Learning over Sets Using Kernel Principal Angles (Kernel Machines Section)
Abstract
We consider the problem of learning with instances defined over a space of sets of vectors. We derive a new positive definite kernel f(A,B) defined over pairs of matrices A,B based on the concept of principal angles between two linear subspaces. We show that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors of A,B to be mapped onto arbitrarily high-dimensional feature spaces.
Cite
Text
Wolf and Shashua. "Learning over Sets Using Kernel Principal Angles (Kernel Machines Section)." Journal of Machine Learning Research, 2003.Markdown
[Wolf and Shashua. "Learning over Sets Using Kernel Principal Angles (Kernel Machines Section)." Journal of Machine Learning Research, 2003.](https://mlanthology.org/jmlr/2003/wolf2003jmlr-learning/)BibTeX
@article{wolf2003jmlr-learning,
title = {{Learning over Sets Using Kernel Principal Angles (Kernel Machines Section)}},
author = {Wolf, Lior and Shashua, Amnon},
journal = {Journal of Machine Learning Research},
year = {2003},
pages = {913-931},
volume = {4},
url = {https://mlanthology.org/jmlr/2003/wolf2003jmlr-learning/}
}