Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold
Learning robust subspaces to maximize class discrimination is challenging, and most current works consider a weak connection between dimensionality reduction and classifier design. We propose an alternate framework wherein these two steps are combined in a joint formulation to exploit the direct con...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Conference Paper |
| Published: |
Springer
2011
|
| Online Access: | http://hdl.handle.net/20.500.11937/42511 |
| _version_ | 1848756439535845376 |
|---|---|
| author | Pham, DucSon Venkatesh, Svetha |
| author2 | D Wang |
| author_facet | D Wang Pham, DucSon Venkatesh, Svetha |
| author_sort | Pham, DucSon |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Learning robust subspaces to maximize class discrimination is challenging, and most current works consider a weak connection between dimensionality reduction and classifier design. We propose an alternate framework wherein these two steps are combined in a joint formulation to exploit the direct connection between dimensionality reduction and classification. Specifically, we learn an optimal subspace on the Grassmann manifold jointly minimizing the classification error of an SVM classifier. We minimize the regularized empirical risk over both the hypothesis space of functions that underlies this new generalized multiclass Lagrangian SVM and the Grassmann manifold such that a linear projection is to be found. We propose an iterative algorithm to meet the dual goal of optimizing both the classifier and projection. Extensive numerical studies on challenging datasets show robust performance of the proposed scheme over other alternatives in contexts wherein limited training data is used, verifying the advantage of the joint formulation. |
| first_indexed | 2025-11-14T09:12:13Z |
| format | Conference Paper |
| id | curtin-20.500.11937-42511 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:12:13Z |
| publishDate | 2011 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-425112023-01-27T05:52:12Z Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold Pham, DucSon Venkatesh, Svetha D Wang M Reynolds Learning robust subspaces to maximize class discrimination is challenging, and most current works consider a weak connection between dimensionality reduction and classifier design. We propose an alternate framework wherein these two steps are combined in a joint formulation to exploit the direct connection between dimensionality reduction and classification. Specifically, we learn an optimal subspace on the Grassmann manifold jointly minimizing the classification error of an SVM classifier. We minimize the regularized empirical risk over both the hypothesis space of functions that underlies this new generalized multiclass Lagrangian SVM and the Grassmann manifold such that a linear projection is to be found. We propose an iterative algorithm to meet the dual goal of optimizing both the classifier and projection. Extensive numerical studies on challenging datasets show robust performance of the proposed scheme over other alternatives in contexts wherein limited training data is used, verifying the advantage of the joint formulation. 2011 Conference Paper http://hdl.handle.net/20.500.11937/42511 10.1007/978-3-642-25832-9_25 Springer restricted |
| spellingShingle | Pham, DucSon Venkatesh, Svetha Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold |
| title | Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold |
| title_full | Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold |
| title_fullStr | Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold |
| title_full_unstemmed | Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold |
| title_short | Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann Manifold |
| title_sort | supervised subspace learning with multi-class lagrangian svm on the grassmann manifold |
| url | http://hdl.handle.net/20.500.11937/42511 |