Dual Laplacian regularized matrix completion for microRNA-disease associations prediction

ABSTRACT

Since lots of miRNA-disease associations have been verified, it is meaningful to discover more miRNA-disease associations for serving disease diagnosis and prevention of human complex diseases. However, it is not practical to identify potential associations using traditional biological experimental methods since the process is expensive and time consuming. Therefore, it is necessary to develop efficient computational methods to accomplish this task. In this work, we introduced a matrix completion model with dual Laplacian regularization (DLRMC) to infer unknown miRNA-disease associations in heterogeneous omics data. Specifically, DLRMC transformed the task of miRNA-disease association prediction into a matrix completion problem, in which the potential missing entries of the miRNA-disease association matrix were calculated, the missing association can be obtained based on the prediction scores after the completion procedure. Meanwhile, the miRNA functional similarity and the disease semantic similarity were fully exploited to serve the miRNA-disease association matrix completion by using a dual Laplacian regularization term. In the experiments, we conducted global and local Leave-One-Out Cross Validation (LOOCV) and case studies to evaluate the efficacy of DLRMC on the Human miRNA-disease associations dataset obtained from the HMDDv2.0 database. As a result, the AUCs of DLRMC is 0.9174 and 0.8289 in global LOOCV and local LOOCV, respectively, which significantly outperform a variety of previous methods. In addition, in the case studies on four significant diseases related to human health including Colon Neoplasms, Kidney neoplasms, Lymphoma and Prostate neoplasms, 90%, 92%, 92% and 94% out of the top 50 predicted miRNAs has been confirmed, respectively.

1. Introduction

As a kind of short non-coding single-stranded RNA, MicroRNAs (miRNAs) (22nt) are found in plants, animals, and some viruses. By binding to the 3ʹ untranslated regions (UTRs) of the target messenger RNAs (mRNAs) through base pairing, miRNAs can suppress the protein production and gene expression [1–5]. On the other hand, some scientific researchers have also shown that miRNAs could also act as positive regulators [6,7]. Since the first two miRNAs, i.e., Caenorhabditis elegans lin-4 and let-7 were discovered more than twenty years ago, more and more miRNAs have been detected in recent years. Meanwhile, large amounts of evidences confirm that miRNAs play vital roles in a variety of crucial cell biological processes, such as proliferation, development, differentiation, apoptosis, metabolism, viral infection, aging, signal transduction and so on [8–14]. Therefore, it is no doubt that miRNAs are closely related to many complex human diseases and some miRNA-disease associations have already been verified. For example, the miRNA deregulation is closely related to the development of various cancers [15–19]. As the first evidence for the fact that miRNAs are involved in cancer formation [20], firstly clarified that miR-15 and miR-16 are deleted in more than half cases of B-cell chronic lymphocytic leukemia. Also, miR-34a and miR-199a/b were found to be down-regulated in solid cancer cells [21]. Besides, researchers revealed that miR-126 were expressed with significantly higher levels in the blood from patients with Crohn Disease [22]. Furthermore, for patients with end-stage renal disease, the circulating levels of miR-15b were significantly suppressed [23]. Apart from the aforementioned miRNA-disease associations, there may exist other ones. Therefore, it is meaningful to discover more miRNA-disease associations for benefiting disease diagnosis and prevention of human complex diseases [24–27]. However, it is expensive and time consuming to identify the associations between miRNAs and diseases using existing biological experimental methods. Hence, it is necessary for us to develop efficient computational methods to predict the potential miRNA-disease associations by using the recent superior computing resources [28,29].

During last decades, many computational methods for predicting potential miRNA-disease associations have been proposed. Some of these methods depend on the assumption that miRNAs with similar functions are more likely to have connections with diseases which share similar phenotypes [30–36]. For example, Wang et al. [37] predicted potential miRNA-disease associations by scoring each miRNA for a disease of interest through the cumulative hypergeometric distribution. Shi et al. [38] exploited the functional associations between miRNA and disease by implementing the algorithm of random walk on protein-protein interaction network. Based on the assumption that miRNAs whose target genes are related to certain diseases are more likely to be associated with these diseases, they discovered the miRNA-target interactions, disease-gene associations, and protein-protein interactions to predict potential associations between the miRNAs and diseases. Xuan et al. [39] developed the HDMP prediction method by calculating the functional similarities of weighted $k$ neighbor miRNAs. Instead of relying on the known miRNA-disease associations, Xu et al. [40] introduced a miRNA prioritization method by evaluating the similarity between the targets of miRNAs and disease genes. By combining protein-disease associations and miRNA-protein interactions together to predict novel miRNA-disease associations, Mork et al. [41] proposed a computational model named miRPD. Luo et al. [42] proposed a transduction learning-based method to prioritize disease-related miRNAs, especially for those diseases that are associated with sparse known miRNAs. In [43], the restricted Boltzmann machine (RBM) which is a two-layer undirected graphical model consisting of layers of visible and hidden units was deployed to construct a computational model called RBMMMDA. Li et al. [44] developed a Matrix Completion for MiRNA-Disease Association prediction model based on the known miRNA-disease associations, during the matrix completion, the known associations are well retained, potential associations are predicted by the completed values. Mugunga et al. [45] presented a prediction model that is based on the theory of path features and random walk to obtain a relevancy score of miRNA-related disease. In their model, highly ranked scores are potential miRNA-disease associations. Li et al. [46] explored the way to predict the miRNA-disease association by using the extensive collaborative filtering in order to diagnose the diseases better, they considered the miRNA functional similarity and disease similarity while used minimal amount of related information. In [47], three inference methods were introduced to predict potential miRNA-disease associations based on the global network similarity measure and the assumption that functionally related miRNAs tend to be associated with phenotypically similar diseases. Chen et al. [28] proposed to prioritize disease miRNAs by using the the between-scores and within-scores of each miRNA-disease pair. By integrating heterogeneous omics data for identifying disease miRNAs, Luo et al. [48] developed a Kronecker regularized least squares-based method for miRNA-disease association prediction. By considering that most of previous approaches strongly rely on the known association information, and only a handful of them could be applied to uncover the potential associations involving novel diseases or miRNAs. Chen et al. [29] presented a model named RLSMDA based on semi-supervised learning which calculates the semantic similarity between different diseases. RLSMDA could identify related miRNAs for diseases without any known associated miRNAs, meanwhile avoiding the problem of using negative associations between miRNAs and diseases. Xiao et al. [49] also introduced a novel framework called GRNMF to infer the unknown miRNA-disease associations in heterogeneous omics data, which could work for both new diseases and miRNAs. You et al. [50] constructed a heterogeneous graph consisting of three interlinked sub-graphs and further adopted depth-first search algorithm to infer potential miRNA-disease associations. By constructing a similarity network and utilizing ensemble learning to combine rank results given by three classic similarity-based algorithms, Chen et al. [35] obtained superior prediction results. Based on the known miRNA-disease associations, disease semantic similarity, miRNA functional similarity, and Gaussian interaction profile kernel similarity for miRNAs and diseases, many computational models have been put forward, e.g., Sparse Subspace Learning [51], matrix completion-based model [52], Extreme Gradient Boosting Machine [53], Bipartite Network Projection [54], Triple Layer Heterogeneous Network [55] and Random Forest [56]. In Table 1, we give a brief summary of the differences between some typical previous computational methods. As can be seen, the three kinds of similarity priors have been widely used in previous methods. A detailed review of previous miRNA-disease associations prediction methods can be found in [33,57].

Table 1.

Differences between some typical previous computational methods for miRNA-disease association prediction. ‘A’ denotes depending on disease semantic similarity, ‘B’ denotes depending on miRNA functional similarity, and ‘C’ denotes depending on Gaussian interaction profile kernel similarity for miRNAs and diseases.

Year	Methods	A	B	C	Characteristic
2010	Phenome-microRNAome network [37]	✓	$\times$	$\times$	Cumulative hypergeometric distribution, phenotypic similarity score
2013	bipartite network [38]	✓	✓	$\times$	PPI network, random walk, global perspective measures
2013	Weighted kNN [39]	✓	✓	$\times$	Weighted kNN, miRNA family and the cluster information
2013	MBSI [47]	$\times$	✓	$\times$	microRNA-based similarity inference, global network similarity measure)
2013	PBSI [47]	✓	$\times$	$\times$	phenotype-based similarity inference, global network similarity measure
2013	NetCBI [47]	$\times$	✓	$\times$	network-consistency-based inference, global network similarity measure
2014	miRNAs Prioritization [40]	$\times$	✓	$\times$	molecular mechanisms, context-dependent miRNA-target interactions
2014	RLSMDA [29]	✓	✓	$\times$	Semi-supervised prediction method, global approach
2014	miRPD [41]	$\times$	$\times$	$\times$	miRNAProteinDisease associations, text mining
2015	RBMMMDA [43]	$\times$	$\times$	$\times$	Restricted Boltzmann machine, inferring multiple types of miRNA-disease pairs
2016	WBSMDA [28]	✓	✓	✓	Within and between score, integrating plenty of heterogeneous biological datasets
2016	HGIMDA [58]	✓	✓	✓	Heterogeneous Graph Inference
2017	BRWH [48]	✓	✓	$\times$	bi-random walk, heterogeneous network, microbe similarity network, disease similarity network
2017	GRNMF [49]	✓	✓	$\times$	graph regularized NMF
2017	PBMDA [50]	✓	✓	✓	special depth-first search algorithm, heterogeneous graph
2017	LRSSLMDA [51]	✓	✓	✓	Laplacian Regularized Sparse Subspace Learning, local structures of the training data
2017	CPTL [42]	✓	✓	$\times$	Collective Prediction, Transduction Learning
2017	RKNNMDA [34]	✓	✓	✓	Ranking-based KNN
2017	MCMDA [44]	$\times$	$\times$	$\times$	Matrix completion, adjacency matrix of known miRNA-disease associations
2018	IMCMDA [52]	✓	✓	✓	Inductive Matrix Completion
2018	EGBMMDA [53]	✓	✓	$\times$	Extreme Gradient Boosting Machine, statistical measures, graph theoretical measures, matrix factorization results
2018	BNPMDA [54]	✓	✓	✓	Bipartite Network Projection, bias ratings, agglomerative hierarchical clustering
2018	TLHNMDA [55]	✓	✓	$\times$	Triple Layer Heterogeneous Network based inference
2018	ELLPMDA [35]	✓	✓	✓	Ensemble Learning, Link Prediction, similarity network
2018	MDHGI [59]	✓	✓	✓	Matrix decomposition and Heterogeneous Graph Inference
2018	BLHARMDA [60]	✓	✓	✓	Bipartite local models, Jaccard similarity, hubness-aware regression, KNN classifier
2018	SNMFMDA [61]	✓	✓	✓	Symmetric NMF, Kronecker regularized least square
2018	RFMDA [56]	✓	✓	✓	Random Forest, robust feature selection

In this work, we introduce a novel dual laplacian regularized matrix completion framework, referred to as DLRMC briefly, to infer the unknown miRNA-disease associations in heterogeneous omics data, which can work well for both new diseases and miRNAs. DLRMC transforms the task of miRNA-disease association prediction into a matrix completion problem, in which the potential missing entries of the miRNA-disease association matrix were calculated, the missing association can be obtained based on the prediction scores after the completion procedure. In DLRMC, the miRNA functional similarity and the disease semantic similarity are fully exploited to serve the miRNA-disease association matrix completion by using a dual Laplacian regularization term, i.e., miRNAs with similar functions are more likely to have connections with diseases which share similar phenotypes and diseases with semantic similarity are tend to be related with similar miRNAs. In addition, during the matrix competition process, an indicator matrix with binary values which indicates the indices of the observed miRNA-disease associations are deployed to preserve the experimental confirmed associations. The experimental results indicate that DLRMC achieves superior performance compared with other methods and can be effectively applied in the discovery of missing or potential associations for novel diseases and miRNAs.

