaction spectral similarity to predict the likelihood of microbe-disease associations [23]. (4) Neural network methods: This category of methods has gained considerable popularity in recent years. Long et al. introduced GATMDA, a framework that represents microbes and diseases and predicts associations using an optimized graph attention network with inductive matrix completion (Fig. 1) [24].

Fig. 1

Framework of MSignVGAE. A Calculate the similarities for diseases and microbes. B Adopt signed message propagation strategy and VGAE to obtain latent representation for microbes and diseases. C Leverage XGBoost for predicting potential disease-related microbes with signs

With the accumulation of microbe-disease association data, no research has yet utilized the information on microbial quantity changes under disease status to predict microbe-disease associations, which hampers the comprehensive capture of data and feature distribution between diseases and microbes. Furthermore, most existing models for signed graph representation learning are predominantly designed for social networks and struggle to effectively capture the signed structural characteristics of biological networks [25, 26]. In the realm of social networks, several notable methods for signed graph representation learning have been developed. Derr et al. pioneered the use of Signed Graph Convolutional Network (SGCN [27]), which builds upon the theory of structural balance to obtain signed graph representations. Huang et al. and Li et al. introduced two models, SiGAT [28] and SNEA [29], respectively, which leverage attention mechanisms to differentiate the importance of different neighboring nodes. More recently, Li et al. combined spectral graph theory with graph signal processing techniques and presented a powerful model called SLGNN [30] for capturing the structural information of signed graphs. Taking a spectral perspective, they effectively retained the similarity and dissimilarity between connected nodes by preserving the low-frequency and high-frequency information.

Although significant progress has been made in microbe-disease association prediction tasks, we still face some challenges [31]. First and foremost, the main challenge lies in how to effectively capture a more comprehensive and authentic data distribution using this signed message in microbe-disease association databases. Furthermore, there is a lack of consistency in the conditions of repeated biological experiment validations, and conflicting microbe-disease signed association information also exists in the signed association databases. Modeling the significant amount of noise in association data remains a key issue. Lastly, addressing biased similarity data solely through similarity fusion is insufficient to completely mitigate this bias. It is crucial to explore effective methods that can reduce bias in microbe-disease association studies.

In this study, based on signed message propagation, we propose a framework, Multi-scale Sign Variational Graph AutoEncoder (MSignVGAE), for microbe-disease signed association prediction. MSignVGAE utilizes a graph variational autoencoder to model noisy signed association data and extends the multi-scale concept from previous work [32] to enhance the representational power of the graph variational autoencoder. The key contribution of our work lies in the development of a novel strategy for propagating signed message in signed networks. This strategy specifically addresses the propagation process between different nodes, effectively managing the heterogeneity and consistency among nodes connected by various signed edges. Additionally, building upon the similarity network fusion [33] method that combines multiple disease similarity matrixes and microbe similarity matrixes, we further employ the idea of denoising autoencoders to add noise to the similarity data and reconstruct signed associations through the graph variational autoencoder to overcome the bias issue present in the similarity data. MSignVGAE utilizes similarity information as node features to represent the heterogeneous graph of microbe-disease associations and then employs a multiple classifier XGBoost [34] for predicting the signed associations between diseases and microbes. Notably, MSignVGAE is the first method that utilizes signed message to predict microbe-disease signed associations. The AUROC value and AUPR value of MSignVGAE reached 0.9742 and 0.9601, respectively. Furthermore, case studies on three different diseases demonstrate that MSignVGAE, by leveraging the signed message, can capture a more comprehensive distribution of associations.

Results and discussion

Experiment settings

In this study, we employed tenfold cross-validation to ensure the accuracy and reliability of MSignVGAE. We utilized a range of commonly used metrics, including AUROC, AUPR, precision, recall, F1, and accuracy, to evaluate the performance of across all comparison experiments [35, 36]. Considering the sparsity and reliability of the microbe-disease signed association data, this work focuses primarily on experiments conducted using the Peryton database. In the SNF section, the number of neighbors for diseases and microbes in the KNN algorithm is set to 5 and 140, respectively. In the sign graph convolution encoder part, we employed three scales of multi-scale encoders for similarity networks. The scales used were 64, 32, and 16. Moreover, we set the parameters of the XGBoost classifier as default. To control the learning rate during training, we adopted the StepLR strategy, where the learning rate progressively updated until it reached the specified number of epochs. This strategy helps optimize the training process and enhance model convergence.

