### Human MDAs

The data of MDAs are obtained from the HMDD v2.0 [19], which contains 5430 experimentally verified MDAs between 495 miRNAs and 383 diseases. To make better use of these information, we construct it as a matrix \(A \in R^{{n_{m} \times n_{d} }}\), where \(n_{d}\) and \(n_{m}\) represent the number of diseases and miRNAs, respectively. In addition, if disease *g* and miRNA _{h} are confirmed to have an association, then \(A\left( {g,h} \right)\) will be 1, otherwise 0.

### MiRNA function similarity

Wang et al. [20] developed a method for calculating the functional similarity of miRNAs, which was based on the assumption that similar miRNAs are more likely to be associated with similar diseases. The similarity score information of all miRNAs was obtained from http://www.cuilab.cn/files/images/cuilab/misim.zip. In this study, a \(n_{m} * n_{m}\) matrix \(MFS\) was constructed to indicate that miRNA similarity and the function similarity between miRNA *g* and miRNA _{h} can be expressed as \(MFS\left( {g,h} \right)\).

### Disease semantic similarity frame *I*

Disease semantic similarity is calculated from the hierarchical directed acyclic graph (DAG) of each disease [20]. The MeSH database (http://www.nlm.nih.gov/) contains the DAG information of all diseases. The semantic similarity scores between different diseases can be calculated by the relationship between their DAGs [19, 20]. Fig. 1 (a) shows the DAGs of brain neoplasms and liver neoplasms, where each node represents a specific disease MeSH descriptor. The DAG for the disease \(Z\) can be denoted as \(DAG_{Z} \left( {N_{Z} ,E_{Z} } \right)\), where \(N_{Z}\) represents the node set, which includes the MeSH descriptor for disease \(Z\) and its ancestor nodes, and \(E_{Z}\) denotes the layer set, which includes all edges connecting the parent node to the child node \(DAG_{Z}\). We assumed that \(l\) is a MeSH descriptor node in \(DAG_{Z}\), and its semantic contribution value in \(DAG_{Z}\) is as follows:

$$\left\{ {\begin{array}{*{20}c} {DS{1}_{Z} \left( l \right) = {1 }if \, l = Z \, } \\ {DS{1}_{Z} \left( l \right) = \max \left\{ {\Delta * DS{1}\left( {l^{\prime}} \right)} \right\}\begin{array}{*{20}c} {} & {} \\ \end{array} if \, l \ne Z} \\ \end{array} } \right.$$

(1)

where \(l^{\prime}\) is the child node of \(l\) and \(\Delta\) is used to indicate the semantic contribution decay, which is set to 0.5 according to previous literature [14] The semantic contribution of disease \(Z\) is defined as formula (2).

$$DV{1}\left( Z \right) = \sum\nolimits_{{l \in N_{Z} }} {DS{1}\left( l \right)}$$

(2)

It can be found that the more shared MeSH descriptor nodes in the DAG of the two diseases, the more similar the two diseases are. Therefore, the formula for calculating the semantic similarity score of disease \(d_{g}\) and \(d_{h}\) is as follows:

$$SD{1}\left( {d_{g} ,d_{h} } \right) = \frac{{\sum\nolimits_{{c \in N_{{d_{g} }} \cap N_{{d_{h} }} }} {\left( {DS{1}_{{d_{g} }} \left( c \right) + DS{1}_{{d_{h} }} \left( c \right)} \right)} }}{{DV{1}\left( {d_{g} } \right) + DV{1}\left( {d_{h} } \right)}}$$

(3)

According to Eq. (3), \(c\) denotes shared ancestral MeSH descriptor nodes by disease \(d_{g}\) and \(d_{h}\). The computational process of semantic similarity based on frame *I* for brain neoplasms and liver neoplasms is shown in Fig. 1 (b).

### Disease semantic similarity frame *II*

To differentiate the semantic contribution values of different diseases, which appear in the same layer of the same disease DAG, another calculation frame [21] was proposed. In this case the formula for calculating the semantic contribution value of disease \(l\) is as follows:

$$DS{2}_{Z} \left( l \right) = - \log \left( {\frac{{N_{l} }}{N}} \right)$$

(4)

where \(N_{l}\) represents the number of disease DAGs contained the MeSH descriptor of disease \(l\) and \(N\) denotes the number of all diseases in the MeSH database, i.e., \(N_{l} /N\) is the probability that the MeSH descriptor of disease \(l\) is present in all DAGs in the MeSH database. Based on frame *II*, the formula for calculating the semantic similarity score of disease \(d_{g}\) and \(d_{h}\) is as follows:

$$SD{2}\left( {d_{g} ,d_{h} } \right) = \frac{{\sum\nolimits_{{c \in N_{{d_{g} }} \cap N_{{d_{h} }} }} {\left( {DS{2}_{{d_{g} }} \left( c \right) + DS{2}_{{d_{h} }} \left( c \right)} \right)} }}{{DV{2}\left( {d_{g} } \right) + DV{2}\left( {d_{h} } \right)}}$$

(5)

where

$$DV{2}\left( Z \right) = \sum\nolimits_{{l \in N_{Z} }} {DS{2}\left( l \right)}$$

(6)

Finally, the similarity of different diseases at the semantic level is obtained by averaging the above two frames, which is shown as follows:

$$DS\left( {d_{g} ,d_{h} } \right) = \frac{{SD{1}\left( {d_{g} ,d_{h} } \right) + SD{2}\left( {d_{g} ,d_{h} } \right)}}{{2}}$$

(7)

### GIP kernel similarity

The GIP kernel [22] similarity aimed to measure the biological entities similarity based on their interaction profile information. GIP kernel similarity has been successfully introduced to the calculation of non-coding RNA and disease similarity [23]. In the adjacency matrix \(A\), the \(g\) row denotes the correlation vector between miRNA \(g\) and 383 diseases, and the \(h\) column indicates the correlation vector between disease \(h\) and 495 miRNAs. We used \(IP\left( {m_{g} } \right)\) and \(IP\left( {d_{h} } \right)\) to represent them respectively. The formula for calculating the GIP kernel similarity of miRNAs and diseases is as follows:

$$KD\left( {d_{g} ,d_{h} } \right) = \exp \left( { - \beta_{d} ||IP\left( {d_{g} } \right) - IP\left( {d_{h} } \right)||^{{2}} } \right)$$

(8)

$$KM\left( {m_{g} ,m_{h} } \right) = \exp \left( { - \beta_{m} ||IP\left( {m_{g} } \right) - IP\left( {m_{h} } \right)||^{{2}} } \right)$$

(9)

where

$$\beta_{d} = \beta^{*}_{d} /\left( {\frac{{\sum\limits_{{h = {1}}}^{n} {||IP\left( {d_{h} } \right)||^{{2}} } }}{{n_{d} }}} \right)$$

(10)

$$\beta_{m} = \beta^{*}_{m} /\left( {\frac{{\sum\limits_{{g = {1}}}^{m} {||IP\left( {m_{g} } \right)||^{{2}} } }}{{n_{m} }}} \right)$$

(11)

The original bandwidth \(\beta^{*}_{d}\) and \(\beta^{*}_{m}\) is set to 1.0 [24, 25].

### Integrating similarity

Whether miRNA functional similarity, disease semantic similarity or GIP kernel similarity, they only provide a single aspect of similarity. Therefore, it is essential to integrate the above similarity information to obtain a more accurate and comprehensive disease or miRNA similarity. For example, if miRNA \(m_{g}\) and miRNA \(m_{h}\) have functional similarity, they will be retained, otherwise it will be equal to \(KM\left( {m_{g} ,m_{h} } \right)\). Disease similarity is integrated using the same way. Therefore, the integration method is showed as follows:

$$FMS\left( {m_{g} ,m_{h} } \right) = \left\{ {\begin{array}{*{20}c} {MS\left( {m_{g} ,m_{h} } \right), \, m_{g} {\kern 1pt} and \, m_{h} \, have \, functional \, similarity} \\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} KM\left( {m_{g} ,m_{h} } \right), \, otherwise} \\ \end{array} {\kern 1pt} } \right.$$

(12)

$$FDS\left( {d_{g} ,d_{h} } \right) = \left\{ {\begin{array}{*{20}c} {DS\left( {d_{g} ,d_{h} } \right), \, d_{g} \, and \, d_{h} \, has \, semantic \, similarity} \\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} KD\left( {d_{g} ,d_{h} } \right), \, otherwise} \\ \end{array} } \right.$$

(13)

An example of data processing, including the calculation of GIP kernel similarity and the process of integrating similarity, is shown in Figure S1 in the supplementary file.

