HMDAD, constructed by Ma et al. (2017), and Disbiome (Janssens et al., 2018), constructed by Janssens et al., are the main publicly available biomedical databases containing microbe-disease association data. As shown in Table 1, HMDAD database covers 483 known microbe-disease associations, and processing these data, we ended up with 450 known microbial-disease associations. The HMDAD database provides a valuable information resource for studying microbial-disease relationships. In addition, the Disbiome, constructed by Janssens et al., is a publicly available database of microbe-disease associations. As shown in Table 1, Disbiome database collects 5,573 known associations from published academic papers for 240 diseases and 1,098 microorganisms. After de-duplication, we had 4,351 known microbe-disease associations covering 218 diseases and 1,052 microorganisms. Due to its extensive data collection and detailed information records, the Disbiome database has become a vital data support for research in this field.

After acquiring the initial data, we performed data preprocessing steps to ensure the quality of the data and the validity of the model training. First, we removed all duplicate records to ensure that the association of each microbe with a disease was unique. Further, we converted the data into a uniform format to facilitate subsequent processing and model training. For simplicity, for each dataset, let M = m 1 m 2 , … , m N M denote the set of newly downloaded different microorganisms, and D = d 1 d 2 , … , d N d represent the set of newly downloaded different diseases. Thus, we can construct a primitive known microbe-disease association network N e t = 〈 M ∪   D , E as follows: for any given m i 1 ≤ i ≤ N m and d j 1 ≤ j ≤ N d , if and only if there is a known association between them, we assume that there is an edge belonging to E . Obviously, based on above definition, we can obtain an adjacency matrix A ∈ R N m × N d as follows: for any given m i 1 ≤ i ≤ N m and d j 1 ≤ j ≤ N d if and only if there is an edge between them in E , there is A i , j = 1 , otherwise, there is A i , j = 0 .

Based on above descriptions, it is easy to see that we can construct a heterogeneous network Y by combining the integrated similarity matrix DS of disease and the integrated similarity matrix MS of microbe with the adjacency matrix A as follows: Y = D S A T A M S

As illustrated in above Figure 1, the DuGEL consists of the following five steps:

• Step 1: Construct a heterogeneous microbe-disease network based on newly downloaded known microbe-disease associations and multiple microbe and disease similarity metrics.

In DuGEL, the input layer is the Microbe-Disease Association Representation Layer, is a component used to convert raw data of known microbe-disease associations into a structured data fame that can be processed by subsequent graph neural networks. Firstly, the newly collected microbe-disease association data need to be pre-processed to ensure consistency and accuracy. The preprocessed data will be used in turn to construct a binary microbe-disease association matrix M, which implies potential relationships between microorganisms and disease (Marsh and Zaura, 2017), and can be defined as follows: Given a microorganism m and a disease n , he known relationship between the microorganism and the disease can be characterized by a binary association matrix M ∈ R m × n , where the matrix element M i j is 1 if there is a known association between the microorganism i and the disease j , and 0 otherwise. Each row of the matrix represents a microorganism, and each column represents a disease. The entries in the matrix indicate the presence or absence of an association. The graph structure G is obtained by the association matrix M , where the nodes in the graph are either microbe nodes or disease nodes, and if there is an association between a microbe node and a disease node (Abuin-Denis et al., 2024), i.e., M i j = 1 , then an edge exists between the nodes.

To enhance the prediction ability of DuGEL, similarity information is also fused in the representation layer (Feng et al., 2023), which contains the microbial similarity matrix S m and the disease similarity matrix S d . Among them, the microbial similarity matrix S m captures similarities between different microorganisms based on genomic, phenotypic, or ecological characteristics. After the microbial similarity matrix S m and disease similarity matrix S d are constructed, we fuse this similarity information with the microbe-disease association matrix M to enhance the performance of the association prediction model. Therefore, at this point, we can obtain the association matrix that incorporates microbial similarity and disease similarity as a graph structure (Yu et al., 2024), which further serves as the initial input form for the dual graph-based feature extraction module. This graph structure captures direct associations and enables the model to learn a more comprehensive representation of features.

In addition, we will initialize each representative microbe or disease node in the graph with a feature vector. Formally, let X m ∈ R m × d represent the initial feature matrix for microbes and X d ∈ R n × d represent the initial feature matrix for diseases, where d is the dimension of the feature vector. The initial embeddings X m and X d are combined into a unified feature matrix X ∈ R m + n × d . X is fed forward as input to the dual graph-based feature extraction module.

