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Found 10 papers, 3 papers with code
Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds
In particular, we introduce: (1) a mixup barcode, which captures geometric-topological interactions (mixup) between two point sets in arbitrary dimension; (2) simple summary statistics, total mixup and total percentage mixup, which quantify the complexity of the interactions as a single number; (3) a software tool for playing with the above.
Activation Landscapes as a Topological Summary of Neural Network Performance
We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN).
Topological data analysis of C. elegans locomotion and behavior
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology.
Time Series Analysis
Topological Data Analysis
Algebraic Topology
Quantitative Methods
55N31 (Primary), 62R40 (Secondary)
Persistent homology detects curvature
We describe a general computational framework for solving inverse problems using the average persistence landscape, a continuous mapping from metric spaces with a probability measure to a Hilbert space.
Embeddings of Persistence Diagrams into Hilbert Spaces
We show that persistence diagrams with the bottleneck distance do not even admit a coarse embedding into a Hilbert space.
Graded persistence diagrams and persistence landscapes
The sum of the graded persistence diagrams is the persistence diagram.
Algebraic Topology 55N31, 06A07
The persistence landscape and some of its properties
We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning.
Topological Data Analysis for Object Data
We also describe the first steps to a new approach to using topology for object data analysis, which applies topology to distributions on object spaces.
Methodology Algebraic Topology
A persistence landscapes toolbox for topological statistics
These are intended to facilitate the combination of statistics and machine learning with topological data analysis.
Computational Geometry Mathematical Software Algebraic Topology Computation
Statistical topological data analysis using persistence landscapes
We define a new topological summary for data that we call the persistence landscape.
Algebraic Topology Computational Geometry Metric Geometry Statistics Theory Statistics Theory 55N99, 68W30, 62G99, 54E35
