Predicting the potential microRNA (miRNA) candidates associated with a disease helps in exploring the mechanisms of disease development. Most recent approaches have utilized heterogeneous information about miRNAs and diseases, including miRNA similarities, disease similarities, and miRNA-disease associations. However, these methods do not utilize the projections of miRNAs and diseases in a low-dimensional space. Thus, it is necessary to develop a method that can utilize the effective information in the low-dimensional space to predict potential disease-related miRNA candidates. We proposed a method based on non-negative matrix factorization, named DMAPred, to predict potential miRNA-disease associations. DMAPred exploits the similarities and associations of diseases and miRNAs, and it integrates local topological information of the miRNA network. The likelihood that a miRNA is associated with a disease also depends on their projections in low-dimensional space. Therefore, we project miRNAs and diseases into low-dimensional feature space to yield their low-dimensional and dense feature representations. Moreover, the sparse characteristic of miRNA-disease associations was introduced to make our predictive model more credible. DMAPred achieved superior performance for 15 well-characterized diseases with AUCs (area under the receiver operating characteristic curve) ranging from 0.860 to 0.973 and AUPRs (area under the precision-recall curve) ranging from 0.118 to 0.761. In addition, case studies on breast, prostatic, and lung neoplasms demonstrated the ability of DMAPred to discover potential disease-related miRNAs.