2. Results

2.1. Leave-one-out cross validation

To investigate the performance of DLRMC, we use global and local leave-one-out cross validation (LOOCV) based on the known miRNA-disease associations obtained from HMDDv2.0 database. As a validation method, LOOCV uses one known association as the test sample and the remaining known associations as the training samples. As to HMDDv2.0 database, we have already obtained 5430 known miRNA-disease associations, these associations can be regarded as the gold standard data set. The miRNA-diseases without known association evidences were considered as candidate samples. The scores of all miRNA-disease pairs can be obtained after DLRMC was implemented. As to global LOOCV, the score of the test sample was compared with the scores of all the candidate samples while in local LOOCV, the test sample was merely compared with the scores of the candidate samples which included the particular disease in the test sample. In this work, we perform 5-fold cross validation experiments for evaluation. The known miRNA-disease associations were randomly divided into five disjoint parts. For each time, one part was picked out as test samples and the rest four parts were used as training samples, and the miRNA-disease pairs without known association evidences were still regarded as candidate samples. Finally, the score of each test sample was compared with the scores of all the candidate samples, respectively. This procedure was repeated five times until each known association was used as test sample and its score was compared with the scores of the candidate samples. Those test samples whose scores rank exceeded the given threshold were considered to predict the miRNA-disease associations correctly.

2.2. Comparison with other methods

In order to demonstrate the efficacy of the proposed DLRMC, we compare its performance with the following methods: HDMP [39], RLSMDA [29], WBSMDA [28], MCMDA [44] and EGBMMDA [53]. We draw a receiver operating characteristics curve (ROC) to compare DLRMC with other previous state-of-the-art methods. In the ROC, true positive rate (TPR, sensitivity) against false positive rate (FPR, 1-specificity) at different thresholds are plotted [62]. TPR/sensitivity denotes the percentage of the test miRNA-disease associations which are ranked higher than the given threshold, while specificity represents the percentage of negative miRNA-disease pairs ranked below the threshold [63]. The area under the ROC curve (AUC) is calculated to evaluate the accuracy of miRNA-disease associations prediction methods. For a specific method, if AUC = 1, it means that the method owns a prefect performance. AUC of 0.5 means that the method merely has a random prediction performance. As to global LOOCV, the AUCs of HDMP, RLSMDA, WBSMDA, MCMDA, EGBMMDA and DLRMC are 0.8366, 0.8030, 0.8030, 0.8749, 0.9123 and 0.9174, respectively. For local LOOCV, HDMP, RLSMDA, WBSMDA, MCMDA, EGBMMDA and DLRMC reach AUCs of 0.7702, 0.0.6953, 0.0.8031, 0.7718, 0.8221 and 0.8289, respectively. Figs. 1a, b) show the ROCs of different methods in terms of global LOOCV and local LOOCV, respectively. As can be seen, DLRMC works more effective in predicting potential miRNA-disease associations when compared with the other previous methods.

Figure 1.

Performance evaluation comparison between DLRMC and other methods in terms of ROC curve and AUC based on global LOOCV and local LOOCV tested by known miRNA-disease associations in the HMDD database. As can be seen, DLRMC achieves AUC of 0.9174 in global LOOCV and 0.8289 in local LOOCV. Thus, the performance of DLRMC is almost better than other methods in some degree and it proves to be effective in predicting the potential miRNA-disease associations.

2.3. Case studies

Similar to previous methods, we also implement case studies to further validate the efficacy of the proposed DLRMC. In detail, four significant diseases related to human health including Colon Neoplasms, Kidney neoplasms, Lymphoma and Prostate neoplasms are used to practically evaluate the prediction accuracy of DLRMC. The top 20 and top 50 predicted miRNAs related with these diseases are examined by another two independent miRNA-disease databases: dbDEMC [64] and miR2Disease [65].

Colon Neoplasms, is known as a malignant cancer which is the third most common type of cancer constituting about 10% of all cancer cases [66]. However, early patients of colon neoplasms only suffer from subtle symptoms, which makes it a fairly hard-to-detect cancer at an early stage [67,68]. Studies have confirmed that some miRNAs are related to Colon Neoplasms, for instance, miR-145 is constantly downregulated in colorectal tumors [69]. MiR-127 has been reported to play a role as a possible tumor suppressor gene [70]. In addition, there exists report indicating that the occurrence rate of colon neoplasms has an increasing trend these years [71]. As a result, it is important to predict the potential miRNAs related to colon neoplasms. In this work, we implement DLRMC to predict the top 50 miRNAs associated with colon neoplasms. Finally, 19 of the top 20 and 45 of the top 50 predicted miRNAs associated with colon neoplasms are validated by dbDEMC and miR2Disease database,the prediction results are shown in Table 2.

Table 2.

The top 50 miRNAs associated with colon neoplasms predicted by our DLRMC. In summary, 19 out of the top 20, and 45 out of the top 50 predicted Colon Neoplasms related miRNAs are confirmed based on dbDEMC and miR2Disease (1st column: top 1–25; 2nd column: top 26–50).

miRNA	Evidence	miRNA	Evidence
hsa-mir-146a	dbdemc	hsa-mir-196a	dbdemc;miR2Disease
hsa-mir-155	dbdemc;miR2Disease	hsa-mir-29c	dbdemc
hsa-mir-132	miR2Disease	hsa-mir-223	dbdemc;miR2Disease
hsa-mir-21	dbdemc;miR2Disease	hsa-mir-143	dbdemc;miR2Disease
hsa-mir-34a	dbdemc;miR2Disease	hsa-let-7a	unconfirmed
hsa-mir-221	dbdemc;miR2Disease	hsa-mir-195	dbdemc;miR2Disease
hsa-mir-20a	dbdemc;miR2Disease	hsa-mir-200b	dbdemc
hsa-mir-16	dbdemc	hsa-mir-214	dbdemc
hsa-let-7a	dbdemc;miR2Disease	hsa-mir-148a	dbdemc
hsa-mir-125b	dbdemc	hsa-mir-106b	dbdemc;miR2Disease
hsa-mir-29a	dbdemc;miR2Disease	hsa-mir-23a	miR2Disease
hsa-mir-29b	dbdemc;miR2Disease	hsa-mir-142	unconfirmed
hsa-mir-15a	dbdemc	hsa-mir-31	dbdemc;miR2Disease
hsa-mir-133a	dbdemc;miR2Disease	hsa-mir-34c	miR2Disease
hsa-mir-222	dbdemc	hsa-mir-141	dbdemc;miR2Disease
hsa-mir-199a	unconfirmed	hsa-mir-182	dbdemc;miR2Disease
hsa-mir-26a	dbdemc;miR2Disease	hsa-mir-200a	unconfirmed
hsa-mir-1	dbdemc;miR2Disease	hsa-let-7c	dbdemc
hsa-mir-19b	dbdemc;miR2Disease	hsa-mir-101	unconfirmed
hsa-mir-19a	dbdemc;miR2Disease	hsa-mir-192	dbdemc;miR2Disease
hsa-mir-15b	miR2Disease	hsa-mir-181a	dbdemc;miR2Disease
hsa-mir-18a	miR2Disease	hsa-mir-9	dbdemc;miR2Disease
hsa-mir-92a	dbdemc	hsa-mir-133b	dbdemc;miR2Disease
hsa-mir-30b	dbdemc;miR2Disease	hsa-mir-34b	dbdemc;miR2Disease
hsa-mir-150	dbdemc;miR2Disease	hsa-mir-183	dbdemc;miR2Disease

