Figure 1 illustrates the architecture of the MKAN-MMI model. In module (A), we gather observed MMIs along with original microbe and medicine information from the database to construct the initial medicine-microbe graph. Subsequently, we mask traversed MMIs by sampling nodes, employing a random walk strategy. In module (B), independent subspace technology is applied to learn weights for each subspace independently, facilitating the extraction of multi-layer representations of microbes and medicines. In module (C), the cross-Hadamard product is applied to the multi-layer output from module (B) to produce the final medicine-microbe pair representation. Subsequently, KAN technology predicts the score and reconstructs the medicine-microbe graph. Module (D) encapsulates the operating rules of KAN.

Recently, GAE technology has achieved significant success due to its self-supervised nature. The architecture of GAE is straightforward, comprising only two main components: a GNN encoder and a decoder. The GAE process is well-defined: the GNN encoder extracts node embeddings from the input graph, and the decoder is trained to reconstruct based on known links. The objective function is defined as Equations 1–3: L 1 = 1 E + ∑ < m , d > ∈ E + l o g I h m , h d , (1) L 2 = 1 E − ∑ < m ̂ , d ̂ > ∈ E − l o g I h m ̂ , h d ̂ , (2) L GAE = − L 1 + L 2 (3) where L 1 ( L 2 ) denotes the loss on positive (negative) links, E + ( E − ) represents the sets of positive (negative) links, I ( ⋅ ) is the decoder function, and h m and h d are the embeddings of nodes m and d , respectively.

Numerous studies have demonstrated that GAE exhibits enhanced performance following appropriate masking of the input graph (Devlin et al., 2019; He et al., 2022; Hou et al., 2022). Similarly, this study aims to identify potential MMIs from unknown medicine-microbe pairs using a self-supervised strategy within the Mask GAE framework. The observed medicine-microbe graph is represented as G = < V , E , X > , where V includes all microbes and medicines, E denotes the observed MMIs, and X is defined as the initial node representation. Inspired by previous research (Tan et al., 2023), we sampled the starting nodes from the observed medicine-microbe graph according to Equation 4: S = B e r n o u l l i G , γ , (4) where S denotes the set of starting nodes, and γ indicates the sampling rate. Then, following the random walk rule, the MMIs traversed from the starting node are masked as Equations 5 and 6: E masked = R a n d o m W a l k S , l , (5) G reserved = < V M , V D , E reserved , X > , E reserved = E − E masked , (6) where E m a s k denotes the masked MMIs, while the reserved MMIs are referred to as E r e s e r v e d . Additionally, G r e s e r v e d represents the reserved medicine-microbe graph. Subsequently, G r e s e r v e d is fed into the GNN encoder to extract embeddings of microbes and medicines.

The GNN model accurately extracts node representations from the graph’s topological information, excelling in various graph tasks and attracting significant attention. The GNN model operates by performing multiple aggregation and update operations using the adjacency and feature matrices to extract features. Aggregation and update operations can be modified to create GNN variants suitable for various scenarios. While this model offers convenience, it also presents some challenges. Studies indicate that during the iteration of GNN models, feature subspaces are likely to exhibit approximate linear correlations (Sun et al., 2023). This significantly diminishes the subspace’s expressive power. The primary cause is the shared weights across multiple layers of feature subspaces (Sun et al., 2023). Inspired by these findings, we have integrated independent subspace technology into the Mask GAE framework to enhance the model’s feature extraction capabilities.

Specifically, we introduce a new GNN architecture centered on using polynomial technology to deshare weights in feature subspaces. According to Chebyshev’s theorem, the aggregation function is expressed as Equation 7: H = ∑ c = 0 C Q c L ̂ X W c , (7) where H represents the representation of microbes (medicines), Q c ( ⋅ ) denotes the c -order term of a polynomial, X is the initial representation of microbes (medicines), and W c is the weight learned in the c -th feature subspace.

