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.
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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
T2 - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
Y2 - 26 June 2016 through 1 July 2016
ER -