ELLPMDA: Ensemble learning and link prediction for miRNA-disease association prediction

ABSTRACT

Recently, accumulating evidences have indicated miRNAs play critical roles in the progression and development of various human complex diseases, which pointed out that identifying miRNA-disease association could enable us to understand diseases at miRNA level. Thus, revealing more and more potential miRNA-disease associations is a vital topic in biomedical domain. However, it will be extremely expensive and time-consuming if we examine all the possible miRNA-disease pairs. Therefore, more accurate and efficient methods are being highly requested to detect potential miRNA-disease associations. In this study, we developed a computational model of Ensemble Learning and Link Prediction for miRNA-Disease Association prediction (ELLPMDA) to achieve this goal. By integrating miRNA functional similarity, disease semantic similarity, miRNA-disease association and Gaussian profile kernel similarity for miRNAs and diseases, we constructed a similarity network and utilized ensemble learning to combine rank results given by three classic similarity-based algorithms. To evaluate the performance of ELLPMDA, we exploited global and local Leave-One-Out Cross Validation (LOOCV), 5-fold Cross Validation (CV) and three kinds of case studies. As a result, the AUCs of ELLPMDA is 0.9181, 0.8181 and 0.9193+/−0.0002 in global LOOCV, local LOOCV and 5-fold CV, respectively, which significantly exceed almost all the previous methods. Moreover, in three distinct kinds of case studies for Kidney Neoplasms, Lymphoma, Prostate Neoplasms, Colon Neoplasms and Esophageal Neoplasms, 88%, 92%, 86%, 98% and 98% out of the top 50 predicted miRNAs has been confirmed, respectively. Besides, ELLPMDA is based on global similarity measure and applicable to new diseases without any known related miRNAs.

KEYWORDS:

• association prediction
• disease
• ensemble learning
• link prediction
• microRNA

Introduction

MicroRNAs (miRNAs) are a family of small non-coding RNAs (containing about 22 nucleotides) that play a significant regulatory roles in animals and plants by targeting mRNAs for cleavage or translational repression [1]. Currently, a great many of studies have indicated that miRNA is one of the most important component in cell, which makes a vital contribution in multiple fundamental biological processes, including cell development, proliferation, signal transduction, differentiation, apoptosis, viral infection, metabolism, aging and so on [2–8]. Apparently, taking all the above functions into account, seeking for comprehensive information about miRNA might be a superior way to understand creatures at cell level. Twenty four years after the discovery of the first two miRNAs (Caenorhabditis elegans lin-4 and let-7), due to various experimental methods and computational models, thousands of miRNAs have been discovered recently [9–12]. In the latest version of miRBase [12] (see http://www.mirbase.org/), there are 28645 entries and more than 1000 human miRNAs. Furthermore, up to now, hundreds of miRNAs with different sequences and expression patterns have been discovered in diverse animals [7,13,14].

In recent years, the relationship between miRNAs and human diseases has attracted the most attention. Accumulating evidences have indicated that miRNA mutations or mis-expression correlate with various human cancers which implies miRNAs can function as tumor suppressors and oncogenes [15]. For instance, the dysregulation of the miRNAs has been confirmed as a main reason of aberrant cell behavior by many studies [11]. Furthermore, Single-nucleotide polymorphisms (SNPs) located at miRNA-binding sites (miRNA-binding SNPs) are likely to affect the expression of the miRNA target and may contribute to the susceptibility of humans to common diseases [16]. Moreover, downregulation of miR-101 is involved in cyclooxygenase-2 overexpression in human colon cancer cells. Also, miR-214 has been confirmed to be related to human ovarian cancer by inducing cell survival and cisplatin resistance [17,18]. Another example is that biological studies pointed out miR-34a inhibits prostate cancer stem cells and metastasis by directly repressing CD44 [19]. Besides, researches had pointed out that the miR-15a–miR-16-1 cluster controls prostate cancer by targeting multiple oncogenic activities [20].

Therefore, considering the close relationship between miRNAs and human diseases, identifying more potential associations between miRNAs and diseases is currently an important goal in biomedical domain because it might contribute a lot to the research about diseases. However, it will be extremely expensive and time-consuming if we test all the miRNA-disease pairs by biological experiment. Thus, in order to avoid the waste of money and time, it is necessary to predict the most potential miRNA-disease pairs. As more and more databases are available, developing computational model would be an effective way to reveal potential association between miRNAs and diseases [21–30].

Based on the assumption that miRNAs with similar functions are more likely to have connections with diseases which share similar phenotypes, various computational methods have been established to predict the potential associations between miRNAs and diseases [31–34]. Jiang et al. [30] prioritized the entire human microRNAome for diseases of interest by integrating predicted miRNA-target associations, disease phenotype similarities, and known miRNA-disease associations. However, this computational model could not reach a satisfactory predictive accuracy because it strongly relies on the predicted miRNA-target interactions with high false-positive and false-negative results. Moreover, Shi et al. [35] advanced a model which mapped disease genes and miRNA targets on the protein-protein interaction (PPI) network by integrating the information of miRNA-target interactions, disease-gene associations and PPIs. Base on the assumption that a miRNA tends to be related with the diseases whose genes are correlated with the target of this miRNA, they paid attention to the aforementioned information to identify miRNA-disease associations. Xu et al. [36] made use of a miRNA prioritization method which exploited the similarity between the miRNAs targets and disease genes instead of exploiting the known miRNA-disease association. They constructed the miRNA target–dysregulated network (MTDN) and trained a support vector machine (SVM) on their own-defined gold standard data set to reveal novel miRNA-disease associations. Although it is a creative challenge, this method could not achieve a satisfactory accuracy because of the aforementioned reason that the miRNA-target interaction is not accurate enough. Besides, by integrating miRNA-protein association scores and protein-disease association scores, Mork et al. [37] presented a miRPD method to create scoring schemes that enable them to rank candidate miRNA–disease pairs. Furthermore, they obtained high-confidence and medium-confidence sets of miRNA-disease associations. However, because of the similar reason that miRNA-target interactions were not reliable enough, the predictive performance is not very satisfactory.

Considering the apparent limitation of miRNA-target interactions, several networks such as miRNA functional similarity network, disease semantic similarity network, disease phenotype similarity network, and miRNA-disease associations network were constructed, after that, multiple methods depending on them were developed. For example, Xuan et al. [29] presented a method names HDMP relied on weighted k most similar neighbors to predict disease-related miRNAs. To increase the accuracy of miRNA functional similarity calculated by the classic methods, they introduced information content of disease terms and disease phenotype similarity. HDMP did get a higher predictive accuracy than most of previous methods. However, it is based on a local similarity measure rather than a global measure which is obviously better. Furthermore, HDMP could not be used on new diseases without any known related miRNAs.

