We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data. We show that, under mild regularity conditions, the ridges of the kernel density estimator consistently estimate the ridges of the true density. When the data are noisy measurements of a manifold, we show that the ridges are close and topologically similar to the hidden manifold. To find the estimated ridges in practice, we adapt the modified mean-shift algorithm proposed by Ozertem and Erdogmus [J. Mach. Learn. Res. 12 (2011) 1249–1286]. Some numerical experiments verify that the algorithm is accurate.

Nonparametric Ridge Estimation / Genovese Christopher, R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry. - In: ANNALS OF STATISTICS. - ISSN 0090-5364. - 42:4(2014), pp. 1511-1545. [10.1214/14-AOS1218]

Nonparametric Ridge Estimation

Perone-Pacifico Marco;
2014

Abstract

We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data. We show that, under mild regularity conditions, the ridges of the kernel density estimator consistently estimate the ridges of the true density. When the data are noisy measurements of a manifold, we show that the ridges are close and topologically similar to the hidden manifold. To find the estimated ridges in practice, we adapt the modified mean-shift algorithm proposed by Ozertem and Erdogmus [J. Mach. Learn. Res. 12 (2011) 1249–1286]. Some numerical experiments verify that the algorithm is accurate.
Ridges; density estimation; manifold learning
File in questo prodotto:
File Dimensione Formato  
Nonparametric Ridge Estimation.pdf

Open Access

Tipologia: Versione dell'editore
Licenza: DRM non definito
Dimensione 3.84 MB
Formato Adobe PDF
3.84 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/182612
Citazioni
  • Scopus 53
  • ???jsp.display-item.citation.isi??? 54
social impact