Accurate screening on cancer biomarkers contributes to health assessment, drug screening, and targeted therapy for precision medicine. The rapid development of high-throughput sequencing technology has identified abundant genomic biomarkers, but most of them are limited to single-cancer analysis. Based on the combination of Fisher score, Recursive feature elimination, and Logistic regression (FRL), this paper proposes an integrative feature selection algorithm named FRL to explore potential cancer genomic biomarkers on cancer subsets. Fisher score is initially used to calculate the weights of genes to rapidly reduce the dimension. Recursive feature elimination and Logistic regression are then jointly employed to extract the optimal subset. Compared to the current differential expression analysis tool GEO2R based on the Limma algorithm, FRL has greater classification precision than Limma. Compared with five traditional feature selection algorithms, FRL exhibits excellent performance on accuracy (ACC) and F1-score and greatly improves computational efficiency. On high-noise datasets such as esophageal cancer, the ACC of FRL is 30% superior to the average ACC achieved with other traditional algorithms. As biomarkers found in multiple studies are more reliable and reproducible, and reveal stronger association on potential clinical value than single analysis, through literature review and spatial analyses of gene functional enrichment and functional pathways, we conduct cluster analysis on 10 diverse cancers with high mortality and form a potential biomarker module comprising 19 genes. All genes in this module can serve as potential biomarkers to provide more information on the overall oncogenesis mechanism for the detection of diverse early cancers and assist in targeted anticancer therapies for further developments in precision medicine.