Ablation study

To analyze the contributions of each module in MSignVGAE, this section conducted ablation experiments based on the Peryton database. The results are shown in Table 1, where MSignVGAE refers to the complete model without removing any modules. Del_Noise represents the model with the similarity feature denoising module removed from MSignVGAE. Del_Multi represents the model with the multi-scale SignGCN removed from the sign graph convolutional encoder module. Del_SignGCN represents the model with a simple GCN module replacing the SignGCN module in MSignVGAE. This section aims to analyze the individual contributions of each component to the overall model accuracy and performance.

Table 1 Performance of ablation experiments based on Peryton database

As shown in Table 1, it is evident that the whole MSignVGAE model, without removing any modules, achieves the highest performance across various metrics. Among the three ablated modules, the SignGCN module contributes the most. In fact, even when using the original GCN, which is not specifically designed for signed graph neural networks, the performance in the prediction task of microbe-disease signed associations is still considerable, with AUROC and AUPR values reaching 0.9418 and 0.9065, respectively. This can be attributed to the fact that the similarity features of diseases and microbes already possess certain representational capacity before undergoing graph representation learning. However, the original GCN fails to further integrate the similarity features with the structural information of the signed graph network, resulting in unsatisfactory performance in signed association prediction task. Furthermore, the improvement brought by the similarity feature denoising module is also significant. It enhances the overall model performance by 0.78% and 1.38% in terms of AUROC and AUPR, respectively. This indicates that the similarity feature denoising module helps further enhance the robustness of the model within the VGAE framework. The last ablated module is the multi-scale SignGCN module. From Table 1, it can be observed that although the performance improvement brought by the multi-scale SignGCN module is relatively small, this module allows the model to learn effective representations even when the AUROC reaches 0.9731. Considering the remaining potential for improvement, the multi-scale SignGCN module achieves a 4.09% improvement in the AUROC metric.

Performance comparison with SOTA methods

Considering that MSignVGAE is the first method to utilize sign information for predicting microbe-disease associations, we selected a subset of state-of-the-art (SOTA) graph representation learning methods from the fields of unsupervised graph representation learning, signed network embedding, and graph theory for comparison. After obtaining node representations using these SOTA graph representation learning methods, we uniformly input them into an XGBoost multi-classification model for microbe-disease signed association prediction. Additionally, considering the notable performance of the GATMDA model in microbe-disease association prediction task, we also compared it in the context of microbe-disease signed association task. Moreover, in line with the approach of the MVGAEW model, this section also compared MSignVGAE from the perspective of reconstructing similarity matrixes. All comparison experiments in this section were conducted on the Peryton database, and the results can be found in Fig. 2 and Table 2. The methods included in these comparisons are as follows:

• MSignVGAE-sign2: This method follows the approach of the MVGAEW model. It utilizes the known microbe-disease signed association matrix as node features and reconstructs the disease-disease similarity matrix and microbe-microbe similarity matrix separately. It employs a multi-classification XGBoost model to predict the presence of associations between diseases and microbes and to identify the associated signs in cases where associations exist.

• TrustSGCN [37]: TrustSGCN is a novel signed network embedding method based on GCN. This model introduces a strategy to measure the credibility of high-order associated sign edges inferred from the theory of structural balance. It further corrects the incorrect embedding propagation process in the structural balance theory based on the credibility strategy.

• GREET [38]: GREET addresses the tendency of existing unsupervised graph representation learning methods to perform smooth learning along all edges, thereby neglecting the heterogeneity of nodes with different attributes. It constructs a homogeneous/heterogeneous edge discriminator to infer the homogeneity/heterogeneity of edges based on both feature and structural information. By minimizing a carefully designed pivot-ranking loss, GREET utilizes a homogeneous/heterogeneous dual-channel encoder to learn node representations.

