Constructing benchmark data is a sufficient and necessary condition for building robust and reliable prediction model (Li and Liu, 2023; Zhang et al., 2023). We collected known association information between miRNAs and diseases, miRNAs identification name corresponding matrices, and miRNAs-diseases association adjacency matrices. We constructed miRNAs functional similarity matrices and diseases semantic similarity data. We generated latent features of miRNAs and diseases based on the miRNAs-diseases association matrix.

In this paper, we experimented with miRNAs-diseases association provided by HMDD v2.0 (http://cmbi.bjmu.edu.cn/hmdd), which includes 495 types of miRNAs and 383 kinds of diseases. We constructed an adjacency matrix of miRNAs-diseases interaction, MD, to facilitate the experiment and better represent the relationship between miRNAs and diseases. Each row in this matrix represents a type of miRNAs, and each column represents a type of diseases. If the ith kind of miRNAs and the jth type of diseases have a known association in the MD matrix, the MD(i, j) is set to 1; if there is no association between that miRNAs and diseases, it is set to 0. This method was used to construct the miRNAs-diseases association adjacency matrix MD.

In HMDD v2.0, there are known 5,430 pairs of miRNA disease associations, which are positive samples. We performed k-means clustering on unknown samples and randomly extracted a corresponding number of samples from each cluster as negative samples (Zhou et al., 2020a). We used downsampling to balance the positive and negative samples.

The SPALP model mainly consists of the following steps.

(i) Based on previous research, construct the miRNAs functional and diseases semantic similarity matrices. Decompose the known miRNAs-diseases association matrix into the miRNAs and diseases feature matrices. The miRNAs feature matrix is the miRNAs-diseases association matrix, and the diseases feature matrix is the transpose of the miRNAs-diseases association matrix.

These steps will be detailed in Figure 1.

The concept of miRNA functional similarity originates from the research conducted by Wang et al. (Wang et al., 2010). This concept is based on the observation that if a certain miRNA is associated with a specific disease, other similar miRNAs are also likely to be associated with that disease. Based on this idea, we constructed the miRNA functional similarity matrix, which each element in the matrix expresses the functional similarity score between two miRNAs.

Based on the approach by Wang et al. (Wang et al., 2010) and the MeSH database, a Directed Acyclic Graph (DAG) can be constructed, where the vertexes of DAG represent diseases, and the edges of DAG represent relationships between the vertexes. There is only one type of relationship can be connected between child vertexes with their parent vertexes. For a given disease A, it can be represented as DAG(A) = (T, E), where T is the set of A and all its ancestor nodes (including itself), and E is the collection of corresponding edges. We define the contribution of t (disease) to the semantic value of A (disease) as Eq. 1: D A A = 1   i f   t = A D A t = ⁡ max ∆ ∗ D A t ′ | t ′ ϵ c h i l d r e n   o f   t   i f   t ≠ A (1)

Here ∆ is the semantic contribution decay factor. Wang et al. set its value at 0.5 in their study on disease semantic similarity. The contribution of disease D to itself is 1, and the contributions of other diseases to D decrease with increasing distance. They define the semantic value DV(A) of disease A as Eq. 2: D V A = ∑ t ∈ T A D A t (2)

Between disease A and disease B, the semantic similarity b is determined using the following formula Eq. 3: S A , B = ∑ t ∈ T A ∩ T B D A t + D B t D V A + D V B (3)

From the adjacency matrix MD of miRNAs-diseases association, we obtain the feature matrix related to miRNAs and the feature matrix related to diseases. The dimension of the M i n i t i a l matrix is 495 × 383, and the dimension of the D i n i t i a l matrix is 383 × 495 as shown in Eqs 4 and 5. M i n i t i a l = M D (4) D i n i t i a l = M D T (5)

These two feature matrices are input into a sparse autoencoder, from which we obtain the latent features of miRNAs (M) and diseases (D). The dimension of the M matrix is 495 × 128, and the dimension of the D matrix is 383 × 128 as shown in Eqs 4, 5.