From the above equation, it is evident that the feature subspace is closely linked to the initial representation of microbes (medicines). In the medicine-microbe graph, the dimensionality of the initial representation may limit the formation of the feature space. Consequently, we apply singular value decomposition to the adjacency matrix as Equation 8: M = UV ̄ , A ̂ = U V Σ T , (8) where U and V represent the principal components and its corresponding singular values, respectively. The aim of this procedure is to expand the feature subspace, thereby enhancing the data. This subspace independently learns the weight W M , and the aggregation function is derived as follows as Equation 9: H = ∑ c = 0 C Q c L ̂ X W c + M W M , (9)

As illustrated in Figure 1, with C equal to 2, the GNN architecture comprises four independent subspaces: Q 0 ( L ̂ ) X , Q 1 ( L ̂ ) X , Q 2 ( L ̂ ) X , and M . This study introduces independent subspace technology to segregate these subspaces and facilitate independent weight learning within them. This approach prevents the approximate linear correlation among multiple GNN subspaces during the iteration process, thereby enhancing their expressive power.

Given a microbe m and a medicine d , the GNN extracts representations htm and htd from the input graph. Typically, the current GAE framework employs cosine similarity or MLP operations during the decoding stage as Equation 10: s m , d = < h m C , h d C > o r s m , d = M L P h m C ∥ h d C , (10) where s represents the predicted score. While these methods appear simple, they are effective. However, applying these operations presents challenges for MMI prediction tasks. The primary challenges are twofold. First, within the Mask GAE framework, masking some MMI may result in the loss of crucial topological information. Second, in the medicine-microbe dataset, the number of observed MMI is significantly lower than that of unknown pairs, contributing to data sparsity.

Research indicates that connecting, adding, or multiplying the multi-layer outputs of GNNs can enhance the data processing. However, a major drawback of this strategy is the introduction of significant noise, which impacts the final microbe (medicine) representation. Drawing inspiration from prior research (Tan et al., 2023), we have implemented collaborative decoding technology and the cross-Hadamard product to integrate representations of microbes and medicines across each GNN layers as Equation 11: h < m , d > = ∥ a , b = 1 L h m a ⊙ h d b , (11) where h < m , d > denotes the final representation of the medicine-microbe pair < m , d > . The terms ⊙ and ∥ refer to the “Hadamard product” and “concatenation” operations, and L indicates the number of encoder layers. The cross-Hadamard product operation effectively integrates multi-layer information, promoting similarity while reducing differentiation between microbes and medicines. This ensures that the output representation of the medicine-microbe pair retains essential information.

MLP is capable of describing nonlinear functions; its simplicity and feasibility have made it the most popular neural network currently. The core of MLP involves performing linear mapping on the input, often incorporating nonlinear activation functions. MLP has been integrated into various network architectures, including GNNs and convolutional neural networks. However, recent studies have highlighted significant challenges facing MLP that cannot be ignored. For instance, MLP often requires stacking, and typically has a large parameter scale. Moreover, MLP’s functionality relies entirely on the interplay of neurons, resulting in limited interpretability. Initially, MLP places the activation function at the neuron level, whereas KAN applies univariate and spline functions to the weights. This approach allows KAN to improve weight learnability and interpretability. KAN theory originates from the concept that multivariate continuous functions can be derived by combining univariate functions via binary addition, as Equation 12: f t = f t 1 , t 2 , … , t n = ∑ v = 1 2 n + 1 φ v ∑ u = 1 n φ v , u t u , (12) where t 1 , t 2 , … , t n are binary univariate variables; φ v , u are binary functions, where n represents the number of neurons, and φ v is a real function. However, some studies have indicated that these univariate functions are occasionally non-smooth, limiting the applicability of KAN theory (Poggio et al., 2020; Girosi and Poggio, 1989). Fortunately, Liu et al. have observed that functions commonly used in daily life are smooth, reigniting interest in KAN theory (Liu Z. et al., 2024).