• SLGNN [30]: SLGNN is based on graph theory and graph signal processing. It designs different low-pass and high-pass graph convolution filters to extract low-frequency and high-frequency information from positive and negative links, respectively. It employs a “self-gating” mechanism to control the influence of low-frequency and high-frequency information during the message passing process, thereby combining them into a unified message propagation framework.

• GATMDA [24]: It incorporates the concept of “Talking Head” into an optimized graph attention network to learn latent representations of microbes and diseases.

Fig. 2

The ROC curve and PR curve for signed association prediction under tenfold cross-validations on Peryton database

Table 2 Performance comparison for signed association prediction under 10-fold cross-validations on Peryton database

Figure 2 displays the receiver operating characteristic curves and precision-recall curves of the comparative methods in signed association prediction task. Table 2 presents the performance of different methods across multiple metrics in signed association prediction task. Compared to other methods, the proposed MSignVGAE model demonstrates superior performance across all metrics, showcasing its excellent performance. It is worth noting that compared to MSignVGAE-sign2, MSignVGAE shows a 5.06% improvement in AUROC and an 8.42% improvement in AUPR. This suggests that directly reconstructing known signed associations and using similarity information as features is more effective than reconstructing disease-disease similarity matrixes and microbe-microbe similarity matrixes separately while using known signed association information as node features. The reason behind this improvement is that when separately reconstructing similarity matrixes, the fusion of heterogeneous graph structure information and similarity information is disconnected. In contrast, reconstructing known signed associations enables an additional cross-fusion of the two types of information.

Furthermore, both GREET and SLGNN exhibit high performance across various metrics. This can be attributed to the utilization of low-pass and high-pass filters in both methods, enabling the models to learn features at different hierarchical levels. In comparison to these two methods, the advantage of MSignVGAE lies in its multi-scale SignGCN module, which integrates different sign propagation processes into a unified whole. This allows the model to capture features at different hierarchical levels without the need to separate low-frequency and high-frequency information of the graph. Notably, TrustSGCN demonstrates superior performance on real-world sign networks but performs poorly in microbe-disease signed association prediction task. This is because there stands a significant difference between real-world sign networks and heterogeneous networks in the bioinformatics domain, making the structural balance theory inapplicable to heterogeneous networks in the bioinformatics field. An intuitive observation is that GATMDA exhibits a noticeable performance gap in signed association prediction task compared to other methods. This discrepancy may be attributed to GATMDA’s failure to consider the influence of sign information. Based on this observation, it can be inferred that using only similarity information can still maintain a certain level of signed association prediction capability.

Performance comparison in unsigned association prediction

To further validate the effectiveness of the MSignVGAE method in efficiently integrating signed features, this section utilizes representations obtained from state-of-the-art graph representation learning methods in signed association prediction tasks. These representations are then inputted into an XGBoost binary classification model for unsigned association prediction. The results can be found in Fig. 3 and Table 3.

Fig. 3

The ROC curve and PR curve for unsigned association prediction under tenfold cross-validations on Peryton database

Table 3 Performance comparison for unsigned association prediction under tenfold cross-validations on Peryton database

Figure 3 displays the receiver operating characteristic curves and precision-recall curves of the comparative methods in unsigned association prediction tasks. Table 3 presents the performance of different methods across multiple metrics in unsigned association prediction tasks. Compared to other methods, the proposed MSignVGAE model is not the optimal one in terms of performance. However, all its performance metrics are comparable to those of MVGAEW on the Peryton database [32]. This indicates that utilizing sign information does not have a significant impact on unsigned association prediction tasks and can improve the accuracy of the model. Notably, in Table 3, both the GREET and SLGNN methods exhibit superior performance compared to the MSignVGAE method. However, interestingly, their performance is relatively lower than the MSignVGAE method in Table 2. This observation suggests that the MSignVGAE method, specifically designed to incorporate sign information, effectively integrates sign features when predicting associations.

