TY - GEN
T1 - Expanding the family of Grassmannian kernels
T2 - 13th European Conference on Computer Vision, ECCV 2014
AU - Harandi, Mehrtash T.
AU - Salzmann, Mathieu
AU - Jayasumana, Sadeep
AU - Hartley, Richard
AU - Li, Hongdong
PY - 2014
Y1 - 2014
N2 - Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g., support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.
AB - Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g., support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.
KW - Grassmann manifolds
KW - Plücker embedding
KW - kernel methods
UR - http://www.scopus.com/inward/record.url?scp=84906335991&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-10584-0_27
DO - 10.1007/978-3-319-10584-0_27
M3 - Conference contribution
SN - 9783319105833
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 408
EP - 423
BT - Computer Vision, ECCV 2014 - 13th European Conference, Proceedings
PB - Springer Verlag
Y2 - 6 September 2014 through 12 September 2014
ER -