Based on the clustering results, the miRNA indices and disease indices are extracted and combined into an index matrix. Then, using the indices from the index matrix, the features of miRNAs and diseases can be retrieved. The latent features of miRNAs (M) are combined with the miRNA functional similarity matrix according to miRNA indices to form the M-feature as shown in Eq. 6. M − f e a t u r e = M , M s im (6)

The latent features of diseases (D) are combined with the disease semantic similarity matrix according to disease indices to form the D-feature as shown in Eq. 7. D − f e a t u r e = D , D s i m (7)

The M-feature and D-feature matrices are combined to create the final M-D feature matrix used for model processing as shown in Eq. 8. M − D − f e a t u r e =   M − f e a t u r e , D − f e a t u r e   (8)

This process allows for a comprehensive representation of miRNA and disease characteristics, incorporating inherent features and relational similarities to enhance the model’s predictive accuracy.

For a sparse autoencoder, the objective function consists of the reconstruction error and the sparsity penalty term. The reconstruction error part trains the network by minimizing the error between the input and output. Its formula is as follows: J r econstruction W , b ; x i = 1 2 y x i − x i 2 (9)

Where W and b are the network weights and biases, x i is the ith sample in the training datasets, and y x i is the output of the network.

The sparsity penalty term can be implemented through a sparsity constraint, which is formulated as follows: J s parse a = ∑ j = 1 s K L ρ ρ ^ j (10)

In this formula, s is the number of neurons in the hidden layer, a represents the output of the hidden layer, ρ is the desired average activation of the neurons, and ρ ^ j is the actual average activation computed. K L ρ ρ ^ j represents the Kullback-Leibler divergence and is calculated using the following formula: K L ρ ρ ^ j = ρ ⁡ log ρ ρ ^ j + 1 − ρ log 1 − ρ 1 − ρ ^ j (11)

Sparse autoencoder uses network to learn features and perform feature extraction. Including the sparsity penalty ensures that the learned representations are robust and that the network does not over fitting the training data. This approach is particularly beneficial for capturing the essential characteristics of the data in a compressed form, which is crucial for effective feature representation in complex datasets like those involving miRNAs and diseases.

A Multi-layer Perceptron (MLP) network consists of an input layer, one or more hidden layers, and an output layer, which is a feed forward neural network that learns the mapping relationship from input to output for pattern recognition and classification tasks.

Assuming there are m samples with n features, the input layer X can be represented as X ∈ R m × n . If the MLP has only one hidden layer with h neurons, then the weights and biases of the hidden layer can be denoted as W h ∈ R n × h and b h ∈ R 1 × h , respectively. If there are q output labels, the weights and biases of the output layer are W o ∈ R h × q and b h ∈ R 1 × q . The outputs of the hidden layer can be computed by the formula (12). The output layer can be calculated using the formula (13). H = X W h + b h (12) O = X W o + b o (13)

We typically use the Rectified Linear Unit (ReLU) activation function. ReLU : y = ⁡ max x , 0 (14)

For the l t h layer ( l = 1,2,., L ), the output is z l before the activation function and the output is a l after activation function. Then, the output of the previous layer after activation becomes the input for the current layer, and the output before activation of the current layer is: z l = W l a l − 1 + b l (15) a l = σ z l (16)

Computing the output values through various weights and biases of layer is commonly known as forward propagation. We use a process called back propagation to calculate the error and update the model. In back propagation, we derive from the output layer back to the input layer to obtain the gradient formulas for each layer’s weights. W l and biases b l .

This structure allows the MLP to effectively capture and model complex relationships in the data, making it a powerful tool for classification and regression in various fields, including bioinformatics and medical research.

