A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis

Monami Banerjee, Rudrasis Chakraborty, Edward Ofori, Michael S. Okun, David E. Vaillancourt, Baba C. Vemuri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Citations (Scopus)

Abstract

Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, generalizations to manifold-valued data are only recently gaining popularity. With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces. In this paper, we present a novel nonlinear kernel-based regression method that is applicable to manifold valued data. Our method is applicable to cases when the independent and dependent variables in the regression model are both manifold-valued or one is manifold-valued and the other is vector or scalar valued. Further, unlike most methods, our method does not require any imposed ordering on the manifold-valued data. The performance of our model is tested on a large number of real data sets acquired from Alzhiemers and movement disorder (Parkinsons and Essential Tremor) patients. We present an extensive set of results along with statistical validation and comparisons.

Original languageEnglish (US)
Title of host publicationProceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
PublisherIEEE Computer Society
Pages4424-4432
Number of pages9
ISBN (Electronic)9781467388504
DOIs
StatePublished - Dec 9 2016
Externally publishedYes
Event29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 - Las Vegas, United States
Duration: Jun 26 2016Jul 1 2016

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume2016-December
ISSN (Print)1063-6919

Conference

Conference29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
CountryUnited States
CityLas Vegas
Period6/26/167/1/16

Fingerprint

Vector spaces
Image analysis
Medical imaging
Linear regression
Computer vision
Learning systems
Statistical methods

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Banerjee, M., Chakraborty, R., Ofori, E., Okun, M. S., Vaillancourt, D. E., & Vemuri, B. C. (2016). A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis. In Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 (pp. 4424-4432). [7780848] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 2016-December). IEEE Computer Society. https://doi.org/10.1109/CVPR.2016.479

A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis. / Banerjee, Monami; Chakraborty, Rudrasis; Ofori, Edward; Okun, Michael S.; Vaillancourt, David E.; Vemuri, Baba C.

Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016. IEEE Computer Society, 2016. p. 4424-4432 7780848 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 2016-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Banerjee, M, Chakraborty, R, Ofori, E, Okun, MS, Vaillancourt, DE & Vemuri, BC 2016, A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis. in Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016., 7780848, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2016-December, IEEE Computer Society, pp. 4424-4432, 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, United States, 6/26/16. https://doi.org/10.1109/CVPR.2016.479
Banerjee M, Chakraborty R, Ofori E, Okun MS, Vaillancourt DE, Vemuri BC. A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis. In Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016. IEEE Computer Society. 2016. p. 4424-4432. 7780848. (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2016.479
Banerjee, Monami ; Chakraborty, Rudrasis ; Ofori, Edward ; Okun, Michael S. ; Vaillancourt, David E. ; Vemuri, Baba C. / A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis. Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016. IEEE Computer Society, 2016. pp. 4424-4432 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).
@inproceedings{383bf254b9e44d3c992908ea4eb86303,
title = "A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis",
abstract = "Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, generalizations to manifold-valued data are only recently gaining popularity. With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces. In this paper, we present a novel nonlinear kernel-based regression method that is applicable to manifold valued data. Our method is applicable to cases when the independent and dependent variables in the regression model are both manifold-valued or one is manifold-valued and the other is vector or scalar valued. Further, unlike most methods, our method does not require any imposed ordering on the manifold-valued data. The performance of our model is tested on a large number of real data sets acquired from Alzhiemers and movement disorder (Parkinsons and Essential Tremor) patients. We present an extensive set of results along with statistical validation and comparisons.",
author = "Monami Banerjee and Rudrasis Chakraborty and Edward Ofori and Okun, {Michael S.} and Vaillancourt, {David E.} and Vemuri, {Baba C.}",
year = "2016",
month = "12",
day = "9",
doi = "10.1109/CVPR.2016.479",
language = "English (US)",
series = "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition",
publisher = "IEEE Computer Society",
pages = "4424--4432",
booktitle = "Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016",

}

TY - GEN

T1 - A Nonlinear Regression Technique for Manifold Valued Data with Applications to Medical Image Analysis

AU - Banerjee, Monami

AU - Chakraborty, Rudrasis

AU - Ofori, Edward

AU - Okun, Michael S.

AU - Vaillancourt, David E.

AU - Vemuri, Baba C.

PY - 2016/12/9

Y1 - 2016/12/9

N2 - Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, generalizations to manifold-valued data are only recently gaining popularity. With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces. In this paper, we present a novel nonlinear kernel-based regression method that is applicable to manifold valued data. Our method is applicable to cases when the independent and dependent variables in the regression model are both manifold-valued or one is manifold-valued and the other is vector or scalar valued. Further, unlike most methods, our method does not require any imposed ordering on the manifold-valued data. The performance of our model is tested on a large number of real data sets acquired from Alzhiemers and movement disorder (Parkinsons and Essential Tremor) patients. We present an extensive set of results along with statistical validation and comparisons.

AB - Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, generalizations to manifold-valued data are only recently gaining popularity. With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces. In this paper, we present a novel nonlinear kernel-based regression method that is applicable to manifold valued data. Our method is applicable to cases when the independent and dependent variables in the regression model are both manifold-valued or one is manifold-valued and the other is vector or scalar valued. Further, unlike most methods, our method does not require any imposed ordering on the manifold-valued data. The performance of our model is tested on a large number of real data sets acquired from Alzhiemers and movement disorder (Parkinsons and Essential Tremor) patients. We present an extensive set of results along with statistical validation and comparisons.

UR - http://www.scopus.com/inward/record.url?scp=84986269148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986269148&partnerID=8YFLogxK

U2 - 10.1109/CVPR.2016.479

DO - 10.1109/CVPR.2016.479

M3 - Conference contribution

AN - SCOPUS:84986269148

T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

SP - 4424

EP - 4432

BT - Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016

PB - IEEE Computer Society

ER -