Kidney neoplasms is known as renal cancer, which starts in the cells of kidney, and it includes various types [72]. For kidney neoplasms patients, the most common symptoms are pains in the lumbar and hematuria [73]. Based on recent biological experiments, many existing kidney neoplasm-related miRNAs have been verified. For instance, the common target ACVR2B of five miRNAs (miRNA-192, miRNA-194, miRNA-215, miRNA-200c and miRNA-141) is strongly expressed in renal childhood neoplasms [74]. In addition, researches had reported that the decreasing miRNA-23b expression might inhibit kidney tumor growth [75]. As a result of the case study for Kidney neoplasms, 17 out of the top-20 predicted miRNAs and 46 out of the top-50 predicted miRNAs of kidney neoplasms were verified by miR2Disease database and dbDEMC database. The prediction results are shown in Table 3.

Table 3.

The top 50 miRNAs associated with kidney neoplasms predicted by our DLRMC. In summary, 17 out of the top 20, and 46 out of the top 50 predicted kidney neoplasms related miRNAs are confirmed based on dbDEMC and miR2Disease (1st column: top 1–25; 2nd column: top 26–50).

miRNA	Evidence	miRNA	Evidence
hsa-mir-155	dbdemc	hsa-mir-92a	dbdemc
hsa-mir-146a	dbdemc	hsa-mir-195	dbdemc
hsa-mir-122	dbdemc;miR2Disease	hsa-mir-126	dbdemc;miR2Disease
hsa-mir-34a	dbdemc	hsa-mir-29c	dbdemc;miR2Disease
hsa-mir-221	unconfirmed	hsa-mir-23a	dbdemc
hsa-mir-16	dbdemc	hsa-mir-143	dbdemc
hsa-mir-125b	unconfirmed	hsa-mir-223	dbdemc
hsa-mir-29a	dbdemc;miR2Disease	hsa-mir-214	dbdemc;miR2Disease
hsa-mir-133a	unconfirmed	hsa-let-7a	dbdemc
hsa-mir-29b	dbdemc;miR2Disease	hsa-mir-148a	dbdemc
hsa-mir-145	dbdemc	hsa-mir-200b	dbdemc;miR2Disease
hsa-mir-26a	dbdemc;miR2Disease	hsa-mir-31	dbdemc
hsa-mir-199a	dbdemc;miR2Disease	hsa-mir-210	dbdemc;miR2Disease
hsa-mir-222	dbdemc	hsa-mir-106b	dbdemc;miR2Disease
hsa-mir-1	dbdemc	hsa-mir-34c	dbdemc
hsa-mir-15b	dbdemc	hsa-mir-182	dbdemc;miR2Disease
hsa-mir-20a	dbdemc;miR2Disease	hsa-mir-200a	dbdemc
hsa-mir-17	dbdemc;miR2Disease	hsa-mir-101	dbdemc;miR2Disease
hsa-mir-30b	dbdemc	hsa-let-7c	dbdemc
hsa-mir-206	dbdemc	hsa-mir-181a	dbdemc
hsa-mir-19a	dbdemc	hsa-mir-9	dbdemc
hsa-mir-196a	dbdemc	hsa-mir-34b	dbdemc
hsa-mir-19b	dbdemc;miR2Disease	hsa-mir-183	dbdemc
hsa-mir-18a	dbdemc	hsa-mir-218	dbdemc
hsa-mir-150	dbdemc;miR2Disease	hsa-let-7b	unconfirmed

Lymphoma often refers to a group of cancerous blood cell tumors, it originates in the lymphatic hematopoietic system [76] which consists of two categories: non-Hodgkin lymphoma (NHL) and Hodgkin’s lymphoma (HL). Worldwide, lymphoma is the seventh most common cancer and makes up 3–4% of all cancers. As to children, lymphomas is also the third-most common cancer. Thanks to the development of high-throughput sequencing technologies, several miRNAs had been already reported to be associated with lymphomas. For example, re-expression of miRNA-150 induces EBV-positive Burkitt lymphoma differentiation by modulating c-Myb in vitro [77]. The expressions proportion of miRNA-21 and miRNA-210 in plasma of previously untreated lymphoma patient group were higher than those of the patients treated for 6 or more courses [78]. In addition, it was found that the plasma miRNA-92a level could be a useful biomarker for NHL diagnosis and patients monitoring after chemotherapy [79]. We implemented DLRMC to predict the related miRNAs for lymphoma based on known associations in the HMDDv2.0 database. As a result, among the top 20 and 50 potential lymphoma-related miRNAs, 19 and 46 were confirmed by miR2Disease and dbDEMC databases, respectively. The prediction results are shown in Table 4.

Table 4.

