Multimodal manifold analysis using simultaneous diagonalization of Laplacians

Davide Eynard; Artiom Kovnatsky; Michael M. Bronstein; Klaus Glashoff; Alexander M. Bronstein

doi:10.1109/TPAMI.2015.2408348

Multimodal manifold analysis using simultaneous diagonalization of Laplacians

Davide Eynard, Artiom Kovnatsky, Michael M. Bronstein, Klaus Glashoff, Alexander M. Bronstein

Research output: Contribution to journal › Article › peer-review

Abstract

We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.

Original language	English
Article number	7053905
Pages (from-to)	2505-2517
Number of pages	13
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	37
Issue number	12
DOIs	https://doi.org/10.1109/TPAMI.2015.2408348
State	Published - 1 Dec 2015
Externally published	Yes

Keywords

Joint diagonalization
Laplace-Beltrami operator
diffusion distances
dimensionality reduction
manifold alignment
manifold learning
multimodal clustering
multimodal data

All Science Journal Classification (ASJC) codes

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/TPAMI.2015.2408348

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title = "Multimodal manifold analysis using simultaneous diagonalization of Laplacians",

abstract = "We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.",

keywords = "Joint diagonalization, Laplace-Beltrami operator, diffusion distances, dimensionality reduction, manifold alignment, manifold learning, multimodal clustering, multimodal data",

author = "Davide Eynard and Artiom Kovnatsky and Bronstein, {Michael M.} and Klaus Glashoff and Bronstein, {Alexander M.}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.",

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doi = "10.1109/TPAMI.2015.2408348",

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AU - Eynard, Davide

AU - Kovnatsky, Artiom

AU - Bronstein, Michael M.

AU - Glashoff, Klaus

AU - Bronstein, Alexander M.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.

AB - We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.

KW - Joint diagonalization

KW - Laplace-Beltrami operator

KW - diffusion distances

KW - dimensionality reduction

KW - manifold alignment

KW - manifold learning

KW - multimodal clustering

KW - multimodal data

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DO - 10.1109/TPAMI.2015.2408348

M3 - مقالة

SN - 0162-8828

VL - 37

SP - 2505

EP - 2517

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 12

M1 - 7053905

ER -

Multimodal manifold analysis using simultaneous diagonalization of Laplacians

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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