In our experiments, the Accuracy, Precision, Recall, F1-score, True Positive Rate (TPR), and False Positive Rate (FPR) as evaluation metrics facilitate the assessment of the performance of SPALP model, which are constructed by True Positive (TP), False Positive (FP), True Negative (TN), False Negative (FN) from confusion matrix of two categories (Ai et al., 2023; Zhu et al., 2023a; Zhu et al., 2023b; Wang et al., 2023c; Qian et al., 2023; Zou et al., 2023). In order to display the performance of the model more intuitively, the Receiver Operating Characteristic (ROC) curve can be plotted by TPR and FPR and the Precision-Recall (PR) curve can be plot by Precision and Recall. The area under the ROC curve is represented by AUC. A c c u r a c y = T P + T N T P + T N + F P + F N (17) P r e c i s i o n = P = T P T P + F P (18) R e c a l l = R = T P T P + F N (19) F 1 − s c o r e = 2 T P 2 T P + F P + F N (20) T P R = T P T P + F N (21) F P R = F P F P + T N (22)

To study the impact of latent feature dimensions on the SPALP model, miRNAs latent features and diseases latent features of 8, 16, 32, 64, 128, 256, and 512 dimension size are adopted to the sparse autoencoder. We first plot the loss function curves for miRNAs and diseases latent features based on different dimension obtained through the sparse autoencoder, respectively, as shown in Figure 2. The curve loss is calculated by the sparse autoencoder, representing the error between the original data and the output of the decoder. Figure 2 shows when the dimension is set to 128, the loss function reliably converges to its minimum value.

By comparing these two loss function graphs, we found that the loss values of miRNAs latent features and diseases latent features continuously decrease from 8 dimensions to 64 dimensions, indicating that the larger the dimension of latent features before 64 dimensions, the better performance can be obtained. However, the loss values of latent features from 64 to 512 dimensions are essentially the same.

To further compare different dimensional size of latent features impacting on the capability of SPALP model, we also plot ROC curves and PR curves for comparison, with the results shown in Figure 3. Figure 3 demonstrates that the ROC and PR curves can converge to the best value when the dimension is 128, because the area below the ROC and PR curves is the largest.

Additionally, to more clearly observe the evaluation metrics for 8, 16, 32, 64, 128, 256, 512 dimensions and to explore the optimal dimension, the results of evaluation are shown in Table 2. When the dimension is 128, the SPALP model can get optimal prediction results. Furthermore, two phenomena can be observed. Firstly, when the latent feature dimension size is below 128, there is a gradual improvement based on various evaluation metrics from 8 to 128 dimensions. This indicates that when the dimension is below 128, the lower the dimension, the less comprehensive the feature representation will be. Secondly, if the dimension size exceeds 128, the performance of the SPALP model progressively worsens with increasing dimension size. This decline in performance may be due to redundancy in the data features, as excessive features can lead to over fitting or noise in the model. Therefore, we selected 128 dimension as the optimal latent feature dimension for the SPALP model.

To explore the effectiveness of our model in predicting miRNAs and diseases association, four sets of experiments about features are designed in following.

The first group used only similarity data, i.e., miRNAs functional similarity data and diseases semantic similarity data. The second group combined similarity data with unprocessed data. The third group used only latent features produced by the sparse encoder, i.e., miRNAs and diseases latent features. The fourth group is SPALP, which used both similarity data and latent features processed by the sparse encoder.

By comparing these four groups, we investigate the effectiveness of our model in the combined prediction of miRNAs and diseases association. We plotted ROC and Precision-Recall (PR) curves for the above combinations, as shown in Figure 4. Additionally, we compiled statistics for the different combinations, including Accuracy, Precision, Recall, F1-score, and AUC values, as shown in Table 3.

From the figures and the table, the accuracy of these four experiments is 0.8203, 0.8954, 0.9382, and 0.9461, respectively, and the AUC value is 0.8991, 0.9591, 0.9811, and 0.9859, respectively. The comparison indicates that the performance of predictions using only similarity data has the worst results. The performance improved when similarity data are combined with unprocessed feature matrices. The best results are achieved using SPALP, which combine latent features with similarity data.

Several commonly used and effective classifiers are compared with MLP, including K-Nearest Neighbors (KNN), Decision Tree, Random Forest, Logistic Regression, XGBoost. ROC and PR curves are plotted based on their performance in the experiments, as shown in Figure 5. The larger the area under the ROC curve, the better the prediction effect. For the PR curve, the larger the area wrapped by the curve and the larger the equilibrium point (Recall = Precision), the better the performance. Figure 5 demonstrates that MLP can reach the optimal performance, which is best classifier.

Table 4 shows the comparison among the six classifiers (Decision Tree, KNN, Logistic Regression, Random Forest, XGBoost, MLP) by accuracy, precision, recall, F1-score and AUC values. Although, the recall value obtained by MLP classifier is slightly lower than XGBoost, MLP is overall optimal classifier.

Evaluation criteria for classifier performance mainly include Accuracy, F1-score, and the AUC value of the ROC curve. MLP had the highest Accuracy, F1-score, and AUC values in this experiment, indicating the most significant classification effect.

To further evaluate the performance of our model on prediction task, we compared the SPALP model with other methods (SMALF (Liu et al., 2021), GBDT-LR (Zhou et al., 2020b), ABMDA (Zhao et al., 2019), HGANMDA (Zhengwei et al., 2022), SAEMDA (Wang et al., 2022), ELMDA (Gu and Li, 2023)).

SMALF uses stacked autoencoders for latent feature extraction and XGBoost for classification. GBDT-LR initially integrates miRNAs similarity and disease similarity to represent miRNAs-diseases relationship, then applies GBDT to extract new features, and finally, the logistic regression algorithm is used to predict miRNAs-diseases association. ABMDA utilizes a boosting algorithm integrated with many decision trees to mine miRNAs-diseases association and accurately calculate miRNAs-diseases similarity. HGANMDA uses a hierarchical attention network to learn the importance of different neighboring nodes and meta paths, and uses bilinear decoders to predict the association of miRNA diseases. SAEMDA uses stacked autoencoders to train and predict miRNA disease associations, while ELMDA extracts structural features of miRNA disease pairs and uses multi classifier voting to predict disease-related miRNAs.

In this section, we designed a comparative experiment to compare the above six models with the SPALP model. The experimental results are shown in Figure 6. Using the data provided in HMDDv2.0, the experimental results showed that the SPALP model had the highest AUC value among these seven models, indicating that the SPALP model has good predictive ability for miRNA disease associations.

To further validate the performance of SPALP, five different diseases are selected as case studies for predicting miRNA-disease associations in our experiments. They are Acute Myeloid Leukemia, Lupus Erythematosus, Cardiovascular disease, Stroke, Diabetes Mellitus(Type 2) respectively. Also, they are common diseases in the elderly population.

The SPALP model can predict unknown miRNAs disease associations by integrating known miRNAs disease associations and similarity information. Firstly, on the HMDD v2.0 database, the SPALP model is trained using known miRNAs disease associations. The association between all miRNAs and a certain disease is used as the test set. Then, the trained model is used to calculate the association miRNAs score for the aforementioned diseases, which is a continuous value; Finally, arrange in descending order based on the predicted score (probability value). After removing miRNAs known to be associated with these diseases in HMDD v2.0, output miRNAs predicted by the SPALP model to be associated with a certain disease. RNARelease V4.0 database can be obtained from http://www.rnadisease.org/# and can be used to validate the top 30 miRNAs.

As shown in Tables 5–9, after validation in RNADisease V4.0, 27 out of the top 30 miRNAs predicted by the SPALP model that may be related to Lupus Erythematosus passed the validation, as shown in Table 5. In Table 6, except for hsa-mir-205, which was not found in the miRNAs database related to Act Myeloid Leukemia, all other miRNAs predicted by the SPALP model were found. However, we found the miRNA hsa-mir-205 in the miRNAs database related to Leukemia. Explain that hsa-mir-205 is associated with Leukemia.Among the top 30 predicted miRNAs, 29 can be validated for Cardiovascular disease through RNADisease V4.0. More interestingly, for Stroke and Diabetes Mellitus(Type 2), 30 miRNAs have been fully verified in the RNADisease V4.0 database. These results indicate that the SPALP model has a strong ability to predict the association between unknown miRNAs and diseases.