Hyperbolic Nature of Differential Expression Signatures

Differentially expressed gene (DEG) signatures play a crucial role in transcriptomics, offering insight into cellular responses and disease mechanisms, thus accelerating drug and target discovery. Understanding the geometric structure of the DEG space is essential for developing more effective computational methods. In this study, we show that the DEG signature space exhibits a scale-free nature, indicating an underlying hyperbolic geometry. To demonstrate the practical implications of this finding, we conducted a comparative analysis of unsupervised dimensionality reduction techniques, evaluating them based on local and global structure preservation. Our results indicate that hyperbolic embeddings better capture DEG signatures, supporting our claim on their underlying geometry. Besides, our prior results on drug-target interaction prediction suggest that hyperbolic embeddings improve performance when DEG signatures are used as input, reinforcing their effectiveness in downstream supervised predictive tasks as well. These findings highlight the relevance of hyperbolic geometry in modeling DEG signatures, suggesting future directions for machine learning applications in transcriptomics.