TY - GEN
T1 - Geometry-adapted Gaussian random field regression
AU - Zhang, Zhen
AU - Wang, Mianzhi
AU - Xiang, Yijian
AU - Nehorai, Arye
N1 - Funding Information:
This work was supported by the AFOSR Grant FA9550-16-1-0386 and the ONR Grant N000141310050.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - In this paper, we provide a novel regression algorithm based on a Gaussian random field (GRF) indexed by a Riemannian manifold (M, g). We utilize both the labeled and unlabeled data sets to exploit the geometric structure of M. We use the recovered heat (H) kernel as the covariance function for the GRF (HGRF). We propose a Monte Carlo integral theorem on Riemannian manifolds and derive the corresponding convergence rate and approximation error. Based on this theorem, we correctly normalize the recovered eigenvector to make it compatible with Riemannian measure. More importantly, we prove that the HGRF is intrinsic to the original data manifold by comparing the pullback geometry and the original geoemtry of M. Essentially it is a semi-supervised learning method, which means the unlabeled data can be utilized to help identify the geometry structure of the unknown manifold M.
AB - In this paper, we provide a novel regression algorithm based on a Gaussian random field (GRF) indexed by a Riemannian manifold (M, g). We utilize both the labeled and unlabeled data sets to exploit the geometric structure of M. We use the recovered heat (H) kernel as the covariance function for the GRF (HGRF). We propose a Monte Carlo integral theorem on Riemannian manifolds and derive the corresponding convergence rate and approximation error. Based on this theorem, we correctly normalize the recovered eigenvector to make it compatible with Riemannian measure. More importantly, we prove that the HGRF is intrinsic to the original data manifold by comparing the pullback geometry and the original geoemtry of M. Essentially it is a semi-supervised learning method, which means the unlabeled data can be utilized to help identify the geometry structure of the unknown manifold M.
KW - Gaussian random field
KW - heat kernel
KW - manifold learning
KW - regression
KW - semi-supervised learning
UR - https://www.scopus.com/pages/publications/85023762920
U2 - 10.1109/ICASSP.2017.7953414
DO - 10.1109/ICASSP.2017.7953414
M3 - Conference contribution
AN - SCOPUS:85023762920
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 6528
EP - 6532
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -