For this study, to assess the model’s ability to predict CMI, we utilized two commonly used datasets, namely, the CMI-9589 dataset and the CMI-9905 dataset. The CMI-9589 dataset is sourced from the CircBank (Liu et al., 2019) database, which is a comprehensive human circRNA database containing detailed annotations for 140,790 human circRNAs from various sources. In addition to providing basic information about circRNA, CircBank also offers a set of interaction data between circRNA and miRNA for predicting and analyzing miRNA interactions. Based on the cleaning and summarizing the data, we acquired known 9,589 circRNA-miRNA pairs, among which 2,115 circRNAs and 821 miRNAs were involved. The CircR2Cancer (Lan et al., 2020) database is a manually curated database that associates circRNA with cancer. The CMI-9905 dataset, obtained by Wang et al. (2022b), comprises data on circRNA-miRNA interactions from the public database CircR2Cancer, including combined 318 circRNA-miRNA pairs among 238 circRNAs and 230 miRNAs. By integrating the data of the two databases, 9,905 good-quality CMI pairs were final acquired, comprising 2,346 circRNAs and 962 miRNAs. In this study, we primarily utilized the CMI-9905 dataset and regarded it as the positive sample, detailed information is available in Table 1. Subsequently, we randomly selected 9,905 unknown CMI pairs from the data pool of 2346 × 962 − 9905 = 2 , 246 , 947 as negative samples.

In bioinformatics, researchers typically analyze the nucleotide sequences of RNA to extract features such as nucleotide composition, base pair frequency, sequence length, etc. These features help reveal the structure, function, and relationships with other biomolecules of RNA. Due to the substantial differences in the length of circRNA nucleotide sequences, with some long circRNAs containing thousands of nucleotides and short circRNAs containing only a few hundred nucleotides, we chose to use the Jaccard similarity coefficient to extract attribute features from circRNA sequences. This is because the Jaccard similarity coefficient can better reflect the similarity between sequences of different lengths. miRNAs usually have relatively short lengths, typically between 20 and 22 nucleotides. To extract attribute features from miRNA sequences, we employed the Bert model. Finally, we integrate the attribute features of circRNAs and miRNAs depending on the interaction relationships and finally obtain the CMI attribute features of known relationship pairs.

Graph embedding (Yan et al., 2006) is a technique that maps every node in a diagram structure to a low-dimensional vector space, and it plays a crucial role in many graph data analysis tasks. In the field of bioinformatics, graph embedding is widely used to study complex biological relationships (Yi et al., 2022), such as molecular interactions and gene regulatory networks. Graph embedding utilizes known interactions among circRNAs with miRNAs to obtain a matrix that the behavior feature of circRNAs with miRNAs. An interaction information network is regarded as G = V , E , in which V denotes the collection of vertices (data objects) and E denotes the collection of edges interactions between vertices. Most graph embedding methods only consider first-order proximity, such as Deepwalk (Perozzi et al., 2014). In this study, we employ the Line (Tang et al., 2015) graph embedding algorithm, which preserves both first-order and second-order proximity, thus better preserving the global structure of the network. By learning low-dimensional representations of nodes, we can more effectively capture the similarity and interaction of nodes in the graph structure.

The first-order proximity in the interaction network of circRNA and miRNA is the local pairwise proximity between two vertices, V c and V m . If there is no edge, the first-order proximity is 0. For each undirected edge c , m , the formula for the first-order joint probability distribution of vertices V c and V m is defined as Formula 4: p 1 V c , V m = 1 1 + ⁡ exp − u → c T ⋅ u → m (4)

Where u → c , u → c ∈ R d are the low-dimensional representation vectors of vertices V c and V m . It is first-order goal function is shown in Formula 5: O 1 = ∑ c , m ∈ E W c m ⋅ ⁡ log ⁡ p 1 V c , V m (5)

