Results 241 to 250 of about 1,143,028 (268)

Universality in random persistent homology and scale-invariant functionals

Communications of the American Mathematical Society
In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we consider the distribution of the ratio of persistence values (death/birth)
O. Bobrowski, P. Skraba
semanticscholar   +1 more source

The Persistence Space in Multidimensional Persistent Homology

2013
Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties ...
Andrea Cerri, LANDI, Claudia
openaire   +2 more sources

Persistence Cycles for Visual Exploration of Persistent Homology

IEEE Transactions on Visualization and Computer Graphics, 2022
Persistent homology is a fundamental tool in topological data analysis used for the most diverse applications. Information captured by persistent homology is commonly visualized using scatter plots representations. Despite being widely adopted, such a visualization technique limits user understanding and is prone to misinterpretation.
openaire   +2 more sources

Persistent homology in tourism

Tourism Management, 2020
Marketing a destination is costly so efficiency of promotion expenditure is critical; identifying improved techniques to achieve this will be of great value. Clustering techniques have sought to identify target markets but are widely criticised for the biases they induce.
Chong, Woonkian, Rudkin, Simon
openaire   +1 more source

Persistent-homology-based machine learning: a survey and a comparative study

Artificial Intelligence Review, 2022
Chi Seng Pun, S. Lee, Kelin Xia
semanticscholar   +1 more source

Computational Tools in Weighted Persistent Homology

Chinese Annals of Mathematics Series B, 2021
Chengyuan Wu, Jie Wu
exaly  

Learning discriminative topological structure information representation for 2D shape and social network classification via persistent homology

Knowledge-Based Systems
Changshuo Wang, R. Cao, Ruiping Wang
semanticscholar   +1 more source

Persistent Homology in Medical Image Processing: A Literature Review

medRxiv
D. Brito-Pacheco, P. Giannopoulos, Constantino Carlos   +2 more
semanticscholar   +1 more source

Persistent Homology of Geospatial Data: A Case Study with Voting

SIAM Review, 2021
Michelle Feng, Mason A Porter
exaly  

Homotopy, homology, and persistent homology using closure spaces

Journal of Applied and Computational Topology
Peter Bubenik, Nikola Milićević
semanticscholar   +1 more source