Persistence diagrams with linear machine learning models

DOI10.1007/s41468-018-0013-5zbMath1405.62250arXiv1706.10082OpenAlexW2963377171MaRDI QIDQ1616398

Masao Kimura, Yasuaki Hiraoka, Ippei Obayashi

Publication date: 6 November 2018

Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.10082

zbMATH Keywords

linear modelsmachine learningtopological data analysispersistent homologypersistence image

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Image analysis in multivariate analysis (62H35) Learning and adaptive systems in artificial intelligence (68T05) Applications of statistics to physics (62P35) Homology of a product, Künneth formula (55U25)

Related Items

Aspects of topological approaches for data science, Volume-Optimal Cycle: Tightest Representative Cycle of a Generator in Persistent Homology, Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning, Functional summaries of persistence diagrams, A density-based approach to feature detection in persistence diagrams for firn data, Using persistent homology topological features to characterize medical images: case studies on lung and brain cancers, Geometric Metrics for Topological Representations, Persistent homology analysis with nonnegative matrix factorization for 3D voxel data of iron ore sinters

Uses Software

• CGAL
• SciPy
• Scikit
• PHAT
• 3D Alpha Shapes
• PRMLT
• PersistenceImages

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Confidence sets for persistence diagrams
• \textsc{Phat} -- persistent homology algorithms toolbox
• Fréchet means for distributions of persistence diagrams
• Stability of persistence diagrams
• Computational homology
• 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
• Coverage in sensor networks via persistent homology
• Optimal rates of convergence for persistence diagrams in Topological Data Analysis
• Optimal homologous cycles, total unimodularity, and linear programming
• Clear and Compress: Computing Persistent Homology in Chunks
• Regression
• Topology and data
• Kernel method for persistence diagrams via kernel embedding and weight factor
• Topology of viral evolution
• Persistence Images: A Stable Vector Representation of Persistent Homology
• Statistical topological data analysis using persistence landscapes