The top 50 miRNAs associated with Lymphoma predicted by our DLRMC. In summary, 19 out of the top 20, and 46 out of the top 50 predicted Lymphoma related miRNAs are confirmed based on dbDEMC and miR2Disease (1st column: top 1–25; 2nd column: top 26–50).

miRNA	Evidence	miRNA	Evidence
hsa-mir-30b	dbdemc	hsa-mir-199b	dbdemc
hsa-mir-148a	dbdemc	hsa-mir-26b	dbdemc
hsa-mir-373	dbdemc	hsa-mir-7i	dbdemc
hsa-mir-196a	dbdemc	hsa-mir-9	dbdemc
hsa-mir-23a	dbdemc	hsa-let-7b	dbdemc
hsa-mir-206	dbdemc	hsa-mir-96	dbdemc
hsa-mir-195	dbdemc	hsa-let-7d	dbdemc
hsa-mir-372	unconfirmed	hsa-mir-93	dbdemc
hsa-mir-199a	dbdemc	hsa-mir-25	dbdemc
hsa-mir-15b	dbdemc	hsa-mir-371a	unconfirmed
hsa-mir-137b	dbdemc;miR2Disease	hsa-let-7e	dbdemc;miR2Disease
hsa-mir-34b	dbdemc	hsa-mir-7	dbdemc
hsa-mir-183	dbdemc	hsa-mir-223	dbdemc
hsa-mir-132	dbdemc	hsa-mir-106a	dbdemc;miR2Disease
hsa-mir-214	dbdemc	hsa-mir-205	dbdemc
hsa-mir-182	dbdemc	hsa-mir-222	dbdemc
hsa-mir-31	dbdemc	hsa-mir-335	dbdemc
hsa-mir-133a	dbdemc	hsa-mir-27a	dbdemc
hsa-mir-212	dbdemc	hsa-mir-181c	dbdemc
hsa-mir-141	dbdemc	hsa-mir-224	dbdemc
hsa-mir-127	dbdemc;miR2Disease	hsa-mir-27b	dbdemc
hsa-mir-192	dbdemc	hsa-mir-30a	dbdemc
hsa-mir-100	dbdemc	hsa-mir-370	unconfirmed
hsa-mir-451a	unconfirmed	hsa-mir-1	dbdemc
hsa-mir-106b	dbdemc	hsa-let-7g	dbdemc

Prostate neoplasms is a malignant tumor which originates in the epithelial cells of prostate [80], it is the second most common type of cancer and the fifth leading cause of cancer-related death in men according to the statistics of the World Health Organization [81]. Up to now, plenty of evidences had confirmed that lots of miRNAs were associated with prostate neoplasms. For instance, the downregulation of miRNA-145 was observed in prostate cancer [82]. It was found that miRNA-183 might be a novel prostate cancer biomarker and inhibiting the expression of miRNA-183 could be beneficial for prostate cancer treatment ([83]). DLRMC predicted the top 20 and top 50 potential miRNAs which might be associated with prostate neoplasms. As a result, 19 of the top 20 and 47 of the top 50 predicted miRNAs were confirmed in the dbDEMC and miR2Disease database, the prediction results are shown in Table 5.

Table 5.

The top 50 miRNAs associated with Prostate neoplasms predicted by our DLRMC. In summary, 19 out of the top 20, and 47 out of the top 50 predicted Prostate neoplasms related miRNAs are confirmed based on dbDEMC and miR2Disease (1st column: top 1–25; 2nd column: top 26–50).

miRNA	Evidence	miRNA	Evidence
hsa-mir-146a	miR2Disease	hsa-mir-150	dbdemc
hsa-mir-122	unconfirmed	hsa-mir-126	dbdemc;miR2Disease
hsa-mir-155	dbdemc	hsa-mir-195	dbdemc;miR2Disease
hsa-mir-21	dbdemc;miR2Disease	hsa-mir-29c	dbdemc
hsa-mir-34a	dbdemc;miR2Disease	hsa-mir-223	dbdemc;miR2Disease
hsa-mir-16	dbdemc;miR2Disease	hsa-mir-143	dbdemc;miR2Disease
hsa-mir-221	dbdemc;miR2Disease	hsa-mir-23a	dbdemc;miR2Disease
hsa-mir-29a	dbdemc	hsa-let-7a	dbdemc;miR2Disease
hsa-mir-133a	dbdemc	hsa-mir-200b	unconfirmed
hsa-mir-29b	dbdemc;miR2Disease	hsa-mir-214	dbdemc;miR2Disease
hsa-mir-15a	dbdemc;miR2Disease	hsa-mir-148a	miR2Disease
hsa-mir-26a	dbdemc;miR2Disease	hsa-mir-106b	dbdemc
hsa-mir-222	dbdemc;miR2Disease	hsa-mir-34c	dbdemc
hsa-mir-199a	dbdemc;miR2Disease	hsa-mir-30c	dbdemc;miR2Disease
hsa-mir-1	dbdemc	hsa-mir-31	dbdemc;miR2Disease
hsa-mir-20a	miR2Disease	hsa-mir-141	miR2Disease
hsa-mir-17	miR2Disease	hsa-mir-182	dbdemc;miR2Disease
hsa-mir-15b	dbdemc	hsa-mir-200a	dbdemc
hsa-mir-19a	dbdemc	hsa-mir-101	dbdemc;miR2Disease
hsa-mir-19b	dbdemc;miR2Disease	hsa-let-7c	dbdemc;miR2Disease
hsa-mir-206	dbdemc	hsa-mir-192	dbdemc
hsa-mir-30b	dbdemc;miR2Disease	hsa-mir-181a	dbdemc;miR2Disease
hsa-mir-181b	dbdemc;miR2Disease	hsa-mir-9	dbdemc
hsa-mir-196a	dbdemc	hsa-mir-34b	dbdemc
hsa-mir-92a	unconfirmed	hsa-mir-133b	dbdemc

2.4. Advantages of DLRMC

The experimental results of above sections demonstrate that DLRMC can obtain higher AUC value than other previous methods, which demonstrates that DLRMC works more effective in predicting potential miRNA-disease associations. The advantages of DLRMC lie in following aspects: Firstly, the low-rank property of miRNA-disease association matrix is exploited to regularize the matrix completing process. Secondly, DLRMC fills the candidate samples without known associations with 0 and then iteratively updates them with the predictive scores. Finally, the known miRNA-disease associations, miRNA functional similarity and the disease semantic similarity are integrated into a unified model to serve the completion of miRNA-disease association matrix.

