Bregman divergences for infinite dimensional covariance matrices

Mehrtash Harandi; Mathieu Salzmann; Fatih Porikli

doi:10.1109/CVPR.2014.132

Bregman divergences for infinite dimensional covariance matrices

Mehrtash Harandi, Mathieu Salzmann, Fatih Porikli

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

79 Citations (Scopus)

Abstract

We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purpose. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.

Original language	English
Title of host publication	Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition
Editors	Ronen Basri, Cornelia Fermuller, Aleix Martinez, René Vidal
Place of Publication	Piscataway NJ USA
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	1003-1010
Number of pages	8
ISBN (Electronic)	9781479951178
DOIs	https://doi.org/10.1109/CVPR.2014.132
Publication status	Published - 2014
Externally published	Yes
Event	IEEE Conference on Computer Vision and Pattern Recognition 2014 - Columbus, United States of America Duration: 23 Jun 2014 → 28 Jun 2014 http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6909096 (IEEE Conference Proceedings)

Publication series

Name	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)	1063-6919

Conference

Conference	IEEE Conference on Computer Vision and Pattern Recognition 2014
Abbreviated title	CVPR 2014
Country/Territory	United States of America
City	Columbus
Period	23/06/14 → 28/06/14
Internet address	http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6909096 (IEEE Conference Proceedings)

Keywords

Action Recognition from Motion Capture Data
Bregman divergences
Covariance Descriptor
Material Categorization
Reproducing Kernel Hilbert Spaces
Riemannian geometry
Texture classification
Virus Classification

Access to Document

10.1109/CVPR.2014.132

Cite this

Harandi, M., Salzmann, M., & Porikli, F. (2014). Bregman divergences for infinite dimensional covariance matrices. In R. Basri, C. Fermuller, A. Martinez, & R. Vidal (Eds.), Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition (pp. 1003-1010). (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CVPR.2014.132

Harandi, Mehrtash ; Salzmann, Mathieu ; Porikli, Fatih. / Bregman divergences for infinite dimensional covariance matrices. Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition. editor / Ronen Basri ; Cornelia Fermuller ; Aleix Martinez ; René Vidal. Piscataway NJ USA : IEEE, Institute of Electrical and Electronics Engineers, 2014. pp. 1003-1010 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).

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title = "Bregman divergences for infinite dimensional covariance matrices",

abstract = "We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purpose. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.",

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author = "Mehrtash Harandi and Mathieu Salzmann and Fatih Porikli",

year = "2014",

doi = "10.1109/CVPR.2014.132",

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series = "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition",

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booktitle = "Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition",

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Harandi, M, Salzmann, M & Porikli, F 2014, Bregman divergences for infinite dimensional covariance matrices. in R Basri, C Fermuller, A Martinez & R Vidal (eds), Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, Institute of Electrical and Electronics Engineers, Piscataway NJ USA, pp. 1003-1010, IEEE Conference on Computer Vision and Pattern Recognition 2014, Columbus, Ohio, United States of America, 23/06/14. https://doi.org/10.1109/CVPR.2014.132

Bregman divergences for infinite dimensional covariance matrices. / Harandi, Mehrtash; Salzmann, Mathieu; Porikli, Fatih.

Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition. ed. / Ronen Basri; Cornelia Fermuller; Aleix Martinez; René Vidal. Piscataway NJ USA : IEEE, Institute of Electrical and Electronics Engineers, 2014. p. 1003-1010 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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AB - We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purpose. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.

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Harandi M, Salzmann M, Porikli F. Bregman divergences for infinite dimensional covariance matrices. In Basri R, Fermuller C, Martinez A, Vidal R, editors, Proceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition. Piscataway NJ USA: IEEE, Institute of Electrical and Electronics Engineers. 2014. p. 1003-1010. (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2014.132

Bregman divergences for infinite dimensional covariance matrices

Abstract

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Keywords

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