Figure 2. RP preserves sample-to-sample information better than state-of-the-art dimension reduction methods including PCA, t-SNE, and UMAP for RanBALL subtype identification.

We compared RP with other state-of-the-art dimensionality reduction methods across different dimensions (400, 600,…, 2000). The upper triangular section of each matrix displayed the PCC between the sample-to-sample distances in the original high-dimensional space (Ori.) and the corresponding reduced-dimensional space for each method. Higher PCC values indicated better preservation of the original data structure. RP consistently achieved higher PCC (highlighted in red) that outperformed PCA, t-SNE, and UMAP. The lower triangular section provided scatter plots of pairwise distances between samples before and after dimensionality reduction, illustrating how well each method preserved the relative distances between points.