To achieve arbitrary depth with KAN, a straightforward approach is the integration of MLP with KAN theory, as Equation 13: K A N t = φ K − 1 ◦ φ K − 2 … φ 1 ◦ φ 0 t , (13) where K denotes the number of KAN layers.

As depicted in Figure 1B, the MKAN-MMI model employs KAN to process the final representation of the medicine-microbe pair for predicting the final score. Subsequent experiments demonstrate that integrating KAN technology significantly enhances the model’s prediction performance.

To verify the accuracy of the MKAN-MMI model in MMI prediction, we conducted evaluations across several publicly accessible MMI databases. Drawing on prior research (Long et al., 2020a), we selected three databases for evaluation: MDAD (Sun et al., 2018), DrugVirus (Andersen et al., 2020), and aBiofilm (Long et al., 2020a). The MDAD database comprises 1,373 medicines, 173 microbes, and 2,470 MMI in total. The aBiofilm database includes 1,720 medicines, 140 microbes, and 2,884 MMIs in total. The DrugVirus database contains 175 medicines, 95 microbes, and 933 MMIs in total.

Additionally, we gathered similarity data for microbes and medicines from previous studies (Tian et al., 2023). For microbes, we gathered functional similarity ( F 1MS ) and Gaussian interaction kernel similarity ( G I P 1MS ) data. Detailed calculations for F 1MS are available in the works of Kamneva (2017). The calculation of G I P 1MS and the integration of F 1MS and G I P 1MS are discussed in previous work (Tian et al., 2023). For medicines, we collected structural similarity ( F 2MS ) and Gaussian interaction kernel similarity ( G I P 2MS ) data. Hattori’s work (Hattori et al., 2010) details the calculation of F 2MS , while the process of calculating G I P 2MS and integrating it with F 2MS can be found in earlier studies (Tian et al., 2023). We used the integrated similarity features of microorganisms and drugs as the model’s initial representation. Negative samples were generated via random sampling. Known MMIs were treated as positive samples, while the remaining unknown drug-disease pairs were considered negative samples.

We compared the MKAN-MMI model against eight models, encompassing classic GNN models such as GCN (Li et al., 2018) and GAT (Veličković et al., 2018), as well as advanced models like DTI-CNN (Peng et al., 2020), NIMCGCN (Li et al., 2020), MMGCN (Tang et al., 2021), and DTIGAT (Wang et al., 2021), Graph2MDA (Deng et al., 2022), SCSMDA (Tian et al., 2023), and GCNMDA (Devlin et al., 2019). Notably, DTI-CNN (Peng et al., 2020), NIMCGCN (Li et al., 2020), MMGCN (Tang et al., 2021), and DTI-GAT (Wang et al., 2021) were not originally designed for MMI prediction tasks. Consequently, these models required modifications, including adjusting the input to the initial representation of microbes and medicines, and to the medicine-microbe graphs. To ensure fairness, the study maintained a consistent data partitioning ratio and conducted uniform 5-fold cross-validation across all experiments. The proposed MKAN-MMI model primarily considers the root node sampling rate, random walk length, and number of feature subspaces. Empirically, these parameters are set to 0.5, 3, and 3 by default. The training-to-test set ratio is set to 4:1, and the positive-to-negative sample ratio is also set to 1:1. The primary evaluation metrics employed were AUC (area under the ROC curve) and AUPR (area under the precision-recall curve). Additionally, for a comprehensive assessment, accuracy (ACC), precision (PRE), F1-score, and Matthews correlation coefficient (MCC) served as auxiliary metrics, similar to previous practice (Zhou et al., 2024; Wei et al., 2024; Wang et al., 2024; Ma et al., 2024; Xu et al., 2023).

