Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds

Gloria Haro; Gregory Randall; Guillermo Sapiro

Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds

Gloria Haro, Gregory Randall, Guillermo Sapiro

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
Pages	553-560
Number of pages	8
State	Published - 2007
Externally published	Yes
Event	20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada Duration: Dec 4 2006 → Dec 7 2006

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Other

Other	20th Annual Conference on Neural Information Processing Systems, NIPS 2006
Country/Territory	Canada
City	Vancouver, BC
Period	12/4/06 → 12/7/06

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

@inproceedings{0c4ff49fa8bb475caf905bdc74345238,

title = "Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds",

abstract = "The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.",

author = "Gloria Haro and Gregory Randall and Guillermo Sapiro",

year = "2007",

language = "English (US)",

isbn = "9780262195683",

series = "Advances in Neural Information Processing Systems",

pages = "553--560",

booktitle = "Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference",

note = "20th Annual Conference on Neural Information Processing Systems, NIPS 2006 ; Conference date: 04-12-2006 Through 07-12-2006",

}

Haro, G, Randall, G & Sapiro, G 2007, Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds. in Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference. Advances in Neural Information Processing Systems, pp. 553-560, 20th Annual Conference on Neural Information Processing Systems, NIPS 2006, Vancouver, BC, Canada, 12/4/06.

Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds. / Haro, Gloria; Randall, Gregory; Sapiro, Guillermo.
Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference. 2007. p. 553-560 (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Stratification learning

T2 - 20th Annual Conference on Neural Information Processing Systems, NIPS 2006

AU - Haro, Gloria

AU - Randall, Gregory

AU - Sapiro, Guillermo

PY - 2007

Y1 - 2007

N2 - The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

AB - The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

UR - http://www.scopus.com/inward/record.url?scp=79951924106&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951924106&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79951924106

SN - 9780262195683

T3 - Advances in Neural Information Processing Systems

SP - 553

EP - 560

BT - Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference

Y2 - 4 December 2006 through 7 December 2006

ER -

Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Other files and links

Fingerprint

Cite this