Furthermore, on the Peryton database, the GREET method demonstrates a significant improvement across various performance metrics compared to the MVGAEW method. This finding further emphasizes the benefits of utilizing sign information, as it leads to enhanced model performance. Consistent with the results presented in Table 2, the MSignVGAE method also outperforms the MSignVGAE-sign2 method in unsigned association prediction tasks. However, it is noteworthy that TrustSGCN, which demonstrates outstanding performance in real-world signed networks, does not perform well in microbe-disease association prediction tasks. This finding highlights the inherent differences between real-world signed networks and the heterogeneous networks present in the field of bioinformatics.

Performance comparison with widely used databases

With the accumulation of data, databases have become more mature and now contain an increasing number of effective signed associations between microbes and diseases. To verify the generalization ability of MSignVGAE on databases of different scales, this section conducts several experiments on three additional databases (HMDAD, Disbiome, and MicroPhenDB), all of which also contain sign information. Considering the sparse matching of microbes between the microbe-disease database and the microbe-drug database, this section calculates the microbial similarity in the latter database without relying on drug-based functional similarity. Table 4 presents the performance comparison of different microbe-disease signed association databases under tenfold cross-validation. It can be observed that the performance of MSignVGAE is lowest on the HMDAD database. This is because the HMDAD data contains fewer signed association samples. Even in the case of a small dataset, MSignVGAE still maintains good signed association prediction ability. Consistent with the trend observed in previous work [32], as the quality and quantity of signed associations between diseases and microbes in the database increase, the performance of the MSignVGAE model also improves.

Table 4 The comparison of different microbe-disease signed association databases under tenfold cross-validation

Interpretation of latent representation

In order to further explore the interpretability of latent representations from the distributional perspective, this section visualizes the feature distributions of microbe representations. Specifically, we achieved this by employing the t-SNE [39] method, which is a dimensionality reduction technique, to project high-dimensional data into a lower-dimensional space for visualization. The visualization results for the Peryton database are illustrated in Fig. 4. Figure 4a displays the distribution of microbe representations obtained after applying MSignVGAE to the microbe-disease sign association matrix, while Fig. 4b shows the distribution of the original microbe-microbe similarity matrix. In Fig. 4, the points labeled as “Increased” and “Decreased” represent different types of changes (increase or decrease) in microbe quantity under disease states. The points labeled as “Non_association” represent microbes that are not associated with Alzheimer’s disease [40] in the Peryton database. The points labeled as “Increased_pred” and “Decreased_pred” represent the top 50 microbes predicted by the MSignVGAE model to have the highest probability of increasing or decreasing in association with Alzheimer’s disease.

Fig. 4

Visualizations of distribution whether adopt MSignVGAE for microbes related to Alzheimer’s disease. a The latent distribution by adopting MSignVGAE. b The raw distribution of integrated similarity network

From Fig. 4b, it can be observed that the two types of microbes in the original Peryton database are roughly distributed together. This indicates that the original microbe feature distribution is difficult to distinguish between the two types of microbes. In Fig. 4a, the dark green and light green points tend to be biased towards the left. This phenomenon is primarily due to the introduction of sign information propagation strategy, which causes the feature distributions of different types of microbes to be pulled apart from each other. One notable observation is the presence of outlier clusters in deep blue in the original feature distribution. These clusters exhibit significant differences in distribution compared to the known signed associations. Most proposed methods for predicting microbe-disease associations tend to predict potential disease-related microbes that fall near the known association distribution, rather than exhibiting outlier clusters similar to the deep blue cluster in Fig. 4a. Regarding the deep blue cluster in Fig. 4a, the prediction of these microbe nodes is likely to rely on the dark green nodes (predicted to be “Decreased” type) as bridges to establish connections between the light blue nodes (predicted to have “Increased” type) and the deep blue nodes (predicted to have “Increased” type).

Case studies

Consistent with previous work [32], this section presents case studies focusing on specific diseases to showcase the predictive capability for disease-related microbes. The diseases examined in this section are colorectal neoplasms [41], Alzheimer’s disease [40], and Crohn’s disease [42]. The analysis is based on the Peryton database, where known microbe-disease signed associations were excluded. The top 20 “Increased” and “Decreased” microbes with the highest predicted probabilities for each respective disease were identified. Furthermore, relevant literature from PubMed was provided to substantiate the presence of these signed associations. The specific microbes associated with colorectal neoplasms, Alzheimer’s disease, and Crohn’s disease can be found in Tables 5, 6, and 7, respectively.

