Expanding the Family of Grassmannian Kernels: An Embedding Perspective

07/04/2014
by   Mehrtash T. Harandi, et al.
0

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.

READ FULL TEXT

page 11

page 12

page 14

research
11/30/2014

Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels

In this paper, we develop an approach to exploiting kernel methods with ...
research
02/10/2018

Disturbance Grassmann Kernels for Subspace-Based Learning

In this paper, we focus on subspace-based learning problems, where data ...
research
01/19/2023

Strictly positive definite kernels on compact Riemannian manifolds

The paper studies strictly positive definite kernels on compact Riemanni...
research
12/13/2014

Optimizing Over Radial Kernels on Compact Manifolds

We tackle the problem of optimizing over all possible positive definite ...
research
01/31/2014

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in v...
research
09/16/2019

More About Covariance Descriptors for Image Set Coding: Log-Euclidean Framework based Kernel Matrix Representation

We consider a family of structural descriptors for visual data, namely c...
research
09/27/2021

Learning from Small Samples: Transformation-Invariant SVMs with Composition and Locality at Multiple Scales

Motivated by the problem of learning when the number of training samples...

Please sign up or login with your details

Forgot password? Click here to reset