4 papers · 1 filter
Local Laplacian: theory and models for data analysis
Jian Liu, Hongsong Feng, Kefeng Liu
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are f…
Parametrization of Symmetry in Data
Jian Liu, Dong Chen, Guo-Wei Wei
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries a…
Topological Sequence Analysis of Genomes: Delta Complex approaches
Jian Liu, Li Shen, Dong Chen +1
Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains…
Persistent interaction topology in data analysis
Jian Liu, Dong Chen, Guo-Wei Wei
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key…