3. Materials and methods

3.1. Methods overview

In order to predict potential undiscovered miRNA-disease associations, we propose a novel method named DLRMC, which consists of three main steps. First, the miRNA functional similarity and the disease semantic similarity are calculated based on the collected data sources. Considering that the two kinds of similarity priors benefit a lot of previous miRNA-disease associations prediction methods, we integrate the two kinds of similarities into a matrix competition model for miRNA-disease associations prediction. The entry values of the completed association matrix are used to infer the potential miRNA-disease associations. Fig. 2 gives a brief flowchart of our proposed method.

Figure 2.

Flowchart of our DLRMC model for predicting the potential miRNA-disease associations.

3.2. Human miRNA-disease associations

In this work, we use the Human miRNA-disease associations dataset obtained from the HMDDv2.0 database [84], which consists of 5430 experimentally confirmed human miRNA-diseases associations. There are 495 miRNAs and 383 human diseases. An adjacency matrix $A$ with binary values is defined to clearly describe the known miRNAs-disease associations, i.e., if a specific miRNA $m(i)$ is confirmed to be associated with a disease $d(j)$, the entity $A(i,j)$ is assigned 1, otherwise 0. Thus, the adjacency matrix $A$ is with size $495\times 383$.

3.3. Similarity measures

3.3.1. miRNA functional similarity

MiRNA functional similarity has been previously calculated by [32], based on the well-known assumption that miRNAs with similar functions are often related to similar diseases. In this work, based on the mentioned miRNA functional similarity, we construct a corresponding miRNA functional similarity matrix $FS$, in which $FS(i,j)$ denotes the functional similarity score between miRNA $m(i)$ and $m(j)$.

3.3.2. Disease semantic similarity

It is well known that the relationship among different diseases can be represented by the hierarchical directed acyclic graph (DAG). In detail, a disease $d$ can be described as $DAG(d)=(d,T(d),E(d))$, where $T(d)$ consists of node $d$ itself and all its ancestor nodes, and $E(d)$ is the edge set including the direct edges linking parent nodes to child nodes [32,85–88]. Then, the semantic value of disease $d$ can be defined as follows:

$$SV(d)=\sum _{\theta \in T(d)}{S}_d(\theta ),$$ (1)

where

$$S_d(\theta )=\left\{\begin{array}{c}1if\theta =d\\ max\{\mathrm{\Delta }\ast S_d({\theta }^{\prime })|{\theta }^{\prime }\in childrenof\theta \}if\theta \ne d\end{array}\right.$$ (2)

In Equation (2), $\mathrm{\Delta }$ represents the semantic contribution factor of disease ${\theta }^{\prime }$ to disease $\theta$. For a given disease $d$, the contribution of itself is 1, while the contribution of another disease $t$ decreases as the distance between $d$ and $t$ increases. Thus, we denote $SS$ as the disease semantic similarity matrix, and the semantic similarity between disease $d(i)$ and $d(j)$ can be calculated as follows:

$$SS(d(i),d(j))=\frac{\sum _{t\in T(d(i))\cap T(d(j))}(S_{d(i)}(t)+S_{d(j)}(t))}{SV(d(i))+SV(d(j))}.$$ (3)

4. Dual Laplacian regularized matrix completion for miRNA-disease associations prediction

4.1. Standard matrix completion

Matrix completion is the task of filling in the missing entries of a partially observed matrix $M$. One of the mostly used model of the matrix completion problem is to find the lowest rank matrix $X$ which matches the matrix $M$, which we wish to recover, for all entries in the set $E$ of observed entries. The basic mathematical formulation of this problem is as follows:

$$\underset{X}{min}rank(X)s.t.X_{ij}=M_{ij}\mathrm{\forall }i,j\in E.$$ (4)

Due to the optimization problem (4) is non-convex and no efficient solution can be obtained, Equation (4) is usually transformed to the following convex problem by relaxing the rank function into the nuclear norm:

$$\underset{X}{min}|\left|X\right|{|}_{\ast }s.t.X_{ij}=M_{ij}\mathrm{\forall }i,j\in E.$$ (5)

where $|\left|\cdot \right|{|}_{\ast }$ is the nuclear norm, which is equal to the sum of singular values of $X$. Equation (5) can be solved by using the singular value thresholding (SVT) algorithm.

4.2. DLRMC

Equation (5) was directly used for miRNAs-disease associations prediction [44] and obtained good results when compared to other previous methods. However, the miRNA functional similarity and disease semantic similarity which have been demonstrated useful in other methods (as shown in Table 1) have not been fully exploited to serve the matrix completion model. Thus, we believe that the miRNA functional similarity and disease semantic similarity can advantage the matrix competition model, of course, better prediction results can be expected. In this work, we propose a novel dual Laplacian regularized matrix completion model (DLRMC) for microRNA-disease associations prediction. In DLRMC, the known microRNA-disease associations, miRNA functional similarity and disease semantic similarity are integrated into a unified model to constrain that miRNAs with similar functions are more likely to have connections with diseases which share similar phenotypes and diseases with semantic similarity are tend to be related with similar miRNAs. The optimization problem of DLRMC can be formulated as follows:

$$\begin{array}{rl}& \underset{X}{min}||X|{|}_{\ast }+\alpha ||X|{|}_F^2+\underset{Knownassociationspreservation}{\underbrace{\beta ||A\circ (X-A)|{|}_F^2}}\\ & \underset{DualLaplacianregularization}{\underbrace{+{\lambda }_n\sum _{i,j=1}^n||x^i-x^j|{|}^{2}FS(i,j)+{\lambda }_m\sum _{p,q=1}^m||x_p-x_q|{|}^{2}SS(i,j),}}\end{array}$$ (6)