Under identical data partitioning conditions, we assessed the performance of the proposed model alongside that of existing comparison models. Table 1 displays the AUC and AUPR performance metrics of all models across the MDAD, DrugVirus, and aBiofilm datasets. Significantly, the MKAN-MMI model achieved the highest performance in both AUC and AUPR metrics across all datasets, ranking first. The SCSMDA model followed closely, securing the second rank. The DTI-CNN model, ranking third in the AUC metric, underscored the autoencoder’s advantage in feature extraction. However, it exhibited slightly inferior performance in the AUPR metric within the DrugVirus and aBiofilm datasets. The underperformance of other GNN models highlights the challenges of strategies relying solely on observed MMIs. GNN model designs heavily depend on network topology during aggregation and updates, often neglecting the nodes’ initial representations. Specifically, in the MDAD, DrugVirus, and aBiofilm datasets, the observed MMIs are significantly fewer than the unknown medicine-microbe pairs, suggesting the initial representation could play a crucial role in MMI prediction.

The SCSMDA model utilizes GCN technology and self-supervised learning strategies, incorporating meta-path and graph contrast learning techniques to enhance node representations, resulting in positive outcomes. However, the increased complexity of its architecture may hinder the model’s generalization. The proposed model adopts the encoder-decoder framework of GAE to reconstruct the medicine-microbe graph, demonstrating greater efficiency and accuracy in identifying unknown MMIs compared to the SCSMDA model. This improvement can be attributed to several factors. First, independent subspace technology is employed to enhance subspace representation capabilities. Second, collaborative decoding technology integrates multi-layer GNN outputs to improve node representations of medicines and microbes. Finally, the proposed model applies KAN technology to enhance its flexibility and generalization capabilities.

The proposed model incorporates several customizable parameters, including GNN encoder type, node sampling rate, and masked path length. We assessed the impact of different parameter settings on the MKAN-MMI model’s performance across three databases, confirming its adaptability to these parameters.

We anticipate that the proposed model will excel in the MMI prediction task, primarily due to the integration of independent subspace, collaborative decoding, and KAN techniques within the Mask GAE framework. To test this hypothesis, we conducted multiple experimental series on the MDAD database. Table 2 displays the outcomes of these experiments. “GCN” and “DG” signify that the MKAN-MMI model’s encoder employs GCN and independent subspace techniques, respectively. “CD” denotes that the MKAN-MMI model’s decoder utilizes collaborative decoding technology. “ID” represents that the model extracts the output of the last layer of the microbe and medicine, performs the Hadamard product, and predicts the medicine-microbe pair score. “KAN” and “MLP” show that the MKAN-MMI model employs KAN and MLP, respectively, to predict the medicine-microbe pair score. Observations reveal that the absence of independent subspace, collaborative decoding, or KAN technology in the MKAN-MMI model leads to reduced performance. This indicates that all three technologies contribute significantly to enhancing MMI prediction. The model’s performance is poorest when it lacks collaborative decoding technology. This suggests that collaborative decoding technology effectively mitigates data sparsity issues, thereby enhancing the model’s robustness. Performance slightly declines when the model operates without independent subspace technology. Performance significantly deteriorates when the model employs MLP technology in place of KAN.

In this study, we employed one-way analysis of variance (ANOVA) (St and Wold, 1989) to systematically assess whether significant differences exist in the AUC performance of various MMI prediction models across the aBiofilm, DrugVirus, and MDAD datasets, as shown in Figures 6–8, respectively. The results indicate that on the MDAD dataset, our model demonstrates a significant advantage, with p-values below 1.0e-07 compared to most models, underscoring its statistical significance. Notably, when compared to the Graph2MDA and DTI-CNN models, our model achieved p-values of 1.00e-04 and 3.20e-03, respectively. While the differences are subtle, they remain statistically significant. On the DrugVirus dataset, our model also showed significance in most comparisons. However, when compared to the NIMCGCN model, the two models performed similarly, with p-values as high as 0.99, indicating their comparable predictive ability on this dataset. Nonetheless, in other comparisons, our model consistently demonstrates significant superiority, with p-values mostly below 1.0e-07. On the aBiofilm dataset, our model also maintains a significant performance advantage. In comparisons with NIMCGCN and Graph2MDA, p-values were 0.66 and 0.98, respectively, indicating that our model performs similarly to these models on some evaluation metrics. Overall, the p-values between our model and all comparison models remain well below the significance threshold of 0.05, further validating its superior performance.