The microbe-disease association representation layer lays the foundation for the entire DuGEL model, and by meticulously structuring the input data, the layer ensures that subsequent graph neural networks are able to effectively capture both local and global patterns in the data. The construction of the graph enables the model to fully utilize all available information, thereby improving the accuracy and robustness of microbe-disease association predictions.

In this study, the dual graph feature extraction module is a core component of the DuGEL designed to extract deep features from the input microbe-disease association feature matrix. The module combines two parallel graph neural network architectures: graph convolutional network (GCN) and graph attention network (GAT), ensuring effective capture of local and global relationships in the graph.

The feature representation H LSTM   output from the sequence learning layer is used as input to the fully connected layer for further processing. The fully connected layer maps the high-dimensional features to the final prediction results through a series of linear transformations and nonlinear activation functions (Feng et al., 2023). The computational process of the fully connected layer can be formally represented as: y ^ = σ W f c H L S T M + b f c where W f c and b f c are the weights and bias parameters of the fully connected layer, respectively, and σ represents the Sigmoid nonlinear activation function.

Ultimately, the output layer gives the predicted probability of microbe-disease association (Marsh and Zaura, 2017). By setting an appropriate threshold, it is possible to determine whether there is an association between microbes and diseases.

To measure the difference between the predicted and true values of the model, in the DuGEL model, we use the cross-entropy loss function to evaluate the effectiveness of microbe-disease association prediction (Mao et al., 2023). The cross-entropy loss function is commonly used in classification problems, and in microbe-disease association prediction, we modeled the problem as a binary classification task, i.e., predicting whether there is an association between a certain pair of microorganisms and a disease. The cross-entropy loss function is defined as follows: L C E = − 1 N ∑ i = 1 N y i ⁡ log y ^ i + 1 − y i log 1 − y ^ i where N denotes the number of samples; y i is the true label of the i -th sample, indicating the presence of an association, and 0 denotes the absence of an association. y ^ i is the predicted probability of the model for the i -th sample, indicating the probability of an association between microorganisms and diseases. The cross-entropy loss function improves the accuracy of the prediction by penalizing the wrong prediction of the model, which makes the model continuously adjust the parameters during the training process.

To prevent model overfitting, we add a regularization term to the loss function. The regularization term improves the generalization ability of the model by adding a penalty to the model complexity in the loss function (Fu et al., 2023), encouraging the model to choose simpler parameter configurations. In the DuGEL model, we use L2 regularization or weight decay. It is defined as follows: L reg   = ∑ k ∥ W k ∥ 2 2

where W k denotes the k rd weight matrix of the model; and ∥ W k ∥ 2 2 is the L2 paradigm of W k , i.e., the sum of squares of the weight matrix. The regularization term prevents the model from overfitting the training data by penalizing excessively large values of the weights, thus improving the model’s performance on the test data.

Ultimately, the integrated loss function of the DuGEL model consists of a cross-entropy loss and a regularization term of the following form: L = L CE + λ   *   L reg   where λ is the number, which controls the weights of the regularization term. This integrated loss function takes into account both the accuracy of the model prediction and the complexity of the model, and by balancing the two (Cui et al., 2019), it ensures that the model not only accurately fits the training data during training, but also has good generalization ability.

In this study, we extracted disease features, microbial features, and disease-microbe association matrices from the HMDAD and Disbiome databases, and the three feature matrices mentioned above were used to construct heterogeneous maps to reflect the interactions between diseases and microbes for disease characterization and microbial characterization. The number of training rounds was set to 4,000 in the training phase. To optimize the algorithm to adjust the weights, the learning rate was set to 0.01. We set the random deactivation strategy for the adjacency matrix with the dropout ratio set to 0.5, thus preventing overfitting. For the subject model, to randomly discard some network connections during the training process to enhance the model’s generalization ability, we similarly set the random deactivation strategy with the dropout ratio set to 0.5. In addition, we set the similarity weight to 6 to weigh the similarity features of diseases and microorganisms. From the above description, it is easy to see that there are several hyperparameters in DuGEL, such as the dimension k of the embedded features, the number of layers L, the initial learning rate r of the optimizer, the total training epoch α, the node dropout β, and the rule dropout γ. As illustrated in Figures 3, 4, the various results for several combinations of parameters k and L in the 5-fold cv. From the figures, it is easy to see that the optimal combination of k and L is L = 2, k = 128, which indicates that the first and second-layer embedded features contain more information than the third-layer embedded features. After analyzing, this may be due to excessive smoothing of LSTM.