where $x^i$ and $x_p$ represent the $i$-th row and $p$-th column of $X$, respectively. $\alpha$, $\beta$, ${\lambda }_n$ and ${\lambda }_m$ are the regularization coefficients, and ‘$\circ$’ denotes the Hadamard product of two matrices. The Tikhonov regularization on $X$ is used to ensure the smoothness of $X$. The third term aims to ensure that the scores of known associations in $X$ are close to those in $A$, i.e., the experimental confirmed miRNAs-disease associations can be preserved after the matrix competition. Since A is with $0-1$ values, we use itself as the indicator matrix to indicate the indices of the observed miRNA-disease associations. The forth and fifth terms constitute the dual Laplacian regularizer which constrain that miRNAs with similar functions are more likely to have connections with diseases which share similar phenotypes and diseases with semantic similarity are tend to be related with similar miRNAs. In Equation (6), since both $\alpha$ and $\beta$ regularize the Frobenius Norm of matrices, we set $\alpha =\beta$ for simplicity. Then we have three parameters in DLRMC need to be tuned, i.e., $\beta$, ${\lambda }_n$ and ${\lambda }_m$. In our experiments, all parameter combinations are considered based on grid search. The optimal ${\lambda }_n$ and ${\lambda }_m$ are determined from $\left\{0.0001,0.001,0.01,0.1,1,10,100,1000,10000\right\}$, while $\beta$ is chosen from $\left\{0.25,0.5,1,2,4\right\}$. Finally, the best results corresponding to the optimal parameters combination are reported. In the discussion section, we will analyze the impact of each parameter on the final results.

Note that a similar dual Laplacian regularization term has been used in [49] for identifying microRNA-disease associations (GRNMF). However, our proposed DLRMC differs from GRNMF in two aspects. Firstly, GRNMF is based on the Non-negative matrix factorization model, which decomposes the miRNA-disease association matrix into a basis matrix and a coefficient matrix, then the two learned matrices are used to recovery the potential miRNA-disease associations, while our DLRMC predicts miRNA-disease associations in a more intuitive way by using the matrix completion model which directly fills the missing values which represent potential miRNA-disease associations. Secondly, the purpose of the dual Laplacian regularization term of the two models is different. In GRNMF, the disease similarity matrix and miRNA functional similarity matrix are used to regularize the geometrical structure of the basis matrix and coefficient matrix, respectively. In our DLRMC, the dual Laplacian regularization term are used to regularize the miRNA-disease association matrix, i.e., miRNAs with similar functions should be more likely to have connections with diseases which share similar phenotypes and diseases with semantic similarity should be related with similar miRNAs, the physical meaning of our regularization term is more intuitive.

4.3. Optimization

To solve the optimization problem in Equation (6), we first transform it into the following form:

$$\begin{array}{cc}\hspace{0.17em}& \underset{X}{min}||X|{|}_{\ast }+\alpha ||X|{|}_F^2+\beta ||A\circ (X-A)|{|}_F^2\\ \hspace{0.17em}& +{\lambda }_{n}Tr(X^T{L}_{n}X)+{\lambda }_{m}Tr(X{L}_m{X}^T),\end{array}$$ (7)

where $L_n\in {\mathbb{R}}^{n\times n}$ is the Laplacian matrix with $L_n=D_n-FS$, and $D_n$ is the diagonal matrix with $D_n(i,i)=\sum _{j}FS(i,j)$. Similarly, $L_m\in {\mathbb{R}}^{m\times m}$ is the Laplacian matrix with $L_m=D_m-SS$, and $D_m$ is the diagonal matrix with $D_m(i,i)=\sum _{j}SS(i,j)$.

Since problem (7) contains Hadamard product of two matrices, it is hard to tackle it directly. Thus, we propose an alternative iterative algorithm to solve this problem based on augmented Lagrange multiplier (ALM) algorithm [89]. We first introduce two auxiliary variables $J$ and $Z$ to make the objective function separable:

$$\begin{array}{cc}\hspace{0.17em}& \underset{X,J,Z}{min}||J|{|}_{\ast }+\alpha ||X|{|}_F^2+\beta ||A\circ (Z-A)|{|}_F^2\\ \hspace{0.17em}& +{\lambda }_{n}Tr(X^T{L}_{n}X)+{\lambda }_{m}Tr(X{L}_m{X}^T)\\ \hspace{0.17em}& s.t.X=J,X=Z.\end{array}$$ (8)

The corresponding augmented Lagrange function of Equation (8) is:

$$\begin{array}{cc}\hspace{0.17em}& \mathcal{L}(X,J,Z,Y_1,Y_2,{\mu }_1,{\mu }_2)\\ \hspace{0.17em}& =||J|{|}_{\ast }+\alpha ||X|{|}_F^2+\beta ||A\circ (Z-A)|{|}_F^2\\ \hspace{0.17em}& +{\lambda }_{n}Tr(X^T{L}_{n}X)+{\lambda }_{m}Tr(X{L}_m{X}^T)\\ \hspace{0.17em}& +\langle Y_1,X-J\rangle +{\mu }_{1}2||X-J|{|}_F^2+\langle Y_2,X-Z\rangle +{\mu }_{2}2||X-Z|{|}_F^2,\end{array}$$ (9)

where $Y_1$ and $Y_2$ are the Lagrange multipliers, ${\mu }_1>0$ and ${\mu }_2>0$ control the penalties for violating the linear constraints, and $\langle \cdot ,\cdot \rangle$ is the standard inner product of two matrices. Then the variables can be solved alternatively.

Solving $J$ with other variables fixed:

The variable $J$ can be solved by following equation with other variables fixed:

$$\begin{array}{cc}\hspace{0.17em}& \underset{J}{min}||J|{|}_{\ast }+\langle Y_1,X-J\rangle +{\mu }_{1}2||X-J|{|}_F^2\\ \hspace{0.17em}& =\underset{J}{min}||J|{|}_{\ast }+{\mu }_{1}2||X-J+Y_1{\mu }_1|{|}_F^2,\end{array}$$ (10)

where $J$ can be solved by singular value thresholding (SVT) operator [90].

4.4. Solving with other variables fixed

When other variables are fixed, $Z$ can be solved by minimizing following function:

$$\begin{array}{cc}\hspace{0.17em}& \underset{Z}{min}\beta ||A\circ (Z-A)|{|}_F^2+<Y_2,X-Z>+{\mu }_{2}2||X-Z|{|}_F^2\\ \hspace{0.17em}& =\underset{Z}{min}\beta ||A\circ (Z-A)|{|}_F^2+{\mu }_{2}2||X-Z+Y_2{\mu }_2|{|}_F^2.\end{array}$$ (11)

Setting the derivative of Equation (11) w.r.t. $Z$ to zero, and using properties of the Hadamard and Kronecker products, it is easy to get that $Z$ can be obtained as:

$$R\cdot vec(Z)=vec(C),$$ (12)

where $R=2\beta Diag(vec(A))+{\mu }_{2}I$, and $C=2\beta (A\circ A)+{\mu }_{2}X+Y_2$. This is a simple linear system and can be solved easily.

4.5. Solving with other variables fixed

We can solve $X$ by dropping other unrelated variables as follows:

$$\begin{array}{cc}\hspace{0.17em}& \underset{X}{min}\alpha ||X|{|}_F^2+{\lambda }_{n}Tr(X^T{L}_{n}X)+{\lambda }_{m}Tr(X{L}_m{X}^T)\\ \hspace{0.17em}& +{\mu }_{1}2||X-J+Y_1{\mu }_1|{|}_F^2+{\mu }_{2}2||X-Z+Y_2{\mu }_2|{|}_F^2,\end{array}$$ (13)

By setting the derivative of Equation (13) w.r.t. $X$ to zero, we have

$$2\alpha X+2{\lambda }_n{L}_{n}X+2{\lambda }_{m}X{L}_m+{\mu }_1(X-J)+{\mu }_2(X-Z)+Y_1+Y_2=0.$$ (14)

Equation (14) is a Sylvester equation [91]. Since $2\alpha +2{\lambda }_n{L}_n$ is strictly positive definite, Equation (14) has stable solution for $X$.

Updating Multipliers:

We update the multipliers by

$$\left\{\begin{array}{c}{Y}_1=Y_1+{\mu }_1(X-J)\\ Y_2=Y_2+{\mu }_2(X-Z).\end{array}\right.$$ (15)

The variables $J$,$Z$ and $X$ are iteratively updated until convergence. Finally, we obtain the predicted miRNA-disease associations based on the completed entities in matrix $X$.

5. Discussion

5.1. Stability analysis

In our experiments, we use the Human miRNA-disease associations dataset obtained from the HMDDv2.0 database [84] for testing, which consists of 5430 experimentally confirmed human miRNA-diseases associations. In order to evaluate the stability of DLRMC to the miRNA-disease database, we change the ratio of training samples and compare the final results. The ratio of training samples varies from $[10\mathrm{\%},15\mathrm{\%},20\mathrm{\%},\cdots ,90\mathrm{\%}]$. For each ratio, the selected associations are used as training samples and the rest are used for testing. For each case, we perform the training samples selecting and associations predicting five times with randomly selected training samples. Finally, the average AUC of the five times are reported for each case. In Fig. 3, we plot the average AUC values with varying ratio of selected training samples. As can be seen, when more than half of the experimentally confirmed human miRNA-diseases associations are selected as training samples, DLRMC can obtain stable results. At present, three kinds of information including the known miRNA-disease associations, miRNA functional similarity and the disease semantic similarity are used for potential associations pridiction, we believe that if more information can be obtained, DLRMC can infer more potential miRNA-disease associations.

Figure 3.

Average AUC values with varying ratio of selected training samples.

5.2. Parameter sensitivity analysis

There are four parameters in our model (i.e., $\alpha$, $\beta$, ${\lambda }_m$ and ${\lambda }_n$). Since we set $\alpha =\beta$, we need to tune three parameters. In order to further demonstrate the performance of the proposed DLRMC, we study its sensitivity w.r.t. the parameters $\beta$, ${\lambda }_m$ and ${\lambda }_n$. Firstly, we fix $\beta =1$ and vary ${\lambda }_m$ and ${\lambda }_n$. Then we fix ${\lambda }_m=1$ and vary $\beta$ and ${\lambda }_n$. Finally, we fix ${\lambda }_n=1$ and vary $\beta$ and ${\lambda }_m$. Figs. 4 and 5 plot the AUC values with varying parameters under global LOOCV and local LOOCV, respectively. As can be seen, the final results are not very sensitive to the parameters. In a certain range, DLRMC can obtain stable results. Through a closer observation, we can find that when $\beta$ is fixed, the best result can be obtained with ${\lambda }_n=100$ and ${\lambda }_m=10000$. When ${\lambda }_m$ or ${\lambda }_n$ is fixed, optimal results can be obtained with $\beta =2$.

Figure 4.

AUC values with varying parameters under global LOOCV.

Figure 5.

AUC values with varying parameters under local LOOCV.

6. Conclusion

It is necessary to develop efficient computational models for predicting the potential miRNA-disease associations since it is expensive and time-consuming to accomplish this task using experimental methods. In this study, we have proposed a computational method, called DLRMC, for miRNA-disease associations prediction. The main contribution of our work is the development a matrix completion model with a dual Laplacian regularizer which constrains that miRNAs with similar functions are more likely to have connections with diseases which share similar phenotypes and diseases with semantic similarity are tend to be related with similar miRNAs. Meanwhile, the experimental confirmed miRNAs-disease associations can be preserved by using a binary indicator matrix after the completion.

The efficacy of our method is validated through cross validations and case studies on the HMDDv2.0 database. The experimental results verify that DLRMC can effectively improve performance compared with other methods, which indicates that DLRMC can be used for novel miRNAs-disease associations prediction.

Our proposed DLRMC can be regarded as an effective complement to experimental methods for discovering miRNA-disease associations. Biomedical researchers can use our model to computationally infer the miRNAs which are potentially associated with the disease of interest, then the most promising associations can be finally chosen for biological confirmation. By this way, experiments could be more effective and productive. In addition, since the identification of disease-related miRNAs is critical to elucidating the development of tumorigenesis, predicted potential associations can further facilitate the discovery of potential drug targets and treatment options.

Funding Statement

This work was partly supported by the National Natural Science Foundation of China under Grant No. 61701451, and partly supported by the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under Grant No. CUG170654, and partly supported by Jiangsu Provincial Commission of Health and Family Planning under Grant No. H201556, and partly supported by the Six Top Talent Peak Projects in Jiangsu under Grant No. WSN-019, and partly supported by the 333 Talent Project of Jiangsu Province under Grant No. BRA2017246.

Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.