High-order Tensor Regularization with Application to Attribute Ranking

Kwang In Kim, Juhyun Park, James Tompkin

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

Abstract

When learning functions on manifolds, we can improve performance by regularizing with respect to the intrinsic manifold geometry rather than the ambient space. However, when regularizing tensor learning, calculating the derivatives along this intrinsic geometry is not possible, and so existing approaches are limited to regularizing in Euclidean space. Our new method for intrinsically regularizing and learning tensors on Riemannian manifolds introduces a surrogate object to encapsulate the geometric characteristic of the tensor. Regularizing this instead allows us to learn non-symmetric and high-order tensors. We apply our approach to the relative attributes problem, and we demonstrate that explicitly regularizing high-order relationships between pairs of data points improves performance.
LanguageEnglish
Title of host publicationProc. CVPR
StatusAccepted/In press - 19 Feb 2018
EventIEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2018 -
Duration: 18 Jun 201822 Jun 2018

Conference

ConferenceIEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2018
Period18/06/1822/06/18

Fingerprint

Tensors
Geometry
Derivatives

Cite this

High-order Tensor Regularization with Application to Attribute Ranking. / Kim, Kwang In; Park, Juhyun; Tompkin, James.

Proc. CVPR. 2018.

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

Kim, KI, Park, J & Tompkin, J 2018, High-order Tensor Regularization with Application to Attribute Ranking. in Proc. CVPR. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2018, 18/06/18.
@inproceedings{ebfc14c36c084a2ba46f3e92e20be46e,
title = "High-order Tensor Regularization with Application to Attribute Ranking",
abstract = "When learning functions on manifolds, we can improve performance by regularizing with respect to the intrinsic manifold geometry rather than the ambient space. However, when regularizing tensor learning, calculating the derivatives along this intrinsic geometry is not possible, and so existing approaches are limited to regularizing in Euclidean space. Our new method for intrinsically regularizing and learning tensors on Riemannian manifolds introduces a surrogate object to encapsulate the geometric characteristic of the tensor. Regularizing this instead allows us to learn non-symmetric and high-order tensors. We apply our approach to the relative attributes problem, and we demonstrate that explicitly regularizing high-order relationships between pairs of data points improves performance.",
author = "Kim, {Kwang In} and Juhyun Park and James Tompkin",
year = "2018",
month = "2",
day = "19",
language = "English",
booktitle = "Proc. CVPR",

}

TY - GEN

T1 - High-order Tensor Regularization with Application to Attribute Ranking

AU - Kim,Kwang In

AU - Park,Juhyun

AU - Tompkin,James

PY - 2018/2/19

Y1 - 2018/2/19

N2 - When learning functions on manifolds, we can improve performance by regularizing with respect to the intrinsic manifold geometry rather than the ambient space. However, when regularizing tensor learning, calculating the derivatives along this intrinsic geometry is not possible, and so existing approaches are limited to regularizing in Euclidean space. Our new method for intrinsically regularizing and learning tensors on Riemannian manifolds introduces a surrogate object to encapsulate the geometric characteristic of the tensor. Regularizing this instead allows us to learn non-symmetric and high-order tensors. We apply our approach to the relative attributes problem, and we demonstrate that explicitly regularizing high-order relationships between pairs of data points improves performance.

AB - When learning functions on manifolds, we can improve performance by regularizing with respect to the intrinsic manifold geometry rather than the ambient space. However, when regularizing tensor learning, calculating the derivatives along this intrinsic geometry is not possible, and so existing approaches are limited to regularizing in Euclidean space. Our new method for intrinsically regularizing and learning tensors on Riemannian manifolds introduces a surrogate object to encapsulate the geometric characteristic of the tensor. Regularizing this instead allows us to learn non-symmetric and high-order tensors. We apply our approach to the relative attributes problem, and we demonstrate that explicitly regularizing high-order relationships between pairs of data points improves performance.

M3 - Conference contribution

BT - Proc. CVPR

ER -