259 citations · 631 across the 36 of their papers we have counts for
5 papers · 1 filter
A Unified Topological Approach to Data Science
Jelena Grbić, Jie Wu, Kelin Xia +1
We establish a new theory which gives a unified topological approach to data science, by being applicable both to point cloud data and to graph data, including networks beyond pair…
Discrete Morse Theory for Weighted Simplicial Complexes
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key diffe…
Persistent-Homology-based Machine Learning and its Applications -- A Survey
Chi Seng Pun, Kelin Xia, Si Xian Lee
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…
Weighted Fundamental Group
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to th…
Weighted (Co)homology and Weighted Laplacian
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the -weighted coboundary operator induced by a weight function . Our weight f…