Table 5 Top-20 “Increased” and “Decreased” microbes associated with colorectal neoplasms

Table 6 Top-20 “Increased” and “Decreased” microbes associated with Alzheimer’s disease

Table 7 Top-20 “Increased” and “Decreased” microbes associated with Crohn’s disease

By cross-referencing the prediction results from this section with the corresponding results from previous work [32], we identified common microbes that were predicted as relevant. These include (1) Epsilonproteobacteria, Schwartzia, and Bacillaceae associated with Crohn’s disease; (2) Erysipelotrichia, Erysipelatoclostridium, and Flavonifractor associated with colorectal neoplasms; and (3) Klebsiella and Oscillospira associated with Alzheimer’s disease. Furthermore, it is noteworthy that all the commonly predicted relevant microbes in both studies belong to the “Decreased” type, indicating that the omission of signed message may introduce a certain bias in the model. Among them, only Erysipelotrichia lacks literature reporting its association with colorectal neoplasms, while all other commonly predicted microbes are supported by literature. This suggests a high likelihood of a “Decreased” association between Erysipelotrichia predicted by the MSignVGAE model and colorectal cancer, despite the lack of specific literature evidence.

Additionally, this section visualizes the distribution of known signed associations and predicted signed associations related to specific diseases, as depicted in Fig. 5. The distribution of “Decreased” associations predicted by MSignVGAE also reveals a pattern where central microbes influence multiple diseases. Furthermore, the distribution of “Increased” associations predicted by MSignVGAE tends to be associated with a single disease, indicating that this pattern arises from the transmission of signed message and was not observed in the case studies of previous work.

Fig. 5

The distribution of existing and predicted Increased/Decreased association related to case diseases

Methods

Data sources

Microbe-disease association databases

Until now, researchers have developed several widely used microbe-disease association prediction databases, summarized in Table 8. Ma et al. [43] developed the first Human Microbe–Disease Association Database (HMDAD). By eliminating redundancy, HMDAD gathered 450 confirmed microbe-disease associations between 292 microbes and 39 diseases from published literature. Among these associations, there were 205 “Decreased” type associations and 245 “Increased” type associations. In 2018, Janssens et al. [44] established Disbiome, a database documenting 8731 known associations between 1622 microbes and 374 diseases. The content was selected from 1,191 published academic papers without redundancy, and the numbers for “Decreased” and “Increased” types were 4157 and 4574, respectively. Subsequently, MicroPhenDB was constructed using the same methodology as HMDAD and Disbiome by Yao et al. [45]. It included 5511 non-redundant associations between 1774 microbes and 500 diseases in 22 newly collected human body sites. Among these associations, there were 1819 “Decreased” type associations and 3692 “Increased” type associations. The last one, Peryton, proposed by Skoufos et al. [46], encompasses 4172 associations that are supported by experimental evidence, linking 1396 microbes with 43 diseases. Specifically, there were 2130 associations categorized as “Decreased” and 2042 associations categorized as “Increased.” To facilitate usability, we transformed the information regarding known microbe-disease signed associations into a matrix ${\text{A}} \in {\mathbb{R}}^{nm \times nd}$. In this matrix, a value of 1 indicates the presence of an increased microbe-disease association in the database, while a value of − 1 indicates the presence of a decreased microbe-disease association. Conversely, a value of 0 signifies the absence of the corresponding item. Let us denote the variables $nd$ and $nm$ to represent the number of diseases and microbes, respectively.