In the training and evaluation phases of the model, we perform multiple cross-validations. In each validation, the dataset is divided into a training set and a test set, which trains the model on the training set and evaluates the model performance on the test set. Specifically, 5-fold cross-validation (k_folds) is used to evaluate the model performance. In each cross-validation, the data are randomly disrupted and divided into five parts, one used as the test set and the rest as the training set. To ensure the stability and reliability of the results, we repeat the execution of the experiment 5 times and report the average performance metrics.

In order to evaluate the method proposed in this paper, we employ a series of evaluation metrics to comprehensively measure the performance of the model, including AUC, accuracy and specificity The formal definitions and calculations of each evaluation metric are given below:

Accuracy is the ratio of the number of correctly categorized samples to the total number of samples, which is defined as follows: Accuracy = T P + T N T P + T N + F P + F N where T P denotes True Positives, F P denotes False Positives, F N denotes False Negatives, and T N denotes True Negatives. Accuracy reflects the overall ability of the model to correctly classify.

AUC (Area Under the ROC Curve) represents the area under the receiver operating characteristic curve (ROC Curve), which is used to measure the classification performance of the model. The ROC Curve plots the True Positive Rate (TPR) and False Positive Rate (FPR) through different thresholds. TPR and FPR are defined as follows: TPR Recall = T P T P + F N FPR = F P F P + T N

The value of AUC is between 0 and 1, with larger values indicating better model performance.

Specificity, also known as True Negative Rate (TNR), is formally defined as follows: Specificity = T N F P + T N

Specificity indicates the proportion of all samples that are actually negative that are correctly predicted to be negative.

In order to compare the methods proposed in this paper horizontally, as shown in Table 3, we introduced nine microbe-disease association prediction methods of.

The above methods can be categorised into four groups, with network-based methods constructing complex network structures based on known microbial disease associations. These network-based methods construct complex network structures based on known microbial-disease associations. Then, the potential probability of associations between microorganisms and diseases is inferred by analyzing the structural features of these networks and the lengths and numbers of connecting paths between the nodes (Wang et al., 2011). For example, Chen et al. proposed the KATZHMDA computational model to infer possible microbe-disease associations using the KATZ measure, which takes measurements to capture global information in a network by counting all paths between nodes and then predicts potential associations (Chen et al., 2017). However, the matrix decomposition-based approach focuses on decomposing the known microbe-disease association matrix into two feature matrices and approximating the original association matrix by the product of these two matrices (Ma and Liu, 2022). Information such as similarity and strength of association between microorganisms and diseases can be obtained. Shen et al. proposed a computational model of CMFHMDA based on synergistic matrix decomposition (Shen et al., 2017). In addition, based on the traditional machine learning approach by using known associations as training samples, we can construct a model for predicting the association between unknown microorganisms and diseases (Long et al., 2021). For example, Wang et al. designed the LRLSHMDA model which represents the network structure by constructing a Laplace matrix and predicts the association by regularized least squares (Wang et al., 2017). Finally, the graph neural network-based approach utilizes neural networks to take microbial and disease-related data as inputs and to extract and explore features and patterns from graph-structured data (Bessadok et al., 2022). They can utilize we can utilize the powerful learning ability of neural networks to discover potential associations between microbes and diseases and mine functional patterns and features from complex graph data. For example, Wang et al. designed GCNMA that captures structural information in the network by introducing a graph convolutional neural network and incorporates a multilayer attention mechanism to enhance the ability to model complex relationships between nodes (Wang et al., 2023).

Although the above models can perform reliably in some aspects, they still have limitations. For example, the computation of Katz path correlation must consider all paths between different nodes (Zhang et al., 2017). This may lead to high computational complexity on large datasets, especially when the network size is large (Kumar et al., 2020). In addition, regularized least squares usually introduce a regularization term to avoid overfitting. However, choosing the appropriate regularization parameter is not easy. If it is not chosen correctly, it may lead to underfitting or overfitting problems. When there is noise in the input data, the regularized least squares method may be too sensitive to the noise, resulting in unstable or inaccurate prediction results (Jung and Park, 2017).