Moreover, to overcome the limitation of local similarity measure, Chen et al. [25] presented the model of Random Walk with Restart for MiRNA–Disease Association (RWRMDA) to infer potential miRNA–disease association. Based on global network information, random walk with restart was implemented on the miRNA functional similarity network. Moreover, RWRMDA was capable of simultaneously ranking all the miRNA-disease pairs. Although the predictive accuracy had been improved a lot, this model could not be exploited for diseases without any known associated miRNAs. In order to solve this problem, Chen et al. [28] further introduced another method called WBSMDA, which is based on miRNA functional similarity, disease semantic similarity, miRNA-disease associations, and Gaussian interaction profile kernel similarity for miRNAs and diseases. Comparing with RWRMDA, WBSMDA could be applied to diseases without any related miRNAs, which is a significant breakthrough in miRNA-disease association prediction. However, the performance of WBSMDA was not very satisfactory and they did not find a way reasonable enough to combine the Within-Score and Between-Score. What's more, to take the prior information regarding the network nodes and the respective local topological structures of the different categories of nodes into account. Xuan et al. [38] introduced another method named MIDP, which took advantage of the characteristics of the nodes and the various ranges of topologies. MIDP was also based on random walk, and it effectively relieved the negative effect of noisy data.

Also, more and more machine learning-based computational models were introduced in miRNA-disease association prediction. For instance, according to the assumption that miRNAs implicated in a specific tumor phenotype will show aberrant regulation of their target genes, Xu et al. [36] established a heterogeneous miRNA-target dysregulated network, extracted four network topological features, and developed Support Vector Machine (SVM)-based Supervised classifier to distinguish positive disease related miRNAs from negative ones. Although SVM is a theoretically accurate method, collecting known negative associations is a very difficult and even impossible task. Thus, this method did not give a good performance. Chen et al. [24] proposed another machine learning method which made use of semi-supervised learning to predict potential disease-related miRNAs (RLSMDA). Though RLSMDA is applicable for diseases without any related miRNAs, there are also limitations in combination of two classifiers in the different spaces and the selection of parameter values.

Considering that both similarity-based algorithms and machine learning methods achieve good results in previous researched [24,27,36], in this study, by combining the advantages of both methods, we advanced a novel computational model of Ensemble Learning and Link Prediction for miRNA-Disease Association prediction (ELLPMDA) to predict potential miRNA-disease associations. Instead of combining the result of a few classifiers, we output the weighted combination of the ranks given by three classic similarity-based algorithms, Common Neighbors, Jaccard index and Katz index. Unlike some methods mentioned above, ELLPMDA based on known miRNA-disease associations, miRNA functional similarity, disease semantic similarity and Gaussian interaction profile kernel similarity for diseases and miRNAs rather than disease-gene associations and miRNA-target interaction which are incomplete and inaccurate. Besides, ELLPMDA is based on global similar measure and is applicable to diseases without any known related miRNAs. Leave-One-Out Cross-Validation (LOOCV) and 5-fold Cross Validation were implemented for ELLPMDA based on the experimentally confirmed associations between miRNAs and diseases. Significantly better than six classic methods (HGIMDA, RLSMDA, HDMP, WBSMDA, RWRMDA and MCMDA) [21,22,24,25,28,29], the AUCs of global and local LOOCV were 0.9181 and 0.8181, respectively. Furthermore, ELLPMDA was evaluated in three distinct kinds of case studies. In the first case study, 44, 46 and 43 out of the top 50 predictive miRNAs for Colon Neoplasms, Esophageal Neoplasms and Kidney Neoplasms were confirmed in dbDEMC [39] and miR2Disease [40] databases. Secondly, to test ELLPMDA's predictive ability for new diseases without any known related miRNAs, we set up a novel case study for Lung Neoplasms. In this case, we removed all the experimentally confirmed miRNA-disease associations which including Lung Neoplasms from the training samples. At this time, Lung Neoplasms could be treated as a new disease without any known related miRNAs. After implementing ELLPMDA, we examined the top 50 miRNAs which were predicted to be associated with lung neoplasms in dbDEMC [39], HMDD v2.0 [41] and miR2Disease [40] databases, and 49 out of top 50 miRNAs have been confirmed. Finally, we utilized the old version of HMDD, a database that only include 1395 associations between 271 miRNAs and 137 diseases to be the training set. In our case study of Breast Neoplasms, 49 out of top 50 miRNAs were affirmed in dbDEMC [39], HMDD v2.0 [41] and miR2Disease [40] databases. Therefore, according to the cross validation and case studies, ELLPMDA is a highly reliable method, which is obviously superior to the aforementioned classic algorithms.

Results

Performance

Based on experimentally verified associations between miRNAs and diseases, we implemented global LOOCV, local LOOCV and 5-fold CV to evaluate the predictive accuracy of ELLPMDA. After that, we compared the evaluation result with six previous methods (HGIMDA, RLSMDA, HDMP, WBSMDA, RWRMDA and MCMDA) [21,22,24,25,28,29]. In LOOCV evaluation, every confirmed association was regard as a test sample in turn while the rest associations were treated as training samples. All the miRNA-disease pairs that had not been confirmed by experimental studies were regard as candidate samples. After executing ELLPMDA, every miRNA-disease pair will obtain a association score. A higher score means a link is more likely to exist between this pair. The difference between global LOOCV and local LOOCV lies in whether we simultaneously inspected all the diseases or not. In global LOOCV, we compared the score of the test sample with all the candidate samples. In local LOOCV, considering that every test sample was a pair consisting of particular disease and miRNA, we merely compared the test sample with candidate samples which included this particular disease. Furthermore, we drew Receiver operating characteristics (ROC) curve by plotting the true positive rate (TPR, sensitivity) against the false positive rate (FPR, 1-specificity) at different thresholds. Sensitivity denotes the percentage of miRNA-disease test samples whose ranks exceeded the given threshold while specificity represents the percentage of negative miRNA-disease associations whose ranks were lower than the threshold [42]. After plotting, we could calculate the area under ROC curve (AUC). In general, AUC = 1 means this method gives a perfect prediction performance while AUC = 0.5 indicates the performance of this method is same as random selection. As a result, the performance comparison of ELLPMDA to (HGIMDA, RLSMDA, HDMP, WBSMDA, RWRMDA and MCMDA) [21,22,24,25,28,29] have been shown in Fig. 1. This figure straightly indicate that for global LOOCV, the AUCs of HGIMDA, RLSMDA, HDMP, WBSMDA and MCMDA is respectively 0.8781, 0.8426, 0.8366, 0.8030 and 0.8759, while the AUC of ELLPMDA is 0.9181. The AUCs of HGIMDA, RLSMDA, HDMP, WBSMDA, RWRMDA and MCMDA in local LOOCV is respectively 0.8077, 0.6953, 0.7702, 0.8031, 0.7891 and 0.7718, as contract, the AUC of ELLPMDA is 0.8181.

Figure 1. AUC of global LOOCV compared with HGIMDA, RLSMDA, HDMP, WBSMDA and MCMDA; AUC of local LOOCV compared with HGIMDA, RLSMDA, HDMP, WBSMDA, RMRMDA and MCMDA. As a result, ELLPMDA obtained AUCs of 0.9181 and 0.8181 in global and local LOOCV, which significantly exceed previous classic methods.

Figure 2. Flow chart of ELLPMDA in novel miRNA-disease association prediction by integrating known miRNA-disease associations, miRNA functional similarity, disease semantic similarity, and Gaussian interaction profile kernel similarity.

Moreover, we exploited 5-fold CV to further examine the predictive accuracy. Similar to LOOCV, in 5-fold CV, we randomly divided all the experimentally confirmed associations between miRNAs and diseases into 5 equal-size parts, and then we treated one part as test samples in turn and the other 4 parts as training samples. After executing ELLPMDA, the score of each test sample was compared with the scores of all the candidate samples, respectively. At this time, we could obtain the rank of every association in test samples. All the associations would obtain a rank after the above 5 parts were regard as test samples separately. In order to avoid random error, we took advantage of 5-fold CV for 100 times. As a result, the AUCs of MCMDA, HDMP and WBSMDA were respective 0.8767+/−0.0011, 0.8342+/−0.0010 and 0.8185+/−0.0009, while the AUC of ELLPMDA is 0.9193+/−0.0002.

