Diffusion scattering transforms on graphs

Fernando Gama; Joan Bruna; Alejandro Ribeiro

Diffusion scattering transforms on graphs

Fernando Gama, Joan Bruna, Alejandro Ribeiro

Computer Science

Research output: Contribution to conference › Paper › peer-review

Abstract

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture “high-frequency” information, akin to the Euclidean Scattering.

Original language	English (US)
State	Published - Jan 1 2019
Event	7th International Conference on Learning Representations, ICLR 2019 - New Orleans, United States Duration: May 6 2019 → May 9 2019

Conference

Conference	7th International Conference on Learning Representations, ICLR 2019
Country/Territory	United States
City	New Orleans
Period	5/6/19 → 5/9/19

ASJC Scopus subject areas

Education
Computer Science Applications
Linguistics and Language
Language and Linguistics

Cite this

@conference{a692832696fe449995b41e32f5a228fe,

title = "Diffusion scattering transforms on graphs",

abstract = "Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture “high-frequency” information, akin to the Euclidean Scattering.",

author = "Fernando Gama and Joan Bruna and Alejandro Ribeiro",

note = "Publisher Copyright: {\textcopyright} 7th International Conference on Learning Representations, ICLR 2019. All Rights Reserved.; 7th International Conference on Learning Representations, ICLR 2019 ; Conference date: 06-05-2019 Through 09-05-2019",

year = "2019",

month = jan,

day = "1",

language = "English (US)",

}

TY - CONF

T1 - Diffusion scattering transforms on graphs

AU - Gama, Fernando

AU - Bruna, Joan

AU - Ribeiro, Alejandro

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture “high-frequency” information, akin to the Euclidean Scattering.

AB - Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture “high-frequency” information, akin to the Euclidean Scattering.

UR - http://www.scopus.com/inward/record.url?scp=85071192523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071192523&partnerID=8YFLogxK

M3 - Paper

T2 - 7th International Conference on Learning Representations, ICLR 2019

Y2 - 6 May 2019 through 9 May 2019

ER -

Diffusion scattering transforms on graphs

Abstract

Conference

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this