English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work we study statistical properties of graph-based algorithms formulti-manifold clustering (MMC). In MMC the goal is to retrieve themulti-manifold structure underlying a given Euclidean data set when this one isassumed to be obtained by sampling a distribution on a union of manifolds$\mathcal{M} = \mathcal{M}_1 \cup\dots \cup \mathcal{M}_N$ that may intersectwith each other and that may have different dimensions. We investigatesufficient conditions that similarity graphs on data sets must satisfy in orderfor their corresponding graph Laplacians to capture the right geometricinformation to solve the MMC problem. Precisely, we provide high probabilityerror bounds for the spectral approximation of a tensorized Laplacian on$\mathcal{M}$ with a suitable graph Laplacian built from the observations; therecovered tensorized Laplacian contains all geometric information of all theindividual underlying manifolds. We provide an example of a family ofsimilarity graphs, which we call annular proximity graphs with angleconstraints, satisfying these sufficient conditions. We contrast our family ofgraphs with other constructions in the literature based on the alignment oftangent planes. Extensive numerical experiments expand the insights that ourtheory provides on the MMC problem.

Large sample spectral analysis of graph-based multi-manifold clustering