Grassmann Discriminant Analysis: a Unifying View on Subspace-Based Learning

Loading...
Thumbnail Image
Penn collection
Departmental Papers (ESE)
General Robotics, Automation, Sensing and Perception Laboratory
Degree type
Discipline
Subject
GRASP
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Hamm, Jihun
Contributor
Abstract

In this paper we propose a discriminant learning framework for problems in which data consist of linear subspaces instead of vectors. By treating subspaces as basic elements, we can make learning algorithms adapt naturally to the problems with linear invariant structures. We propose a unifying view on the subspace-based learning method by formulating the problems on the Grassmann manifold, which is the set of fixed-dimensional linear subspaces of a Euclidean space. Previous methods on the problem typically adopt an inconsistent strategy: feature extraction is performed in the Euclidean space while non-Euclidean distances are used. In our approach, we treat each subspace as a point in the Grassmann space, and perform feature extraction and classification in the same space. We show feasibility of the approach by using the Grassmann kernel functions such as the Projection kernel and the Binet-Cauchy kernel. Experiments with real image databases show that the proposed method performs well compared with state-of- the-art algorithms.

Advisor
Date of presentation
2008-07-06
Conference name
Departmental Papers (ESE)
Conference dates
2023-05-17T02:40:34.000
Conference location
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Reprinted from the Proceedings of the 25th International Conference on Machine Learning (ICML 2008), July 2008. URL: http://icml2008.cs.helsinki.fi/index.shtml
Recommended citation
Collection