The analysis results not only confirm the performance advantage of our model but also emphasize its stability and reliability across various data environments. Additionally, the results strongly support the application value of decoupled representation learning and multi-scale fusion technology in enhancing model generalization and addressing complex interaction prediction challenges.

This study employed a five-fold cross-validation method to assess the performance of the MKAN-MMI model across the MDAD, DrugVirus, and aBioFilm databases. As detailed in Table 3, the proposed model demonstrated stable performance on the MMI prediction task, surpassing the current state-of-the-art SCSMDA model. Specifically, the proposed model achieved an average AUC of 99.58% on the MDAD dataset, which is 4.43% higher than SCSMDA’s 95.15%. On the DrugVirus dataset, the proposed model recorded an average AUC of 94.54%, 0.87% higher than SCSMDA’s 93.67%. On the aBioFilm dataset, our model excelled with an average AUC of 99.50%, marking an increase of 1.27% over SCSMDA’s 98.23%. Additionally, for the AUPR metric, the proposed MKAN-MMI model significantly outperforms the SCSMDA model. These results underscore the model’s effectiveness and its robust generalization capability across various settings.

We conducted a series of case studies to assess the model’s performance under isolation. We chose the medicine Berberine from the DrugVirus database for analysis and validation. Berberine, an alkaloid derived from plants like Coptis chinensis and Phellodendron chinense, has been used historically to treat various diseases (Song et al., 2020). This medicine exhibits multiple biological activities, including antimicrobial, anti-inflammatory, antioxidant properties, and the regulation of blood sugar and lipids. Berberine inhibits protein synthesis in microbial cells, reduces inflammatory factor expression, enhances the antioxidant enzyme system, and activates AMP-activated protein kinase (AMPK). Consequently, it holds potential for treating type 2 diabetes, cardiovascular diseases, and gastrointestinal disorders. Although considered relatively safe, Berberine may interact with specific microbes. Thus, studying Berberine and its associated microbes is essential.

Epstein–Barr virus (EBV) is a γ -herpesvirus prevalent across various human populations (Young and Rickinson, 2004). EBV exhibits tumorigenic properties and is implicated in diseases like infectious mononucleosis and Hodgkin’s disease, which affect ENT regions such as the throat and lymph nodes (Macsween and Crawford, 2003). Cohen et al. explored EBV-associated lymphoproliferative diseases, including aggressive T-cell and NK-cell diseases that may impact the nasal cavity and other ENT regions, as well as ENT-related conditions like vesiculoderma-like lymphoma (Macsween and Crawford, 2003). Green et al. highlighted the role of EBV in post-transplant lymphoproliferative diseases, particularly in ENT areas like the oropharynx, with clinical presentations ranging from asymptomatic infections to aggressive lymphomas in solid organ transplant recipients (Cohen et al., 2009). Thus, investigating EBV-related drugs may aid in developing new ENT-related therapeutic strategies.

Specifically, we excluded Berberine, EBV and their associated MMIs from the dataset during model training. Subsequently, the trained model predicted the likelihood of interactions between all microbes (medicines) and Berberine (EBV). Following analysis, the top 10 microbes were identified, with results detailed in Table 4. It was confirmed that nine microbes interact with Berberine, as documented in the DrugVirus database. The results in Table 5 indicate that all 10 medicines predicted by the trained model interact with EBV and have been verified in DrugVirus. Therefore, the proposed model is demonstrably effective in independently identifying potential MMIs.