Table 8 Databases for microbe-disease association prediction

Similarity calculation

Based on previous related work [32, 47,48,49,50,51,52,53], This study extends the similarity calculation methods within the MVGAEW model framework. The key distinction lies in the utilization of disease-disease similarity and microbe-microbe similarity compared to the known microbe-disease association matrix. In the MVGAEW model framework, the association matrix elements are binary, taking values of either 0 or 1 to indicate the absence or presence of an association, respectively. However, in this study, the known microbe-disease signed association matrix is used. In this matrix, elements representing edges connecting decreased associations are assigned a value of − 1, whereas edges connecting increased associations are assigned a value of 1. Elements corresponding to no association retain a value of 0. The disease-disease similarity measures employed in this study encompass disease Gaussian interaction profile kernel similarity (GIP-D), disease semantic similarity (DSS1), and disease symptom similarity (DSS2). For microbe-microbe similarity, the measures include microbe Gaussian interaction profile kernel similarity (GIP-M), disease-based functional similarity (DFS1), and drug-based functional similarity (DFS2). Finally, a similarity network fusion approach [33] is employed to separately integrate the similarities of diseases and microbes, enabling a comprehensive analysis and understanding of the relationships within the system.

MSignVGAE

The overall framework of MSignVGAE is depicted in Fig. 1. Firstly, MSignVGAE employs a similarity network fusion approach independently integrate multiple disease similarities and microbe similarities. Furthermore, MSignVGAE utilizes a graph variational autoencoder with a signed message propagation strategy to reconstruct the known microbe-disease signed association matrix. The noisy similarity data, which has undergone a denoising process, is employed as the initial feature input for the variational autoencoder component. Notably, signed graph structural features are leveraged to characterize diseases and microbes. Lastly, based on the representations of diseases and microbes, a multi-class XGBoost classifier is applied to determine the presence of associations between given microbe-disease pairs and identify the corresponding signs for the associations. Figure 1 illustrates the framework of MSignVGAE, and subsequent sections of this paper will elaborate on each component in the framework in detail.

Similarity feature noising

Similarity feature noising refers to the introduction of Gaussian noise to the similarity data during the processing. Building upon the utilization of a similarity network fusion approach to integrate multiple disease similarity matrixes and microbe similarity matrixes, further advancements are achieved by incorporating the concept of a denoising autoencoder. This involves the addition of Gaussian noise to the similarity data and utilizing a graph variational autoencoder to reconstruct signed associations, thereby overcoming biases present in the similarity data. For convenience, the node similarity features were represented as $F$, as shown below:

$$F = \left( \begin{gathered} SM,O \hfill \\ O,SD \hfill \\ \end{gathered} \right)^{(nd + nm)} ,$$

(1)

where $SD$ denotes the integrated disease similarity matrix, $SM$ denotes the integrated microbe similarity matrix, $O$ denotes the zero matrix, and $F$ is a $(nd + nm)$-dimensional square matrix. After applying Gaussian noise, the node similarity features $F^{\prime}$ can be expressed as:

$$F^{\prime} = F + \varepsilon^{(nd + nm)} , \, where \, \varepsilon^{(nd + nm)} \in N(0,1),$$

(2)

where $\varepsilon^{(nd + nm)}$ represents Gaussian noise following a standard normal distribution, with dimensions matching $F$.

Sign graph convolution encoder

For convenience, in this section, the initial graph node features $X$ denotes the node similarity features $F^{\prime}$ after adding Gaussian noise. This module consists of two shared SignGCN layers and a multi-scale variational inference layer. Each scale of the variational inference layer has two SignGCN modules, which calculate the mean $\mu$ and variance $\sigma$ of the latent variable $Z$, respectively. Additionally, $W_{0}$ represents the model parameters that need to be learned in the first SignGCN layer. The first shared SignGCN layer can be represented by the following equation:

$$\overline{{X_{1} }} = SignGCN\left( {X,A} \right) = {\text{ReLU}}\left( {\overline{{A_{norm} }} \cdot X \cdot W_{0} } \right),$$

(3)

$$\overline{{A_{norm} }} = \widetilde{D}^{{ - \frac{1}{2}}} \cdot \overline{A} \cdot \widetilde{D}^{{ - \frac{1}{2}}} ,\widetilde{D} = \overline{D} + I,$$

(4)

$$\overline{D} = diag\left\{ {\overline{d}_{1} , \cdots ,\overline{d}_{nd + nm} } \right\},\overline{d}_{i} = \sum\nolimits_{j} {\left| {A_{ij} } \right|} ,$$

