A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate
dramatically different properties in a protein folding process. Even with the enormous …

In this paper, we systematically review weighted persistent homology (WPH) models and
their applications in biomolecular data analysis. Essentially, the weight value, which reflects …

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold
of low intrinsic dimension, is a staple of modern machine learning research. However, recent …

Animal aggregations are visually striking, and as such are popular examples of collective
behavior in the natural world. Quantitatively demonstrating the collective nature of such …

Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in
tissues, resulting in numerous biological discoveries. Various computational methods have …

We establish a new theory which unifies various aspects of topological approaches for data
science, by being applicable both to point cloud data and to graph data, including networks …

With the great advancement of experimental tools, a tremendous amount of biomolecular
data has been generated and accumulated in various databases. The high dimensionality …

While the spatial topological persistence is naturally constructed from a radius-based
filtration, it has hardly been derived from a temporal filtration. Most topological models are …

Fueled by increasing computing power and ever-growing datasets, novel methods for
complex systems analyses seem to emerge daily. With this whirlwind flows excitement and …