Case study

Furthermore, we designed three kinds of case studies to comprehensively evaluate the predictive accuracy of ELLPMDA. Firstly, we took experimentally confirmed miRNA-disease associations captured from HMDD v2.0 [41] as the training set and did case studies for three common human cancers: Colon Neoplasms, Esophageal Neoplasms and Kidney Neoplasms. In this part, after implementing ELLPMDA, we obtained the scores of all the miRNA-disease pairs. Similar to cross-validation, we set experimentally verified associations as training samples and other miRNA-disease pairs were considered as candidate samples. Then for every disease mentioned above, we examined the top 10 and top 50 of predictive potential miRNA-disease pairs in dbDEMC [39] and miR2Disease [40] databases.

Colon Neoplasms is a big threaten of people's live with low detection rate in early stage, moreover, studies showed that about half of the Colon Neoplasms patients die of metastatic disease within 5 years from diagnosis [43]. Obviously, it is really urgent for us to achieve more information about it, which might contribute a lot to improve the accuracy of detection [44,45]. After a great many of biological experiments, lots of miRNAs had been proved to be associated with Colon Neoplasms. For example, miR-126 suppresses the growth of neoplastic cells by targeting phosphatidylinositol 3‐kinase signaling and is frequently lost in colon neoplasms [46]. Hsa-miR-181b and hsa-miR-200c were over-expressed in colon tumor tissues compared to normal tissues [47]. Also, hsa-miR-145 can inhabits the growth of Colon Neoplasms cells by targeting the insulin receptor substrate-1 [48]. Taking Colon Neoplasms as a case study, we implemented ELLPMDA and 9 out of top 10 and 44 out of top 50 potential related miRNAs given by ELLPMDA had been confirmed in miR2Disease and dbDEMC (See Table 1). Taking the top 5 predicted miRNAs as examples, miR-155(2nd) and miR-20a (5th) were confirmed to be up-regulated in colon neoplasms [49]. MiR-21(1st) post-transcriptionally downregulates tumor suppressor Pdcd4 and stimulates invasion in colon neoplasms [50]. What's more, miR-221(3rd), a miRNA directly amplified from plasma, is a potential diagnostic and prognostic marker of colon neoplasms [51]. Also, studies showed that miR-125b (4th) is straightly involved in cancer progression and is linked with poor prognosis in human colon neoplasms [52].

Table 1. Prediction of the top 50 predicted miRNAs associated with Colon Neoplasms based on known associations in HMDD v2.0 database. The first column records top 1–25 related miRNAs. The second column records the top 26–50 related miRNAs.

miRNA	Evidence	miRNA	Evidence
hsa-mir-21	miR2Disease:dbDEMC:	hsa-mir-141	miR2Disease:dbDEMC:
hsa-mir-155	miR2Disease:dbDEMC:	hsa-mir-31	miR2Disease:dbDEMC:
hsa-mir-221	miR2Disease:dbDEMC:	hsa-mir-34c	miR2Disease:
hsa-mir-125b	dbDEMC:	hsa-let-7e	dbDEMC:
hsa-mir-20a	miR2Disease:dbDEMC:	hsa-mir-101	unconfirmed
hsa-mir-34a	miR2Disease:dbDEMC:	hsa-mir-142	unconfirmed
hsa-mir-16	dbDEMC:	hsa-mir-15a	dbDEMC:
hsa-mir-222	dbDEMC:	hsa-let-7f	miR2Disease:dbDEMC:
hsa-mir-199a	unconfirmed	hsa-mir-29b	miR2Disease:dbDEMC:
hsa-mir-200b	dbDEMC:	hsa-let-7i	dbDEMC:
hsa-mir-18a	miR2Disease:dbDEMC:	hsa-mir-205	dbDEMC:
hsa-let-7a	miR2Disease:dbDEMC:	hsa-let-7d	dbDEMC:
hsa-mir-19a	miR2Disease:dbDEMC:	hsa-mir-122	unconfirmed
hsa-mir-143	miR2Disease:dbDEMC:	hsa-mir-196a	miR2Disease:dbDEMC:
hsa-mir-29a	miR2Disease:dbDEMC:	hsa-mir-106b	miR2Disease:dbDEMC:
hsa-mir-146a	dbDEMC:	hsa-mir-210	dbDEMC:
hsa-mir-19b	miR2Disease:dbDEMC:	hsa-let-7g	miR2Disease:dbDEMC:
hsa-mir-200c	miR2Disease:dbDEMC:	hsa-mir-34b	miR2Disease:dbDEMC:
hsa-let-7b	miR2Disease:dbDEMC:	hsa-mir-214	dbDEMC:
hsa-mir-92a	unconfirmed	hsa-mir-125a	miR2Disease:dbDEMC:
hsa-mir-223	miR2Disease:dbDEMC:	hsa-mir-10b	miR2Disease:dbDEMC:
hsa-mir-200a	unconfirmed	hsa-mir-182	miR2Disease:dbDEMC:
hsa-mir-1	miR2Disease:dbDEMC:	hsa-mir-93	miR2Disease:dbDEMC:
hsa-mir-9	miR2Disease:dbDEMC:	hsa-mir-181b	miR2Disease:dbDEMC:
hsa-let-7c	dbDEMC:	hsa-mir-25	miR2Disease:dbDEMC:

Esophageal Neoplasms is reported as the eighth most common cancer worldwide and the sixth leading cause of deaths related with cancers based on the pathological characteristics and it affect males more times than females [45,53]. Because of the potential characteristics of invasion and metastasis in esophageal carcinoma cells, the overall 5-year survival rate is poor despite of advanced treatment [45,53,54]. Previous studies indicated that miRNAs is important in tumorigenesis of esophageal neoplasms [53]. For instance, miR-373 post-transcriptionally regulates large tumor suppressor in human esophageal neoplasms [55]. Down-regulation of miR-27a might reverse multidrug resistance of esophageal squamous cell carcinoma [56]. Also, research pointed out that miR-203 inhibits the proliferation and self-renewal of esophageal neoplasms stem-like cells by suppressing stem renewal factor Bmi-1 [57]. In this case, as a result, 9 out of top 10 and 46 out of top 50 predictive miRNAs given by ELLPMDA had been verified in miR2Disease and dbDEMC (See Table 2).