### BLNIMDA

On the basis of the hypothesis that functionally similar miRNAs are more likely to be linked with similar diseases, we proposed a method named BLNIMDA that combines the above-processed data, including integrated miRNA similarity, integrated disease similarity and MDAs and these data are mapped into a bi-level weighted network. The BLNIMDA predicts the MDAs based on this network and Fig. 2 provides a detailed visualization of the BLNIMDA flow. Accordingly, the BLNIMDA integrates four main computational steps, including: (i) The determination of the miRNA function similarity, the disease semantic similarity and GIP kernel similarities; (ii) The integration of the estimated similarities and mapping MDAs into a bi-level weighted network; (iii) The generation of two side information properties for each MDAs through bidirectional information construction and assignment of all MDAs into three categories, namely strong associations, potential associations, and no associations. (iv) The estimation of two affinity weights for each MDP through bidirectional information construction strategy and its association type, and then averaged as the final MDAs score. Considering the direction of miRNAs to diseases as an example, the information properties of each MDP is defined as formula (14):

$$S_{1} \left( {m_{g} ,d_{h} } \right) = \frac{{\sum\limits_{{k = {1}}}^{n} {HM\left( {m_{g} ,m_{k} } \right)A\left( {m_{k} ,d_{h} } \right)} }}{{\sum\limits_{{k = {1}}}^{n} {FMS\left( {m_{g} ,m_{k} } \right)A\left( {m_{k} ,d_{h} } \right)} }}$$

(14)

where

$$HM\left( {m_{g} ,m_{k} } \right) = \left\{ {\begin{array}{*{20}c} {FMS\left( {m_{g} ,m_{k} } \right) \, FMS\left( {m_{g} ,m_{k} } \right) \ge T \, } \\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \, otherwise} \\ \end{array} } \right.$$

(15)

Considering that the weak similarity nodes of \(m_{g}\) may affect the accuracy of prediction results, we set the parameter \(T\) to remove weak similar nodes. The MDAs are defined into three types: (i) \(m_{g}\) and \(d_{h}\) have strong association when they display unequivocal reciprocal association; (ii) \(m_{g}\) and \(d_{h}\) have potential association when they do not display direct association but the most similar node \(m_{s}\) to \(m_{g}\) has an unequivocal association with \(d_{h}\). (iii) otherwise, there is not any potential association. Three types of MDAs are shown in the formula (16).

$$W_{r} \left( {m_{g} ,d_{h} } \right) = \left\{ {\begin{array}{*{20}c} {\exp \left( {FMS\left( {m_{g} ,m_{s} } \right)} \right){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} A\left( {m_{g} ,d_{h} } \right) = {0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} and{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} A\left( {m_{s} ,d_{h} } \right) \ne {0}} \\ {\exp \left( {A\left( {m_{g} ,d_{h} } \right)} \right){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} A\left( {m_{g} ,d_{h} } \right) \ne {0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} } \\ {{0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} otherwise{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} } \\ \end{array} } \right.$$

(16)

where \(m_{s}\) is the miRNA with the greatest similarity to \(m_{g}\). From miRNA to disease, the affinity weight of each MDP are defined through a bidirectional information construction strategy and its association type according to formula (17):

$$S_{d} = S_{{1}} *W_{r}$$

(17)

From disease to miRNA direction, the information property of each MDP is the same as the above steps, and the details are as follows:

$$S_{2} \left( {d_{h} ,m_{g} } \right) = \frac{{\sum\limits_{k = 1}^{n} {HD\left( {d_{h} ,d_{k} } \right)A\left( {d_{k} ,m_{g} } \right)} }}{{\sum\limits_{k = 1}^{n} {FDS\left( {d_{h} ,d_{k} } \right)A\left( {d_{k} ,m_{g} } \right)} }}$$

(18)

where

$$HD\left( {d_{h} ,d_{k} } \right) = \left\{ {\begin{array}{*{20}c} {FDS\left( {d_{h} ,d_{k} } \right) \, FDS\left( {d_{h} ,d_{k} } \right) \ge T} \\ {{0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \, {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} otherwise} \\ \end{array} } \right.$$

(19)

The three types of miRNA-disease association are as follows:

$$W_{d} \left( {d_{h} ,m_{g} } \right) = \left\{ {\begin{array}{*{20}c} {\exp \left( {FDS\left( {d_{h} ,d_{s} } \right)} \right){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} A\left( {d_{h} ,m_{g} } \right) = {0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} and{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} A\left( {d_{s} ,m_{g} } \right) \ne {0}} \\ {\exp \left( {A\left( {d_{h} ,m_{g} } \right)} \right){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} A\left( {d_{h} ,m_{g} } \right) \ne {0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} } \\ {{0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} otherwise{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} } \\ \end{array} } \right.$$

(20)

In the same way, from disease to miRNA, the affinity weight of each MDP are determined through information property and the MDA type. The specific definition is as follows:

$$S_{r} = S_{2} *W_{d}$$

(21)

According to formulas (14)- (21), two affinity weights for each MDP are determined, and then averaged them as the final MDAs score following the formula (22):

$$S_{f} = \frac{{S_{d} + S_{r} }}{{2}}$$

(22)

A BLNIMDA calculation example, including the generation of two side information properties, the calculation of two affinity weights for each MDP and the MDA score, is shown in Figure S2 in the supplementary file.