# DiffRS-net: A Novel Framework for Classifying Breast Cancer Subtypes on Multi-Omics Data
## 3 Results
### Analysis of the Selected Genes by DiffRS-net  
To investigate whether the genes detected by DiffRS-net are highly correlated, we select the top 30 genes with the highest weights from each omics for the Pearson correlation analysis. Figure 5 depicts the correlation coefficient matrix between pairs of omics, where each cell represents the Pearson correlation coefficient for a specific pair of genes (i.e., Sox10 and ANKRD17). The depth of color within each cell indicates the strength of the correlation, with a deeper color (tending towards red) indicating a higher degree of association. Moreover, we calculate the \(p\)-values of the correlation coefficients and mark the cells with \(p\)-values less than 0.0001 with an \"\(\times\)\" in the figure, indicating that these gene pairs have a statistically significant correlation that is not due to chance. The statistical analysis reveals that the proportions of \(p\)-values falling below the threshold for mRNA and miRNA, mRNA and DNA methylation, and miRNA and DNA methylation are 36.11%, 74.44%, and 42.56%, respectively. As can be seen from Figure 5, the correlation between mRNA and DNA methylation is significantly higher than the relationship between mRNA and miRNA. This is likely because the synthesis of mRNA is derived directly from the transcription of DNA, and the state of DNA methylation has a direct impact on this process [47]. Changes in DNA methylation can significantly regulate the expression levels of mRNA. In contrast, miRNAs regulate the stability and translation of mRNA through interaction, rather than being directly involved in the generation of mRNA [48]. Considering that a single miRNA can target multiple mRNAs, and an mRNA may be regulated by multiple miRNAs, a relatively complex regulatory network is established [49]. Hence, the correlation between mRNA and miRNA is comparatively lower. In summary, from the display in Figure 5, we can observe that the top 30 genes selected from each omics group show significant correlation with the 30 genes from other omics groups. Many of these gene correlations reach a level of statistical significance. This finding confirms that our algorithm has successfully identified features that are statistically significant in terms of their correlation. Figure 4: Normalized confusion matrices of various DiffRS-net models on the breast cancer multi-classification dataset. Figure 5: Pairwise correlation between any two omics data. And “\(\times\)” denotes that the gene pair reaches the significance level (\(p\)-value < 0.00001). (**a**) Correlation matrix of mRNA and miRNA. (**b**) Correlation matrix of mRNA and DNAAm. (**c**) Correlation matrix of miRNA and DNAAm. To unravel the possible molecular mechanisms underlying the breast cancer, we select the top 500 weighted mRNA genes for a Gene Ontology (GO) analysis and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis to facilitate the identification of breast cancer subtypes. As can be seen in Figure 6, the results of the GO analysis reveal key biological processes (BPs), molecular functions (MFs), and cellular components (CCs) associated with breast cancer. Significant biological processes include the regulation of transcription, the control of gene expression, the activation of signaling mechanisms, and processes related to aging. Notably, the regulation of transcription initiated by RNA polymerase II is prominent in the results, which may point to a critical role of transcriptional control in breast cancer. The molecular function analysis highlights functions such as Wnt-protein binding and receptor binding, which are likely closely related to signaling and cellular communication in cancer cells. In terms of cellular components, proteins in the extracellular region and cell surface are of particular interest due to their interactions within the tumor microenvironment.