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07/21/2022
A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science
Topological data analysis (TDA) is a tool from data science and mathemat...
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03/11/2021
Geometric Approaches on Persistent Homology
We introduce several geometric notions, including thick-thin decompositi...
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03/10/2021
Topology Applied to Machine Learning: From Global to Local
Through the use of examples, we explain one way in which applied topolog...
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12/12/2020
Lions and contamination, triangular grids, and Cheeger constants
Suppose each vertex of a graph is originally occupied by contamination, ...
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11/01/2020
Support Vector Machines and Radon's Theorem
A support vector machine (SVM) is an algorithm which finds a hyperplane ...
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10/07/2020
Capturing Dynamics of Time-Varying Data via Topology
One approach to understanding complex data is to study its shape through...
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02/05/2020
An Iterative Method for Structured Matrix Completion
The task of filling-in or predicting missing entries of a matrix, from a...
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06/29/2019
Multidimensional Scaling on Metric Measure Spaces
Multidimensional scaling (MDS) is a popular technique for mapping a fini...
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12/08/2018
On Vietoris-Rips complexes of planar curves
A Vietoris--Rips complex is a way to thicken a (possibly discrete) metri...
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12/18/2017