Cancer is a highly complex disease caused by multiple genetic factors. MicroRNA (miRNA) and mRNA expression profiles are useful for identifying prognostic biomarkers for cancer. Kidney renal clear cell carcinoma (KIRC), which accounts for more than 70% of all renal malignant tumour cases, was selected for our analysis. Traditional methods of identifying cancer prognostic markers may not be accurate. Tensor decomposition (TD) is a useful method uncovering the underlying low-dimensional structures in the tensor. The TD-based unsupervised feature extraction method was applied to analyse mRNA and miRNA expression profiles. Biological annotations of the prognostic miRNAs and mRNAs were examined utilizing the pathway and oncogenic signature databases DIANA-miRPath and MSigDB. TD identified the miRNA signatures and the associated genes. These genes were found to be involved in cancer-related pathways, and 23 genes were significantly correlated with the survival of KIRC patients. We demonstrated that the results are robust and not highly dependent upon the databases we selected. Compared with traditional supervised methods tested, TD achieves much better performance in selecting prognostic miRNAs and mRNAs. These results suggest that integrated analysis using the TD-based unsupervised feature extraction technique is an effective strategy for identifying prognostic signatures in cancer studies.