Generalized penalty for circular coordinate representation

DOI10.3934/fods.2021024zbMath1493.62649arXiv2006.02554OpenAlexW3203777403MaRDI QIDQ2072668

Jisu Kim, Alice Patania, Mikael Vejdemo-Johansson, Hengrui Luo

Publication date: 26 January 2022

Published in: Foundations of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.02554

zbMATH Keywords

high-dimensional datatopological data analysispersistent cohomologynonlinear dimension reduction

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Computational aspects of data analysis and big data (68T09) Topological data analysis (62R40)

Related Items (1)

Asymptotics of lower dimensional zero-density regions

Uses Software

• javaPlex
• Adam
• t-SNE
• GitHub
• Ripser
• UMAP

Cites Work

• Confidence sets for persistence diagrams
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• Persistent cohomology and circular coordinates
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• The main contributions of robust statistics to statistical science and a new challenge
• Matrix multiplication via arithmetic progressions
• Finding the homology of submanifolds with high confidence from random samples
• javaPlex: A Research Software Package for Persistent (Co)Homology
• Sparse and Redundant Representations
• Topology and data
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Relative clustering validity criteria: A comparative overview
• Zigzag persistent homology in matrix multiplication time
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• CONTINUOUS INSPECTION SCHEMES
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