Table 2. Prediction of the top 50 predicted miRNAs associated with Esophageal Neoplasms based on known associations in HMDD v2.0 database. The first column records top 1–25 related miRNAs. The second column records the top 26–50 related miRNAs.

miRNA	Evidence	miRNA	Evidence
hsa-mir-200b	dbDEMC:	hsa-mir-29b	dbDEMC:
hsa-let-7e	dbDEMC:	hsa-mir-146b	dbDEMC:
hsa-let-7d	dbDEMC:	hsa-mir-191	dbDEMC:
hsa-let-7f	unconfirmed	hsa-mir-106a	dbDEMC:
hsa-let-7i	dbDEMC:	hsa-mir-18b	dbDEMC:
hsa-mir-18a	dbDEMC:	hsa-mir-194	miR2Disease:dbDEMC:
hsa-mir-125a	dbDEMC:	hsa-mir-302b	dbDEMC:
hsa-mir-17	dbDEMC:	hsa-mir-24	dbDEMC:
hsa-mir-19b	dbDEMC:	hsa-mir-7	dbDEMC:
hsa-mir-429	dbDEMC:	hsa-mir-199b	dbDEMC:
hsa-let-7g	dbDEMC:	hsa-mir-181b	dbDEMC:
hsa-mir-218	unconfirmed	hsa-mir-30d	dbDEMC:
hsa-mir-132	dbDEMC:	hsa-mir-20b	dbDEMC:
hsa-mir-125b	dbDEMC:	hsa-mir-302c	dbDEMC:
hsa-mir-127	dbDEMC:	hsa-mir-195	dbDEMC:
hsa-mir-30c	dbDEMC:	hsa-mir-30a	dbDEMC:
hsa-mir-106b	dbDEMC:	hsa-mir-181a	dbDEMC:
hsa-mir-9	dbDEMC:	hsa-mir-107	miR2Disease:dbDEMC:
hsa-mir-10b	dbDEMC:	hsa-mir-142	dbDEMC:
hsa-mir-16	dbDEMC:	hsa-mir-182	dbDEMC:
hsa-mir-29a	dbDEMC:	hsa-mir-373	miR2Disease:dbDEMC:
hsa-mir-222	dbDEMC:	hsa-mir-92b	dbDEMC:
hsa-mir-1	dbDEMC:	hsa-mir-30e	unconfirmed
hsa-mir-221	dbDEMC:	hsa-mir-204	unconfirmed
hsa-mir-93	dbDEMC:	hsa-mir-367	dbDEMC:

Kidney Neoplasm, also known as renal cancer, is a cancer starting in the cells of kidney that includes many different types. It accounts for 3% of adult malignancies [58,59]. Renal cell carcinoma (RCC) and transitional cell carcinoma (TCC, also known as urothelial cell carcinoma) are the most common types of kidney neoplasms [60]. According to previous studies, various miRNAs had been examined to be linked with kidney neoplasms. For example, evidence had pointed out that miR-519 suppresses tumor growth in human kidney neoplasms by reducing HuR levels [61]. Also, VHL-regulated miR-204 is able to suppress tumor growth through inhibition of LC3B-mediated autophagy in renal clear cell carcinoma [62]. Besides, Overexpression of miR-210 causes centrosome amplification in renal carcinoma cells [63]. In this case, 8 out of top 10 and 43 out of top 50 predicted potential miRNAs had been confirmed (See Table 3). For instance, the miR-17-92(2nd) cluster is overexpressed in renal cell carcinoma and has an oncogenic effect on it [64]. Studies also indicated that miR-145 (3rd) functions as tumor suppressor and targets two oncogenes, ANGPT2 and NEDD9, in renal cell carcinoma [65]. What's more, miR-34a (4th) promote renal senescence by suppressing mitochondrial antioxidative enzymes [66] while miR-155(1st) expression was absent in nonlymphoid organs such as lung, heart and kidney [67].

Table 3. Prediction of the top 50 predicted miRNAs associated with Kidney Neoplasms based on known associations in HMDD v2.0 database. The first column records top 1–25 related miRNAs. The second column records the top 26–50 related miRNAs.

miRNA	Evidence	miRNA	Evidence
hsa-mir-155	dbDEMC:	hsa-mir-29b	miR2Disease:dbDEMC:
hsa-mir-17	miR2Disease:	hsa-let-7c	dbDEMC:
hsa-mir-145	dbDEMC:	hsa-mir-1	dbDEMC:
hsa-mir-34a	dbDEMC:	hsa-mir-429	dbDEMC:
hsa-mir-125b	unconfirmed	hsa-mir-210	miR2Disease:dbDEMC:
hsa-mir-200b	miR2Disease:dbDEMC:	hsa-mir-34b	dbDEMC:
hsa-mir-221	unconfirmed	hsa-let-7f	miR2Disease:dbDEMC:
hsa-mir-20a	miR2Disease:dbDEMC:	hsa-mir-106b	miR2Disease:dbDEMC:
hsa-mir-199a	miR2Disease:dbDEMC:	hsa-mir-143	dbDEMC:
hsa-mir-146a	dbDEMC:	hsa-mir-93	dbDEMC:
hsa-mir-126	miR2Disease:dbDEMC:	hsa-let-7e	unconfirmed
hsa-mir-200a	dbDEMC:	hsa-mir-218	dbDEMC:
hsa-let-7a	dbDEMC:	hsa-mir-27a	miR2Disease:dbDEMC:
hsa-mir-19a	dbDEMC:	hsa-mir-223	dbDEMC:
hsa-mir-18a	dbDEMC:	hsa-mir-182	miR2Disease:dbDEMC:
hsa-mir-16	dbDEMC:	hsa-mir-10b	dbDEMC:
hsa-mir-19b	miR2Disease:dbDEMC:	hsa-let-7i	dbDEMC:
hsa-mir-222	dbDEMC:	hsa-mir-196a	dbDEMC:
hsa-mir-29a	miR2Disease:dbDEMC:	hsa-mir-101	miR2Disease:dbDEMC:
hsa-mir-92a	unconfirmed	hsa-mir-133a	unconfirmed
hsa-mir-205	unconfirmed	hsa-mir-29c	miR2Disease:dbDEMC:
hsa-let-7b	unconfirmed	hsa-mir-214	miR2Disease:dbDEMC:
hsa-mir-9	dbDEMC:	hsa-mir-146b	dbDEMC:
hsa-mir-34c	dbDEMC:	hsa-mir-181a	dbDEMC:
hsa-let-7d	dbDEMC:	hsa-let-7g	dbDEMC:

Besides the aforementioned disease, we took advantage of ELLPMDA to rank all the miRNA-disease pairs between 383 diseases and 495 miRNAs in HMDD v2.0 [41] database (See Supplementary Table 1). We hope future biological experiments can confirm the prediction of ELLPMDA.

Secondly, in order to validate the predictive ability of ELLPMDA in new diseases without any known linked miRNAs, we set up a special case study. In this case, we examined ELLPMDA on Lung Neoplasms, a common human cancer which has a lot of experimentally verified related miRNAs. Similar to case study 1, we utilized the experimentally verified miRNA-disease associations achieved from HMDD v2.0 database [41] as the initial training set, however, by this time, we removed all the associations including lung neoplasms from the training set. Hence, lung neoplasms could be regard as a disease without any known related miRNAs. After executing ELLPMDA base on the brand new training set, we chose the top 50 of predicted miRNAs and examined them in dbDEMC [39], HMDD v2.0 [41] and miR2Disease [40] databases. As a result, 10 out of top 10 and 49 out of top 50 (See Table 4) potential associations were confirmed. For example, focus on the top 5 predicted miRNAs. High expression of miR-21(1st) and miR-155 (2nd) could predict recurrence and unfavorable survival in non-small cell lung neoplasms [68]. Also, studies indicated that circulating miR-125b (5th) is a novel biomarker for screening non-small-cell lung neoplasms [69]. Besides, miR-17-92 (4th) is overexpressed in human lung neoplasms cell and evidences had proved that it plays a key role in lung neoplasms development [70,71]. What's more, the reduction of miR-221 (3rd) inhibited cell proliferation and induced mitochondrial-mediated apoptosis in human lung neoplasms cells [72].