(5)

where $\overline{A}$ represents the matrix $A$ with self-loops, which can be denoted as $\overline{A} = A + I$. $\overline{{A_{norm} }}$ represents the matrix after symmetrically normalized Laplacian matrix processing. Compared with unsigned GCN, in SignGCN, the used $\widetilde{D}$ is no longer the degree matrix of the input graph structure matrix with self-loops but the absolute degree matrix of the signed association matrix in Eqs. (4) and (5). In essence, the matrix in this section corresponds to the low-pass feature aggregation filter [54]. The propagation of sign information in this filter is illustrated in the sign information propagation module in Fig. 1 and can be represented by the following equation:

$${h}_{i}^{l}=\frac{1}{{\overline{d} }_{i}}{h}_{i}^{l-1}-\sum_{k\in {\mathcal{N}}_{i}^{-}}\frac{1}{\sqrt{\left({\overline{d} }_{i}+1\right)\left({\overline{d} }_{k}+1\right)}}{h}_{k}^{l-1}+\sum_{j\in {\mathcal{N}}_{i}^{+}}\frac{1}{\sqrt{\left({\overline{d} }_{i}+1\right)\left({\overline{d} }_{j}+1\right)}}{h}_{j}^{l-1}$$

(6)

In details, $h_{i}^{l}$ represents the feature vector of the i-th node in the l-th layer of SignGCN. ${\mathcal{N}}_{i}^{-}$ represents the neighboring nodes that have “Decreased” associations with node $i$, while ${\mathcal{N}}_{i}^{+}$ represents the neighboring nodes that have “Increased” associations with node $i$. By utilizing the absolute degree matrix as weights for aggregating information from nodes connected by different signed edges, the model can effectively control the diversity and consistency among nodes with different signed associations. The equation for the second shared SignGCN layer can be expressed as follows:

$$\overline{{X_{2} }} = SignGCN\left( {\overline{{X_{1} }} ,A} \right) = {\text{ReLU}}\left( {\overline{{A_{norm} }} \cdot \overline{{X_{1} }} \cdot W_{1} } \right),$$

(7)

where $W_{1}$ represents the model parameters that need to be learned in the second shared SignGCN layer. Similarly, the third multi-scale SignGCN layer represents the data distribution using the logarithm of the mean $\mu$ and the logarithm of the variance $\sigma$, as follows:

$$\mu_{i} = SignGCN_{\mu } \left( {\overline{{X_{2} }} ,A} \right) = \overline{{A_{norm} }} \cdot \overline{{X_{2} }} \cdot W_{\mu }^{i} , \, i \in \left\{ {1,2,3} \right\},$$

(8)

$$\log \sigma_{i} = SignGCN_{\sigma } \left( {\overline{{X_{2} }} ,A} \right) = \overline{{A_{norm} }} \cdot \overline{{X_{2} }} \cdot W_{\sigma }^{i} , \, i \in \left\{ {1,2,3} \right\},$$

(9)

Considering that the concatenation and reparameterization technique in previous work, the resulting latent variables are shown below:

$$Z = Z_{1} |Z_{2} |Z_{3} , \, Z_{i} = \mu_{i} + \sigma_{i} * \varepsilon , \, \varepsilon \in N\left( {0,1} \right),$$

(10)

where $|$ denotes concatenation procedure.

Dot decoder

After obtaining low-dimensional representations $Z$ through a multi-scale encoder, in this section, a simple and efficient dot product decoder is utilized to reconstruct the signed association matrix, denoted as $\widehat{A}$. The matrix $\widehat{A}$ is used to reconstruct the input matrix $A$, as shown below [32]:

$$\widehat{A} = Z \cdot Z^{T} ,$$

(11)

In fact, the dot product decoder module alone can achieve satisfactory outcomes for microbe-disease signed association prediction task. However, considering that the objective of the decoder in the graph variational autoencoder framework is to reconstruct the original input matrix as accurately as possible, its core lies in the fusion of similarity features with heterogeneous network structure information. Therefore, relying solely on the predictions of the simple dot product decoder tends to favor known associations. To overcome this limitation, an efficient ensemble learning method, XGBoost, is employed to fully leverage the strengths of the graph variational autoencoder in effectively integrating similarity features with heterogeneous network structure information. This approach enhances the overall performance of the MSignVGAE model framework.

