@article{Rong2026, 
author = {Ziqi Rong and Jinpu Cai and Jiahao Qiu and Pengcheng Xu and Lana X. Garmire and Qiuyu Lian and Hongyi Xin},
title = {Enhancing Distance Entropy Preservation via L2 Normalization and Geodesic Distances in High-Dimensional Single-Cell Data Visualization},
year = {2026},
journal = {Big Data Mining and Analytics},
volume = {9},
number = {4},
pages = {978-994},
keywords = {dimension reduction, normalization, geodesic distance, manifold learning, bioinformatics},
url = {https://www.sciopen.com/article/10.26599/BDMA.2025.9020085},
doi = {10.26599/BDMA.2025.9020085},
abstract = {In the realm of high-dimensional single-cell sequencing data analysis, the accurate measurement of similarity between cells is pivotal. However, conventional metrics like Euclidean distance after L1-normalization may fail by losing distinguishable information when handling high-dimensional data, where the distance between different observations gradually converges to a shrinking interval. In this article, we use distance entropy to quantify the amount of information contained in the distances, and discuss the influence of normalization by different p-norms and the defect of Euclidean distance. We discover that observation differences are better preserved when normalizing data by a higher p-norm and using geodesic distance rather than Euclidean distance as the similarity measurement. We further identify that L2-normalization onto the hypersphere is often sufficient in preserving delicate differences even in relatively high dimensional data while maintaining computational efficiency. Subsequently, we present hypersphere t-distributed stochastic neighbor embedding (HS-SNE), a hypersphere-representation-system-based augmentation to t-distributed stochastic neighbor embedding (t-SNE), which effectively addresses the intricacy of high-dimensional data visualization and similarity measurement. Our results on multiple single-cell sequencing datasets show that this hypersphere representation system has improved resolution to identify more subtle differences between high-dimensional data points, while balancing distance entropy preservation and computational efficiency.}
}