In this section, we provide a detailed analysis of the experimental results of our proposed DuGEL model on the HMDAD and Disbiome datasets and compare it with nine other state-of-the-art microbe-disease association prediction methods. First, Tables 4, 5 show the performance of our proposed DuGEL model, and the nine compared methods on the HMDAD and Disbiome datasets, respectively, are mainly compared under the AUC assessment metrics. On the HMDAD dataset, the DuGEL model performs well, with its AUC values of 0.9698 and 0.9606 in 5-fold cross-validation and 2-fold cross-validation, respectively, The higher AUC values indicate the more vital overall predictive ability of the model, which indicates that DuGEL can effectively distinguish between positive and negative samples. For the Disbiome dataset, the DuGEL model still performs well. Under 5-fold cross-validation and 2-fold cross-validation settings, DuGEL reaches 0.9119 and 0.8932.

In comparison with previous methods, the DuGEL model demonstrates excellent performance. we attribute the results to the intrinsic structure of DuGEL. DuGEL successfully achieves efficient prediction of microbial-disease associations by combining a graph convolutional neural network (GCN) and a graph Attention Network (GAT), as well as introducing a Long Short-Term Memory Network (LSTM) to process fused features, enabling efficient prediction of microbe-disease associations. This multilevel feature extraction and sequence modeling approach enables DuGEL to perform well on key metrics (e.g., AUPR and AUC),demonstrating its robustness in microbe-disease association prediction tasks.

In particular, the DuGEL model combines the strengths of GCN and GAT; GCN can efficiently capture both local and global spatial features in the graph and extract complex relationships between microbes and diseases by performing convolutional operations on the features of neighboring nodes. Moreover, through the attention mechanism, GAT can assign different importance weights to its neighbors when processing nodes, thus better capturing the information of critical nodes. After combining the two, the outputs of GCN and GAT are fused through the Dual Graph Enhanced Layer of the DuGEL model, which effectively integrates the structural features and node importance.

Furthermore, introducing the LSTM module further enhances the model’s capabilities. LSTM is good at processing sequence data and can better identify potential associations between microbes and diseases by capturing temporal dependencies (Baranwal et al., 2022). The memory unit of LSTM can preserve information of long-time dependencies (Wu et al., 2021), which is especially important for analyzing potential microbe-disease relationships over long periods.

In addition, considering the role and contribution of every sub-module in the DuGEL model proposed in this study, we function ablation experiments on the HMDAD dataset to inspect the effect of distinctive parts of the model. We carried out three specific ablation experiments:

1. Doing away with the diagram convolution sublayer (denoted as “-GCN Layer”)

Overall, each sub-module of the DuGEL model improves the primary mannequin’s effectiveness by taking pictures of the correlation between microorganisms and diseases. Table 6 suggests the results of the ablation experiments. In the first ablation experiment, after getting rid of the graph convolution sublayer, the mannequin’s AUC drops to 0.9465 and 0.9392 in 5-fold cross-validation and 2-fold pass validation, respectively, which suggests that GCN plays a crucial role in shooting nearby and international spatial points between microbes and diseases. By performing convolutional operations on the elements of neighboring nodes, GCN can extract complex correlation information, and removing this component considerably decreases the model’s predictive power.

In the second ablation experiment, doing away with the GAT sublayer reduces the model’s AUC to 0.9520 and 0.9408 in 5-fold cross-validation and 2-fold pass-validation, respectively. GAT can better capture facts about key nodes via an attention mechanism that assigns unique weights of importance to its neighbors when processing nodes. This mechanism is necessary for improving the model’s prediction accuracy, and the mannequin’s performance in a similar fashion decreases after its removal.

Finally, we explored the function of the BiLSTM module. After eliminating the BiLSTM module, the AUC of the mannequin diminished to 0.9602 and 0.9510 in the 5-fold move validation and 2-fold move validation, respectively. The LSTM module appropriately processes sequence information and can become aware of attainable associations between microbes and diseases by capturing time dependencies. The reminiscence unit of the LSTM can retain lengthy time-dependent information, which is especially essential for examining the viable microbes’ disease. This is mainly necessary for analyzing doable microbe-disease relationships over lengthy periods. The elimination of this module resulted in a considerable reduction in the predictive energy of the model, in addition to demonstrating the necessary function of the BiLSTM module in the DuGEL model.

Overall, every sub-module had a practical impact on the expected performance of the DuGEL model. The GCN and GAT successfully extracted complicated associations between microbes and diseases through shooting spatial features and node importance statistics in the diagram structure, while the BiLSTM module furthermore desirable the predictive capacity of the mannequin via processing sequence features. The effects of the ablation experiments validate the effectiveness and necessity of these sub-modules and reveal the rationality and superiority of the DuGEL model sketch in the microbe-disease affiliation prediction task.3.6.