Table 4. Prediction of the top 50 predicted miRNAs associated with Lung Neoplasms based on known associations in HMDD v2.0 database. In this case study, we eliminate all the known associations which including Lung Neoplasms to consider Lung Neoplasms as a new disease without any known related miRNAs. The first column records top 1–25 related miRNAs. The second column records the top 26–50 related miRNAs.

miRNA	Evidence	miRNA	Evidence
hsa-mir-21	miR2Disease:dbDEMC:HMDD:	hsa-mir-205	miR2Disease:dbDEMC:HMDD:
hsa-mir-155	miR2Disease:dbDEMC:HMDD:	hsa-mir-223	HMDD:
hsa-mir-221	dbDEMC:HMDD:	hsa-mir-200c	miR2Disease:dbDEMC:HMDD:
hsa-mir-17	miR2Disease:HMDD:	hsa-mir-34b	dbDEMC:HMDD:
hsa-mir-125b	miR2Disease:HMDD:	hsa-mir-29b	miR2Disease:dbDEMC:HMDD:
hsa-mir-222	dbDEMC:HMDD:	hsa-mir-93	miR2Disease:dbDEMC:HMDD:
hsa-mir-34a	dbDEMC:HMDD:	hsa-mir-210	miR2Disease:dbDEMC:HMDD:
hsa-mir-199a	miR2Disease:dbDEMC:HMDD:	hsa-mir-200a	miR2Disease:dbDEMC:HMDD:
hsa-mir-16	miR2Disease:dbDEMC:	hsa-mir-106b	dbDEMC:
hsa-mir-20a	miR2Disease:dbDEMC:HMDD:	hsa-mir-182	miR2Disease:dbDEMC:HMDD:
hsa-mir-146a	miR2Disease:dbDEMC:HMDD:	hsa-mir-214	miR2Disease:dbDEMC:HMDD:
hsa-mir-145	miR2Disease:dbDEMC:HMDD:	hsa-let-7c	miR2Disease:dbDEMC:HMDD:
hsa-mir-18a	miR2Disease:dbDEMC:HMDD:	hsa-let-7d	miR2Disease:dbDEMC:HMDD:
hsa-mir-126	miR2Disease:dbDEMC:HMDD:	hsa-mir-181a	dbDEMC:HMDD:
hsa-mir-29a	miR2Disease:dbDEMC:HMDD:	hsa-mir-143	miR2Disease:dbDEMC:HMDD:
hsa-mir-19b	dbDEMC:HMDD:	hsa-mir-133a	dbDEMC:HMDD:
hsa-mir-19a	miR2Disease:dbDEMC:HMDD:	hsa-mir-122	unconfirmed
hsa-let-7a	miR2Disease:dbDEMC:HMDD:	hsa-mir-196a	dbDEMC:HMDD:
hsa-mir-1	miR2Disease:dbDEMC:HMDD:	hsa-mir-141	miR2Disease:dbDEMC:
hsa-mir-200b	miR2Disease:dbDEMC:HMDD:	hsa-let-7e	miR2Disease:HMDD:
hsa-mir-15a	dbDEMC:	hsa-mir-101	miR2Disease:dbDEMC:HMDD:
hsa-mir-34c	dbDEMC:HMDD:	hsa-mir-31	miR2Disease:dbDEMC:HMDD:
hsa-mir-9	miR2Disease:HMDD:	hsa-mir-29c	miR2Disease:dbDEMC:HMDD:
hsa-let-7b	miR2Disease:HMDD:	hsa-let-7f	miR2Disease:HMDD:
hsa-mir-92a	HMDD:	hsa-mir-27a	dbDEMC:HMDD:

Table 5. Prediction of the top 50 predicted miRNAs associated with Breast Neoplasms based on known associations in old version of HMDD database. The first column records top 1–25 related miRNAs. The second column records the top 26–50 related miRNAs.

miRNA	Evidence	miRNA	Evidence
hsa-let-7b	dbDEMC:HMDD:	hsa-mir-335	miR2Disease:dbDEMC:HMDD:
hsa-let-7i	miR2Disease:dbDEMC:HMDD:	hsa-mir-106a	dbDEMC:
hsa-let-7e	dbDEMC:HMDD:	hsa-mir-26a	miR2Disease:dbDEMC:HMDD:
hsa-let-7c	dbDEMC:HMDD:	hsa-mir-128b	miR2Disease:
hsa-let-7g	dbDEMC:HMDD:	hsa-mir-203	miR2Disease:dbDEMC:HMDD:
hsa-mir-191	miR2Disease:dbDEMC:HMDD:	hsa-mir-181a	miR2Disease:dbDEMC:HMDD:
hsa-mir-92b	dbDEMC:	hsa-mir-135a	dbDEMC:HMDD:
hsa-mir-101	miR2Disease:dbDEMC:HMDD:	hsa-mir-199b	dbDEMC:HMDD:
hsa-mir-126	miR2Disease:dbDEMC:HMDD:	hsa-mir-532	dbDEMC:
hsa-mir-520b	dbDEMC:HMDD:	hsa-mir-130b	dbDEMC:
hsa-mir-30e	unconfirmed	hsa-mir-24	dbDEMC:HMDD:
hsa-mir-130a	dbDEMC:	hsa-mir-99a	dbDEMC:
hsa-mir-223	dbDEMC:HMDD:	hsa-mir-95	dbDEMC:
hsa-mir-18b	dbDEMC:HMDD:	hsa-mir-186	dbDEMC:
hsa-mir-27a	miR2Disease:dbDEMC:HMDD:	hsa-mir-520c	miR2Disease:HMDD:
hsa-mir-373	miR2Disease:dbDEMC:HMDD:	hsa-mir-22	miR2Disease:dbDEMC:HMDD:
hsa-mir-98	miR2Disease:dbDEMC:	hsa-mir-196b	dbDEMC:
hsa-mir-100	dbDEMC:HMDD:	hsa-mir-491	dbDEMC:
hsa-mir-99b	dbDEMC:	hsa-mir-455	dbDEMC:
hsa-mir-372	dbDEMC:	hsa-mir-193b	miR2Disease:dbDEMC:HMDD:
hsa-mir-192	dbDEMC:	hsa-mir-29c	miR2Disease:dbDEMC:HMDD:
hsa-mir-32	dbDEMC:	hsa-mir-23b	dbDEMC:HMDD:
hsa-mir-16	dbDEMC:HMDD:	hsa-mir-30a	miR2Disease:HMDD:
hsa-mir-92a	HMDD:	hsa-mir-224	dbDEMC:HMDD:
hsa-mir-182	miR2Disease:dbDEMC:HMDD:	hsa-mir-340	dbDEMC:HMDD:

Finally, in order to examine the robustness of ELLPMDA's predictive accuracy in different databases, we utilized old version of HMDD, a database which only include 1395 experimentally verified associations between 271 miRNAs and 137 diseases, and these associations were treated as training samples. In this case, we tested ELLPMDA on Breast Neoplasms, a popular human disease which threating female's health a lot. Breast Neoplasms is now considered as the most leading type of invasive cancer in women with 1,384,155 estimated new cases worldwide and with nearly 459,000 related deaths each year [73]. It has been predicted that the worldwide incidence of female breast cancer will reach approximately 3.2 million new cases per year by 2050 [73]. These scary numbers indicate that it is extremely urgent for us to get more information about breast neoplasms to further interpret it and develop more effective methods for disease detection and treatment. In fact, lots of evidences had proved that various miRNAs were linked with breast neoplasms. For example, the overexpression of miR-21 in human breast neoplasms is associated with advanced clinical stage, lymph node metastasis and patient poor prognosis [74]. MiR-17-5p regulates breast neoplasms cell proliferation by inhibiting translation of AIB1 mRNA [75] while miR-125b acts as a marker predicting chemoresistance in breast neoplasms [76]. Besides, biological researches had convinced that miR-210 is an independent prognostic factor in breast neoplasms [77] .We took advantage of old version of HMDD as training set and implemented ELLPMDA. As a result, 10 out of top 10 and 49 out of top 50 predicted miRNAs had been confirmed in dbDEMC [39], HMDD v2.0 [41] and miR2Disease [40] databases (see Table 5).

