Sparse Circular Coordinates via Principal $$\mathbb {Z}$$-Bundles

DOI10.1007/978-3-030-43408-3_17zbMath1450.62140arXiv1809.09269OpenAlexW2893905706MaRDI QIDQ5118379

Jose A. Perea

Publication date: 8 September 2020

Published in: Topological Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09269

zbMATH Keywords

data analysisimage analysisprincipal bundlesnonlinear dimensionality reduction

Mathematics Subject Classification ID

Image analysis in multivariate analysis (62H35) Persistent homology and applications, topological data analysis (55N31) Topological data analysis (62R40)

Related Items (2)

Persistent extensions and analogous bars: data-induced relations between persistence barcodes ⋮ Twisty Takens: a geometric characterization of good observations on dense trajectories

Uses Software

• GitHub
• Ripser
• COIL-20

Cites Work

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• Persistent cohomology and circular coordinates
• Construction of universal bundles. II
• On the local behavior of spaces of natural images
• The nonlinear statistics of high-contrast patches in natural images
• Multiscale projective coordinates via persistent cohomology of sparse filtrations
• Principal component analysis.
• Generalized inverses. Theory and applications.
• Twisty Takens: a geometric characterization of good observations on dense trajectories
• Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
• Decoding of Neural Data Using Cohomological Feature Extraction
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation

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