Where W c m is the connection weight between vertices V c and V m . The second-order proximity in the interaction network of CircRNA and miRNA is the similarity between the neighborhood network structures of two vertices V c and V m . If there is no neighborhood network structure, the second-order proximity is 0. In the second-order proximity, each vertex has two tasks: Task 1: the vertex itself, Task 2: a specific context with other vertices. For each edge c , m , the second-order joint probability distribution formula is Formula 6: p 2 V m | V c = exp u → m ′ T ⋅ u → c ∑ k = 1 V exp u → k ′ T ⋅ u → c (6) where V is the number of vertices or contexts. It is second-order goal function is shown in Formula 7: O 2 = ∑ c , m ∈ E W c m ⋅ ⁡ log ⁡ p 2 V m | V c (7)

To expedite the learning process, we modify the Formula 7 using negative sampling. The modified objective function is expressed as Formula 8: O 2 = ⁡ log ⁡ σ u → m ′ T ⋅ u → c + ∑ i = 1 K E V n ∼ P n V log ⁡ σ − u → n ′ T ⋅ u → c (8)

Where σ x = 1 1 + ⁡ exp − x is the sigmoid function, K is the number of negative samples, and P n V ∼ d V 3 4 is usually set, where d V represents the degree of vertex V .

Autoencoder is an unsupervised learning neural network model designed to learn efficient representations of data. It can be utilized for tasks such as data compression, denoising, and feature extraction. The autoencoder model is instrumental in aiding the exploration and prediction of interactions among non-coding RNAs. In this study, we use the Autoencoder in Autoencoder Networks (Zhang et al., 2019) model to effectively fuse circRNA and miRNA with multi-angle features, that is, to fuse the two angular features of circRNA and miRNA, so that the fused features not only have complementarity between behavioral features and attribute features, but also have complementarity between behavioral features and attribute features. It also has the consistency between behavior characteristics and attribute characteristics. The Autoencoder in Autoencoder Networks model mainly includes the First-AE network and the Second-AE network, which can learn single-angle feature representation and complete multi-angle feature representation together. Then the First AE network is used to extract the implicit information of each Angle automatically, and the degradation process of the Second AE network is used to encode the implicit information of each Angle into the potential representation. We represent the sample of multi-angle features as X = X 1 , X 2 , . . . , X V , X V ∈ R d v × n is the feature matrix of the V − t h Angle feature, where V represents the number of angles of the V − t h Angle feature, n represents the number of samples of the V − t h Angle feature, and d v represents the feature dimension of the V − t h Angle feature.

XGBoost (Chen and Guestrin, 2016) is referred to as extreme gradient boosting, and it is an integrated learning algorithm based on gradient boosting decision trees (GBDT). It is employed to solve machine learning issues such as classification, regression, and ranking. XGBoost benefits from its efficiency, regularization processing, feature importance analysis, and ability to handle missing values, making it a powerful tool for many data science problems. We employ XGBoost as a classifier for predicting circRNA-miRNA interactions. Through multiple iterations, we gradually construct a decision tree model, emphasizing error samples to enhance model performance. The objective function of XGBoost is composed of the loss function and regularization, and is formulated as Formula 14: L u = ∑ i = 1 M l y i , y ^ i u − 1 + f u x i + ∑ u φ f u (14)

Here, i represents the i − t h sample, u represents the u − t h tree, y i is the true value of the i − t h sample x i , y ^ i is the predicted value of the i − t h sample x i , l is the differentiable loss function computing the difference between the predicted value y ^ i and the target value y i , and φ ∙ represents the complexity of the tree. By expanding the second-order Taylor series and regularization term, separately optimizing the loss function term and regularization term, and merging similar terms, the final objective function is obtained as Formula 15: L u = ∑ j = 1 U B n w n + D n + λ w n 2 2 + γ U (15)

Here, B n and D n respectively represent the sums of the first and second-order partial derivatives of the samples contained in leaf node n , w n represents the weight of the n − t h leaf node, and U represents the number of trees.