In conclusion, based on the evaluation in all cross validation (global LOOCV, local LOOCV and 5-fold CV) and three kinds of case studies, ELLPMDA achieved an excellent predictive accuracy which is significantly better than most of previous methods. What's more, ELLPMDA was based on global similar network and could be applied to new diseases without any know linked miRNAs.

Discussions

With the rapid development of human society, human health is currently one of the most concerned topics worldwide, furthermore, how to overcome more and more human diseases is an international problem which has received a great many of attentions. Considering that miRNAs play a critical role in multiple biological processes as well as the developments and progressions of various human diseases, identifying potential miRNA-disease associations is currently a vital research topic which might contribute a lot in the protection, detection and treatment of complex human diseases. However, it will be very expensive and time-consuming if we test all the miRNA-disease pairs using biological experiment. Therefore, lots of computational models have been proposed to predict novel associations between miRNAs and diseases. Although these previous methods have successfully predicted a great many of miRNA-disease associations, there were always limitations in these methods, such as applicable scope and predictive accuracy. To solve these problems, in this study, we developed a novel predictive method ELLPMDA, which utilized ensemble learning to combine results given by three classic algorithms to reveal potential miRNA-disease associations. As mentioned above, in LOOCV, the AUCs of ELLPMDA is 0.9181 and 0.8181 in global case and local case, respectively. Also, in 5-fold CV, the AUC of ELLPMDA is 0.9193+/−0.0002, which means the predictive accuracy of ELLPMDA in different cases is obviously better than most of previous methods. Furthermore, case studies indicated that ELLPMDA could be implemented in all kinds of diseases, whatever related miRNAs exist or not, and ELLPMDA gave excellent performances in various diseases.

The success of ELLPMDA can be mainly attributed to several factories. First and the most important factory is that we exploited ensemble learning into novel miRNA-disease association prediction. In this study, we developed three models depending on classic similarity-based algorithms and utilized these models into prediction works. Every model gave ranks of all the miRNA-disease pairs and we obtained the overall predictive result by exploiting ensemble learning to weightedly combine the sorted results given by these separate models. Concrete weight was calculated according to the predictive accuracies of these methods in case study 1. By combining results from three models, we achieved an overall result which was better than all the three results given by single model. Secondly, integrated similarity for miRNAs and diseases, which obtained by integrating Gaussian interaction profile kernel similarity, miRNA functional similarity and disease semantic similarity gave us precise information about the similarities between every miRNA-miRNA pair and disease-disease pair. Such information enabled us to take advantage of similarity-based algorithms on miRNA-disease network. Besides, experimentally verified associations between miRNA-disease given by HMDD v2.0 database [41] helped a lot, because it is the foundation to construct the miRNA-disease networks.

Although ELLPMDA achieved a great performance, there are still a few ways to further improve it. First, the current miRNA-disease association is insufficient. Thus, more information about experimentally confirmed miRNA-disease associations could help a lot by completing the miRNA-disease association network and further improving the accuracy of all the existing similarity networks. Apparently, ELLPMDA will perform better when more information is available. Besides, there is not a powerful method to choose the optimal parameter $\beta$ for ELLPMDA. What's more, the weight of three methods might be calculated in a more reasonable way.

For future work, we would like to pay attention to the following two aspects. First, as discussed in [78], biological systems are seen as a network of interconnected components, which indicates the importance of taking the interconnection into account. In our approach, after obtaining the predicted similarities between all the miRNAs and diseases given by ELLPMDA, examining the existence of certain regular loops between these similarities is a wise practice to further improve the performance of our method. For example, we would expect an association exists between disease $d_i$ and miRNA $r_j$ if all the diseases which are associated with miRNA $r_m$ and $r_n$ are associated with miRNA$r_j$, and disease $d_i$ is associated with both miRNA $r_m$ and $r_n$. In addition, [79] offers us a method to modeling existing data, which invites us countless inspiration for further study.

Materials and methods

Human miRNA-disease associations

Information about human miRNA-disease associations is available in HMDD v2.0 database [41], which includes 5430 distinct experimentally confirmed miRNA-disease associations about 495 miRNAs and 383 diseases. For convenience, we constructed an adjacency matrix $A_{495*383}$ to better describe these associations. The element $A\left(i,j\right)$ equals to 1 if there is an experimentally confirmed association between miRNA $r_i$ and disease$d_j$. Otherwise, $A\left(i,j\right)$equals to 0.

MiRNA functional similarity

Based on the assumption that functionally similar miRNAs tend to be associated with phenotypically similar diseases, the miRNA functional similarity was calculated in previous work [32]. Thanks to these excellent works, we can straightly download the miRNA functional similarity data from http://www.cuilab.cn/files/images/cuilab/misim.zip. Similar to adjacency matrix $A_{495*383}$, the matrix $M{S}_{495*495}$ was constructed, in which the entity $MS\left(i,j\right)$ represented the value of similarity between the miRNAs $r_i$ and $r_j$.

Disease semantic similarity model 1

It is reasonable to use a distinct Directed Acyclic Graph (DAG) to describe each disease. To state it more clearly, we exploited a $DAG\left(D\right)=\left(D, T\left(D\right),E\left(D\right)\right)$ to represent a disease D, in which every disease is regard as a node and there are directed edges from parent nodes to child nodes. $T\left(D\right)$ is a node set which contains disease D itself and its parent nodes and $E\left(D\right)$ is a edge set including all the directed edges. Then we defined the contribution of disease d in DAG (D) to the semantic value of disease D as follows:

(1) $\{\begin{array}{l}D{1}_D\left(d\right)=1ifd=D\\ D{1}_D\left(d\right)=max\left\{\Delta *D{1}_D\left(d\text{'}\right)\text{|}{d}^{\prime }\epsilon childrenofd\right\}ifd\ne D\end{array}$(1)

where $\Delta$ is the semantic contribution factor. The contribution score for disease d is inversely proportional to the distance from d to D. The semantic value of disease D can be defined as follows:

(2) $\text{DV}1\left(\text{D}\right)={\displaystyle \sum }_{d\in T\left(D\right)}D{1}_D\left(d\right)$(2)

According to the observation that two diseases will have larger similarity score if they have larger shared part of their DAGs, the semantic similarity value between diseases $d_i$ and $d_j$ can be defind as follows:

(3) $\text{SS}1\left(d_i,d_j\right)=\frac{{{\displaystyle \sum }}_{t \in T\left(d_i\right)\cap T\left(d_j\right) }\left(D{1}_{d_i}\left(t\right)+ D{1}_{d_j}\left(t\right)\right)}{DV1\left(d_i\right)+DV1\left(d_j\right)}$(3)

Where $SS{1}_{383*383}$ is the disease semantic similarity matrix 1.

