Kernel method for persistence diagrams via kernel embedding and weight factor
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Publication:4558518
zbMath1472.62179arXiv1706.03472MaRDI QIDQ4558518
Kenji Fukumizu, Genki Kusano, Yasuaki Hiraoka
Publication date: 22 November 2018
Full work available at URL: https://arxiv.org/abs/1706.03472
kernel methodtopological data analysiskernel embeddingpersistence diagramspersistence weighted Gaussian kernel
Applications of statistics in engineering and industry; control charts (62P30) Topological data analysis (62R40)
Related Items (15)
Persistence diagrams with linear machine learning models ⋮ Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams ⋮ A framework for differential calculus on persistence barcodes ⋮ Interactions Between Kernels, Frames, and Persistent Homology ⋮ Approximating continuous functions on persistence diagrams using template functions ⋮ Stable volumes for persistent homology ⋮ The Persistence Landscape and Some of Its Properties ⋮ Same But Different: Distance Correlations Between Topological Summaries ⋮ Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis ⋮ Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 ⋮ Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport ⋮ On the expectation of a persistence diagram by the persistence weighted kernel ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the choice of weight functions for linear representations of persistence diagrams
Uses Software
Cites Work
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- Confidence sets for persistence diagrams
- A topological approach for protein classification
- Persistence stability for geometric complexes
- A persistence landscapes toolbox for topological statistics
- Stability of persistence diagrams
- On the local behavior of spaces of natural images
- Lipschitz functions have \(L_{p}\)-stable persistence
- Computing persistent homology
- Topological persistence and simplification
- Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
- Categorification of persistent homology
- A topological measurement of protein compressibility
- Coverage in sensor networks via persistent homology
- Optimal rates of convergence for persistence diagrams in Topological Data Analysis
- Learning Theory for Distribution Regression
- PHAT – Persistent Homology Algorithms Toolbox
- A Hilbert Space Embedding for Distributions
- Topology and data
- Kernel Mean Embedding of Distributions: A Review and Beyond
- Persistence Images: A Stable Vector Representation of Persistent Homology
- Universality, Characteristic Kernels and RKHS Embedding of Measures
- Statistical topological data analysis using persistence landscapes
- Triangle distribution and equation of state for classical rigid disks
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