Cross-validation is a commonly used method in the field of machine learning for assessing model performance and reducing the bias of evaluation results. In this work, we employ 5-fold cross-validation (5-fold CV) to assess the predictive power of BJLD-CMI over CMI-9905 dataset. We initially randomly divided the dataset into five subsets, ensuring a balanced distribution of categories in each subset as much as possible. Four subsets were utilized for pieces of training of the model and then one remaining subset was used for validation of the model. This process is repeated five times, ensuring that each subset is used for validation once. The results of the five validations were averaged to get the final performance evaluation metrics (Wang et al., 2018). The experimental evaluation of BJLD-CMI includes accuracy (ACC), precision (Prec.), recall (Rec.), F1-score (F1), and Matthews correlation coefficient (MCC) as reliability assessment criteria. The formula for accuracy is Formula 16, for precision is Formula 17, for recall is Formula 18, for F1-score is Formula 19, and for Matthews correlation coefficient is Formula 20: A C C . = T N + T P T N + T P + F N + F P (16) P r e c . = T P T P + F P (17) R e c . = T P T P + F N (18) F 1 − s c o r e = 2 × P r e c i s i o n × R e c a l l P r e c i s i o n + R e c a l l (19) M C C . = T P × T N − F P × F N T P + F P × T P + F N × T N + F P × T N + F N (20)

In the above formula, true positives (TP) indicate the sample counts in which the model predicts that circRNAs interact with miRNAs and in which the interaction is realistically confirmed, false positives (FP) indicate the sample counts in which the model predicts that circRNAs interact with miRNAs but in reality are not interaction, true negative (TN) indicates the sample count in which the model predicts that circRNAs not interact with miRNAs and realistically confirms that there is no interaction, false negative (FN) indicates the sample count in which the model predicts that circRNAs not interact with miRNAs but the interaction is confirmed in reality. We also plotted the Receiver Operating Characteristic (ROC) curve of BJLD-CMI under 5-fold cross-validation (Zweig and Campbell, 1993) and computed the AUC to evaluate the performance of the models.

In this experiment, we tested the performance of BJLD-CMI in predicting circRNA-miRNA interactions over the CMI-9905 dataset with a 5-fold cross-validation method. Table 2 lists the details of the experimental results. From Table 2, we can see that our model obtained a mean accuracy of 83.41%. The accuracies for the five experiments were 83.47%, 84.07%, 82.53%, 83.06%, and 83.90% respectively, with a standard deviation of 0.56%. In the evaluation criteria of precision (Prec), recall (Rec), F1-score, and Matthews correlation coefficient (MCC), BJLD-CMI demonstrated an accuracy of 85.31%, 80.70%, 82.94%, and 66.91%, with respective standard deviations of 0.38%, 0.93%, 0.64%, and 1.10%. In addition, we also computed the AUC and AUPR that BJLD-CMI generated over the CMI-9905 dataset with their ROC curves and PR curves plotted. Concerning AUC, the five experiments yielded results of 90.56%, 91.41%, 90.21%, 90.49%, and 90.75%, with a mean value of 90.69% and a standard deviation of 0.45%. Concerning AUPR, the five experiments resulted in 88.87%, 90.06%, 89.01%, 88.66%, and 89.39% with a mean value of 89.20% and a standard deviation of 0.55%, respectively. Figure 3A shows the ROC curves generated by five experiments, and Figure 3B shows the PR curves generated by five experiments. Through the experimental results described above, it is clearly observed that the BJLD-CMI is able to predict CMI effectively on CMI-9905, and shows excellent comprehensive performance, exhibits good application prospects, and may be considered as a potential tool for exploring the unknown CMI.

The model utilizes the Line algorithm in graph embedding to learn low-dimensional embeddings of nodes in the circRNA-miRNA relationship network, preserving the network structure and relationships between nodes. Determining the dimension is a crucial factor in describing the features of circRNA and miRNA. Choosing a big dimension could increase the computational workload and intricacy of the suggested model, resulting in longer execution times and potentially lower accuracy. Conversely, selecting a small dimension might lead to an insufficient feature extraction. Therefore, we chose a series of commonly used dimensions, specifically 32, 64, 128, 256, 512, and conducted a 5-fold cross-validation experiment to select the optimal dimension. Based on the experimental results in Table 3; Figure 4, we observed a continuous improvement in the overall performance of the model with increasing dimensions. When the dimension parameter increases to 128, the model achieves optimal performance, as reflected in the maximum values of ACC, AUC, Prec., and MCC. However, when the dimension exceeds 128, the performance gradually declines. Therefore, we decided to fix the dimension parameter at 128.

Our proposed BJLD-CMI model uses the XGBoost classifier for data training and classification tasks over the CMI-9905. To validate the performance of the XGBoost classifier, we replaced it with four other classifiers while keeping the dataset and other conditions unchanged. These classifiers are Random Forest (RF) (Breiman, 2001), Gaussian Naive Bayes (GaussianNB), Support Vector Machine (SVM) (Suykens and Vandewalle, 1999), and Logistic Regression (LR) (Dreiseitl and Ohno-Machado, 2002). The performance of these five classifiers in predicting CMI was evaluated by 5-fold cross-validation and their categorization performance is compared. Table 4 concludes the average results of the five classifiers combined with the CMI-9905 dataset after 5-fold cross-validation and is presented in line graph form. From Figure 5, we can intuitively observe that XGBoost achieved the highest results in six evaluation metrics, including ACC, Prec, Rec, F1, MCC, and AUC. This indicates that XGBoost performs better in predicting unknown CMI in the proposed model.

Currently, numerous outstanding computational approaches have been proposed, relying on benchmark datasets CMI-9589 [from the Circbank database (Liu et al., 2019)] and CMI-9905 [from the Circbank database (Liu et al., 2019) and Circr2cancer database (Lan et al., 2020)]. These methods include WSCD (Guo et al., 2022), SGCNCMI (Yu et al., 2022), KGDCMI (Wang et al., 2022b), DeepCMI (Li et al., 2023), CMIVGSD (Qian et al., 2021b), GCNCMI (He et al., 2022), JSNDCMI (Wang et al., 2023), aim to forecast potential CMIs. In order to further assess BJLD-CMI’s predictive performance, we have compared it to these methods in two datasets, respectively. For fairness, we chose the AUC generated by the fivefold CV method as the parameter for evaluation. Table 5 presents the contrasting outcomes of CMIVGSD, SGCNCMI, KGDCMI, GCNCM, JSNDCMI, and DeepCMI with BJLD-CMI utilizing the CMI-9589 dataset. Table 6 shows the contrasting outcomes of KGDCMI, WSCD, SGCNCM, JSNDCMI, and DeepCMI with BCMCMI utilizing the CMI-9905 dataset. The results in Tables 5, 6 indicate that our model achieved the highest AUC results, surpassing the averages by 0.00986 and 0.03158, respectively. Overall, BJLD-CMI demonstrates strong competitiveness among existing methods.

In order to validate the genuine predictive ability of BJLD-CMI for miRNA-associated circRNA, we performed a case study utilizing the CMI-9905 dataset. In the experiment, we trained the BJLD-CMI model using known CMIs extracted from the CMI-9905 dataset and then used the trained model to predict unknown CMIs. Following the acquisition of the prediction outcomes, we organized the prediction scores in descending order and validated the top 10 circRNA-miRNA pairs in the published literature. The specific findings are outlined in Table 7. From the table, we can conclude that 7 pairs have been confirmed in PubMed, confirming the involvement of circRNA as miRNA sponges in the biological processes of diseases such as lung cancer (Wang et al., 2019; Yao et al., 2019; Zhou et al., 2019), prostate cancer (Wu et al., 2019), and gastric cancer (Zhong et al., 2018; Liang et al., 2019). It’s worth noting that the lack of confirmation in existing literature for the other 4 pairs does not necessarily negate the possibility of an interaction between them. The results of the case study indicate that BJLD-CMI is a powerful tool with the prospect of exploring the interaction of unknown circRNAs with miRNAs.