Disease semantic similarity model 2

What's more, we further constructed another disease semantic similarity matrix by considering the difference between the contributions of different disease terms in the same layer of $DAG\left(D\right)$. Apparently, in the SS1 defined above, the disease terms in the same layer of $DAG\left(D\right)$ have the same contribution to the semantic value of disease D. However, it might be unfair if we give two diseases the same contribution when they appear different times in disease DAGs. To state it more clearly, if two diseases lie in the same layer of $DAG\left(D\right)$ and the first disease appears much more times in disease DAGs than the second disease, we believed that the second disease is more specific to disease D. Thus, it is reasonable to give the second disease a higher weight. Thus, the contribution of disease term d in $DAG\left(D\right)$ to the semantic value of disease $D$ can be defined as follows:

(4) $D{2}_D\left(d\right)=-\log \left[\frac{the numberofDAGsincludingd}{the number of diseases}\right]$(4)

Combining the weighted contributions and the similar ways in Disease semantic similarity model 1, the disease semantic similarity value 2 between diseases $d_i$ and $d_j$ can be calculated as follows:

(5) $\text{SS}2\left(d_i,d_j\right)=\frac{{{\displaystyle \sum }}_{t \in T\left(d_i\right) \cap T\left(d_j\right)}\left(D{2}_{d_i}\left(t\right)+D{2}_{d_j}\left(t\right)\right)}{DV2\left(d_i\right)+DV2\left(d_j\right)}$(5)

Where $SS{2}_{383*383}$ is the disease semantic similarity matrix 2.

Gaussian interaction profile kernel similarity

According to the assumption that functionally similar miRNAs tend to be associated with similar diseases, Gaussian interaction profile kernel similarity for diseases are calculated by considering the topologic information of known miRNA–disease association network. We respectively used binary vector $IV\left(d_i\right)$ and $IV\left(r_j\right)$ to denote the interaction profiles of disease $d_i$ and miRNA $r_j$. Because the adjacency matrix contains the information about the associations between diseases and miRNAs, we use the $IV\left(d_i\right)$ and $IV\left(r_j\right)$ to represent the i-th row and j-th column in the adjacency matrix $A_{495*383}$ which was defined above. Thus, the Gaussian interaction profile kernel similarity of diseases and miRNAs can be defined as follows:

(6) $GD\left(d_i,d_j\right)=\exp \left(-{\beta }_{d }\parallel IV\left(d_i\right)- IV\left(d_j\right){\parallel }^2\right)$(6)

(7) $GR\left(r_i,r_j\right)=\text{exp}\left(-{\beta }_{r }\parallel IV\left(r_i\right)- IV\left(r_j\right){\parallel }^2\right)$(7)

where parameter ${\beta }_{d }$ and ${\beta }_{r }$ were used to control the kernel bandwidth, which can be obtained by normalizing the new bandwidth parameter $\beta {\text{'}}_{d }$ and ${{\beta }^{\prime }}_{r }$(Both were set as 1 based on previous work (van Laarhoven, T. et al.. (2011)) [80]) which can be denoted as follows:

(8) ${\beta }_{d }=\beta {\text{'}}_{d }/\left(\frac{1}{n}{\displaystyle \sum }_{i=1}^n\parallel IV\left(d_i\right){\parallel }^2\right)$(8)

(9) ${\beta }_{r }=\beta {\text{'}}_{r }/\left(\frac{1}{m}{\displaystyle \sum }_{i=1}^m\parallel IV\left(r_i\right){\parallel }^2\right)$(9)

Yet we got two matrix $G{D}_{383*383}$ and $G{R}_{495*495}$, in which the entity $GD\left(i,j\right)$ represent the Gaussian interaction profile kernel similarity between disease $d_i$ and diseases $d_j$, and $GR\left(i,j\right)$ represent the Gaussian interaction profile kernel similarity between miRNAs $r_i$ and $r_j$.

Integrated similarity for miRNAs and diseases

After the above processes, we now have two matrices $M{S}_{495*495}$ and $G{R}_{495*495}$ including similarity value between miRNAs, and three matrices $SS{1}_{383*383}$, $SS{2}_{383*383}$ and $G{D}_{383*383}$ including similarity value between diseases. By combining these matrices, the integrated similarity for miRNAs and diseases were defined as follows:

(10) $SD\left(d_i,d_j\right)=\{\begin{array}{l}\frac{SS1\left(d_i+d_j\right)+SS2\left(d_i+d_j\right)}{2}{d}_{i}and{d}_{j}havesemanticsimilarity\\ GD\left(d_i,d_j\right)otherwise\end{array}$(10)

(11) $SR\left(r_i,r_j\right)=\{\begin{array}{l}MS\left(r_i,r_j\right)r_{i}and{r}_{j}havefunctionalsimilarity\\ GR\left(r_i,r_j\right)otherwise\end{array}$(11)

Where the $S{D}_{383*383}$ represents the integrated similarity value between diseases and $S{R}_{495*495}$ represent the integrated similarity value between miRNAs.

Ellpmda

In this study, we exploited ensemble learning into novel miRNA-disease association prediction. In short, ensemble learning is a common machine learning method which could improve the classification accuracy by combining classified results given by different classifiers. Based on this method, we weightedly combined the rank results given by Common Neighbors, Jaccard index and Katz index to achieve a better prediction result (see Fig. 2).

Common neighbors

For a note x, let $\text{γ}\left(\text{x}\right)$ donates the neighbor nodes set of node x. Intuitively speaking, if two nodes x and y share more neighbor nodes, a link is more likely to exist between x and y. In general, Common Neighbors score between node x and node y can be defined as follows:

(12) $S_{xy}^{CN}= \left|\text{ γ}\left(\text{x}\right)\cap \text{γ}\left(\text{y}\right)\right|$(12)

Obviously, this equation directly count the number of nodes which are the neighbor of both x and y. In our study, considering the structure of our integrated network, which was obtained by combining human miRNA-disease associations and integrated similarity for miRNAs and diseases, we defined ${\gamma }_d\left(x\right)$ as the neighbor nodes set of x which only contains disease nodes while the ${\gamma }_m\left(x\right)$ donates the neighbors nodes set of x which only contain miRNA nodes. We can then redefine CN score between disease $d_i$ and miRNA $r_j$ as:

(13) $S_{d_i{r}_j}^{CN\text{'}}={\displaystyle \sum }_{\begin{array}{l}{z}_1\in {\gamma }_d\left(d_i\right)\mathrm{I}{\gamma }_d\left(r_j\right)\\ z_2\in {\gamma }_m\left(d_i\right)\mathrm{I}{\gamma }_m\left(r_j\right)\end{array}}SD\left(d_i,z_1\right)+SR\left(z_2,r_j\right)$(13)

After calculating the scores of all the miRNA-disease pairs (between 495 miRNAs and 383 diseases), we were able to rank all the candidate samples based on CN score and further obtain an rank matrix $RankCN$, where the element $RankCN\left(i,j\right)$ represents the rank of $r_i- d_j$ pair. For example, if the CN score between miRNA 35 and disease 46 is highest and miRNA 78 and disease 365 achieved the second highest CN score, $RankCN\left(35,46\right)$ equals to 1 and $RankCN\left(78,365\right)$equals to 2.

