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Found 9 papers, 5 papers with code
A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science
One of the core strengths of persistent homology is how interpretable it can be, so throughout this paper we discuss not just the patterns we find, but why those results are to be expected given what we know about the theory of persistent homology.
Geometric Approaches on Persistent Homology
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology.
Algebraic Topology Computational Geometry Geometric Topology 55N31, 55U10, 57R19, 62R40
Topology Applied to Machine Learning: From Global to Local
Additionally, we survey work connecting persistent homology to geometric features of spaces, including curvature and fractal dimension, and various methods that have been used to incorporate persistent homology into machine learning.
Lions and contamination, triangular grids, and Cheeger constants
Suppose each vertex of a graph is originally occupied by contamination, except for those vertices occupied by lions.
Combinatorics Data Structures and Algorithms
Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes
Encoding the complex features of an energy landscape is a challenging task, and often chemists pursue the most salient features (minima and barriers) along a highly reduced space, i. e. 2- or 3-dimensions.
Chemical Physics Mathematical Physics Algebraic Topology Mathematical Physics
Support vector machines and Radon's theorem
A support vector machine (SVM) is an algorithm that finds a hyperplane which optimally separates labeled data points in $\mathbb{R}^n$ into positive and negative classes.
Capturing Dynamics of Time-Varying Data via Topology
One approach to understanding complex data is to study its shape through the lens of algebraic topology.
Persistence Images: A Stable Vector Representation of Persistent Homology
We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs.
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