Artículo
Intrinsic persistent homology via density-based metric learning
Fecha de publicación:
12/2020
Editorial:
Cornell University
Revista:
ArXiv
ISSN:
2331-8422
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We address the problem of estimating intrinsic distances in a manifold from a finite sample. We prove that the metric space defined by the sample endowed with a computable metric known as sample Fermat distance converges a.s. in the sense of Gromov–Hausdorff. The limiting object is the manifold itself endowed with the population Fermat distance, an intrinsic metric that accounts for both the geometry of the manifold and the density that produces the sample. This result is applied to obtain intrinsic persistence diagrams, which are less sensitive to the particular embedding of the manifold in the Euclidean space. We show that this approach is robust to outliers and deduce a method for pattern recognition in signals, with applications in real data.
Palabras clave:
PERSISTENT HOMOLOGY
,
MANIFOLD LEARNING
,
DISTANCE LEARNING
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Borghini, Eugenio; Fernández, Ximena Laura; Groisman, Pablo Jose; Mindlin, Bernardo Gabriel; Intrinsic persistent homology via density-based metric learning; Cornell University; ArXiv; 12-2020; 1-30
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