Jaccard index

The Jaccrad index [81] could be regard as the normalized Common Neighbors. Considering that if a node x have only 5 neighbor nodes and a node y have 200 neighbor nodes, however, they both have 5 common neighbor nodes with node z. It is reasonable to believe x is more ‘valuable’ to node z. As a result, to eliminate the bias to nodes with a lot of neighbor nodes, we defined JI score between disease $d_i$ and miRNA $r_j$ as follows:

(14) $S_{d_i{r}_j}^{JI}=\frac{\left|\text{ γ}\left(d_i\right)\cap \text{γ}\left(r_j\right) \right|}{\left|\text{ γ}\left(d_i\right)\cup \text{γ}\left(r_j\right) \right|}$(14)

where

(15) $\left|\text{γ}\left(d_i\right)\cap \text{γ}\left(r_j\right) \right|=S_{d_i{r}_j}^{CN\text{'}}$(15)

(16) $\left|\text{γ}\left(d_i\right)\cup \text{γ}\left(r_j\right)\right|={\displaystyle \sum }_{\begin{array}{l}{z}_1\in {\gamma }_d\left(d_i\right)\cup {\gamma }_m\left(d_i\right)\\ z_2\in {\gamma }_d\left(r_j\right)\cup {\gamma }_m\left(r_j\right)\end{array}}SD\left(d_i,z_1\right)+A\left(d_i,z_1\right)+SR\left(z_2,r_j\right)+A\left(z_2,r_j\right)$(16)

In general, we ought to normalize CN score between disease $d_i$ and miRNA $r_j$ by dividing the number of neighbor nodes of them. However, to take the integrated similarity for miRNAs and diseases into account, we used the similarity between two nodes to replace the existence of a link between them. Thus, equation (16) is easy to understand. Similar to Common Neighbors, we obtained a rank matrix $RankJI$ to save the ranks for all the miRNA-disease pairs.

Katz index

The Katz index [82] is a path-dependent global measure which directly sums all the possible paths between two nodes in a network and is exponentially damped to give the shorter paths more weight [83] .In order to take all the aforementioned materials into account, the matrix $M{D}_{878*878}$, a biadjacency matrix consist of human miRNA-disease associations matrix and integrated similarity for miRNAs and diseases, has been constructed. It can be represented as follow:

(17) $MD=\left[\begin{array}{l}SRA\\ {{\displaystyle A}}^{T}SD\end{array}\right]$(17)

In this way, we could construct a network, in which every miRNA and disease represents a node. Undirected edges exist between two miRNAs or two diseases, and the weight of edge equals to the similarity between them (An edge won't exist if the similarity between two nodes is 0). Moreover, every experimentally confirmed miRNA-disease association corresponds an edge with a weight of 1. After establishing this network, path-depended algorithm could be applied on our network.

In our work for potential miRNA-disease association prediction, calculating the similarity between diseases and miRNAs could be transform to the problem of counting the walks from one miRNA nodes to a disease node. Considering that shorter walks tend to contribute more, we introduced a nonnegative parameter $\beta$ to control the weight of walks with different lengths. A smaller value of $\beta$ means the weights of longer walks is smaller. Thus, the Katz index could be calculated as follows:

(18) $S_{d_i{r}_j}={\displaystyle \sum _{l=1}^k{\beta }_l{S}_{l(d_i{r}_j)}}$(18)

where $S_{l\left(d_i{r}_j\right)}$ denotes the number of walks with length l which links node $d_i$ and node $r_j$. Then, we further let $\text{k}\to \infty$ and replaced the ${\beta }_{l }\text{by} {\beta }^l$, the whole Katz index could be written in matrix form as:

(19) $S^{Katz}={\left(I- \beta *MD\right)}^{-1}-I$(19)

The $S^{Katz}$ records the similarities between all the nodes. Specifically, it can be represented by a partitioned matrix:

(20) $S^{Katz}=\left[\begin{array}{l}S1S3\\ S2S4\end{array}\right]$(20)

Being aware of it was generated based on matrix $M{D}_{878*878}$, it could be easily detected that S3 record the association probability between every miRNA-disease pair. Also, to ensure that the Katz index converge, the value of$\beta$must be less than the reciprocal of the largest eigenvalue of $M{D}_{878*878}$. Considering that longer walks tend to be meaningless for our predictive work, we set k to 1, 2 and 3 respectively to evaluate the influence of this parameter. Based on equation (18), the $S^{Katz}$ can be writing as follows:

(21) $S^{Katz}= \beta S_1+ {\beta }^2{S}_2+ \cdots + {\beta }^n{S}_n+ \cdots$(21)

Here, $S_i$ means the probability of going from node x to node y in i steps which could be represented by matrix A, SD and SR as follows:

(22) $S_1=\text{A}$(22)

(23) $S_2=SR *A+A*SD$(23)

(24) $S_3=\left(S{R}^3*A+A*A^T*SR*A+SR*A*A^T*A+A*SD*A^T*A\right)+\left(A*A^T*A*SD+S{R}^2*A*SD+SR*A*S{D}^2+A*S{D}^3\right)$(24)

According to previous research [84] and our own test, we chose β as 0.01. Similar to Common Neighbors, we obtained a rank matrix $RankKI$ to save the ranks for all the miRNA-disease pairs.

Ensemble learning

As mentioned above, we would achieve a rank matrix of every method which enabled us to examine these methods in case study 1. We chose 14 popular human diseases and predicted the top 50 potential associations for them. Therefore, there were 700 predictive results and we confirmed these results in miR2Disease and dbDEMC [39,40]. Let $e_m\left(m=1,2,3\right)$ denoted as the predicted error rate of every method respectively. Base on classic ensemble learning method, we calculated the weight of methods as follows:

(25) ${\alpha }_m=\frac{1}{2}\log \frac{1-e_m}{e_m}$(25)

As a result, the final weights of Common Neighbor, Jaccard index and Katz index are 0.1725, 0.3992 and 0.4283. By this time, we could take advantage of these weights to weightedly combine $RankCN$, $RankJI$ and $RankKI$ to obtain the overall rank matrix. As mentioned above, every miRNA-disease pair could obtain a rank based on Common Neighbor, Jaccard index and Katz index. To accurately combine these ranks, we exploited reciprocal ranking method, which means a pair ranks t will achieve a score $\frac{1}{t}$. Hence, every miRNA-disease pair could achieve three scores depending on its ranks in the aforementioned three methods. Exploiting the final weight to weightedly combine the three scores of all the miRNA-disease pairs and taking advantage of the same sorting method used in Common Neighbor, we finally obtained the overall rank matrix Rank, which records the ranks of every miRNA-disease pair given by ELLPMDA.

Disclosure of potential conflicts of interest

No potential conflicts of interest were disclosed.

Acknowledgments

XC was supported by National Natural Science Foundation of China under Grant Nos. 61772531 and 11631014.

Additional information

Funding

XC was supported by the National Natural Science Foundation of China under Grant Nos. 61772531 and 11631014.