Loss function

The loss function can be formulated as below [55]:

$$\begin{gathered} L = \frac{1}{nd \cdot nm}\sum\limits_{i}^{nd} {\sum\limits_{j}^{nm} {\left( {\widehat{A}_{ij} - A_{ij} } \right)^{2} } } \hfill \\ \, + \frac{1}{M}\sum\limits_{m = 1}^{M} {\left( {KL[q(Z_{m} |A,X)|p(Z_{m} )]} \right)} \hfill \\ \end{gathered}$$

(12)

In details, the first part $\sum\nolimits_{i}^{nd} {\sum\nolimits_{j}^{nm} {\left( {\widehat{A^{\prime}}_{ij} - A^{\prime}_{ij} } \right)^{2} } } /\left( {nd \cdot nm} \right)$ represents the mean square error loss between the input signed association matrix $A$ and the reconstructed signed association matrix $\widehat{A}$. The second part represents the Kullback–Leibler divergence loss between the latent representation distributions $q(Z_{m} |SM,X)$ at all scales and the prior standard normal distribution $p(Z_{m} ) \sim N(0,I)$. Additionally, similar to MVGAEW, each iteration of MSignVGAE involves training on the entire graph and utilizes the Adam optimizer [56] to optimize the learnable parameters of the MSignVGAE model. To ensure model convergence, a stepLR learning rate decay strategy is employed during the training phase of MSignVGAE to control the learning rate.

XGBoost classifier

In this work, similar to MVGAEW, MSignVGAE also utilizes the concatenation of disease representations and microbe representations to train an XGBoost [34] multiclass classification model. The objective is to predict the existence of associations between pairs of microbes and diseases as well as the specific type of association (e.g., an edge indicating an increase in microbe abundance or a decrease in microbe abundance).

XGBoost is known for its excellent scalability [57,58,59,60] and can be easily extended from binary classification to multiclass task. In the multiclass XGBoost setting, the One-vs-All strategy is employed for classification. This means that a separate binary classification XGBoost model is trained for each class, treating the target class as the positive class and the other classes as the negative class. The goal of each binary classification XGBoost model is to differentiate whether a sample belongs to the current class or not. The models are then optimized using gradient boosting algorithms. The multiclass algorithm in XGBoost uses class scores to indicate the degree of membership for each class. It employs the soft-max Loss function for optimization. By normalizing the class scores, it yields the probability distribution of a sample belonging to each class.

Conclusions

In this work, we propose a novel model framework called MSignVGAE, which can effectively identify disease-associated microbes and predict trends in microbial quantity changes. Firstly, we start with fine-grained signed message and design a new strategy for signed message propagation that defines the information dissemination process between different nodes while controlling the heterogeneity and consistency among nodes connected by different signed edges. Secondly, we employ a graph variational autoencoder framework with a multi-scale perspective to model the signed association data and address the issue of inconsistent signed associations. Additionally, we utilize the denoising autoencoder approach to handle the noise in similarity feature information, which helps overcome biases in the fused similarity data. Notably, MSignVGAE is the first method that utilizes signed message to predict microbe-disease signed associations. The AUROC value and AUPR value of MSignVGAE reached 0.9742 and 0.9601, respectively. Furthermore, case studies on three different diseases demonstrate that MSignVGAE, by leveraging the signed message, can effectively capture distinct feature distribution patterns in signed networks.

It is worth noting that the signed message propagation strategy designed in MSignVGAE only controls the information propagation process among nodes connected by different signed edges, without considering the differences among neighbors of nodes connected by the same type of edges. Thus, the utilization of signed message is still not fully optimized. In reality, the introduction of signed message can improve the performance ceiling of the microbe-disease association prediction task. Further exploration of information related to diseases and microbes can help complete the global distribution of microbe-disease associations. The relationship between diseases and microbes is highly complex, and both are intricately connected to the bridge of medications. Solely focusing on processing microbe-disease association data may overlook this information. The next focus should be on constructing various bridges that connect diseases and microbes, considering factors such as polysaccharide information that can simultaneously affect the states of both diseases and microbes.