2.6k citations · 4.2k across the 77 of their papers we have counts for
6 papers · 1 filter
PLPCA: Persistent Laplacian Enhanced-PCA for Microarray Data Analysis
Sean Cottrell, Rui Wang, Guowei Wei
Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to ide…
Persistent Path Laplacian
Rui Wang, Guo-Wei Wei
Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology w…
Persistent sheaf Laplacians
Xiaoqi Wei, Guo-Wei Wei
Recently various types of topological Laplacians have been studied from the perspective of data analysis. The spectral theory of these Laplacians has significantly extended the sco…
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…
HERMES: Persistent spectral graph software
Rui Wang, Rundong Zhao, Emily Ribando-Gros +3
Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work intr…
Evolutionary homology on coupled dynamical systems
Zixuan Cang, Elizabeth Munch, Guo-Wei Wei
Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavio…