Learning anchor planes for classification
Local Coordinate Coding (LCC) [18] is a method for modeling functions of data lying on non-linear manifolds. It provides a set of anchor points which form a local coordinate system, such that each data point on the manifold can be approximated by a linear combination of its anchor points, and the li...
| Autors principals: | , , , |
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| Format: | Conference item |
| Idioma: | English |
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Neural Information Processing Systems
2011
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| _version_ | 1826314918486343680 |
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| author | Zhang, Z Ladický, L Saffari, A Torr, PHS |
| author_facet | Zhang, Z Ladický, L Saffari, A Torr, PHS |
| author_sort | Zhang, Z |
| collection | OXFORD |
| description | Local Coordinate Coding (LCC) [18] is a method for modeling functions of data lying on non-linear manifolds. It provides a set of anchor points which form a local coordinate system, such that each data point on the manifold can be approximated by a linear combination of its anchor points, and the linear weights become the local coordinate coding. In this paper we propose encoding data using orthogonal anchor planes, rather than anchor points. Our method needs only a few orthogonal anchor planes for coding, and it can linearize any (α, β, p)-Lipschitz smooth nonlinear function with a fixed expected value of the upper-bound approximation error on any high dimensional data. In practice, the orthogonal coordinate system can be easily learned by minimizing this upper bound using singular value decomposition (SVD). We apply our method to model the coordinates locally in linear SVMs for classification tasks, and our experiment on MNIST shows that using only 50 anchor planes our method achieves 1.72% error rate, while LCC achieves 1.90% error rate using 4096 anchor points. |
| first_indexed | 2024-12-09T03:16:46Z |
| format | Conference item |
| id | oxford-uuid:6926b898-ed01-4d86-a811-fad39c005691 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:16:46Z |
| publishDate | 2011 |
| publisher | Neural Information Processing Systems |
| record_format | dspace |
| spelling | oxford-uuid:6926b898-ed01-4d86-a811-fad39c0056912024-10-22T09:39:08ZLearning anchor planes for classificationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:6926b898-ed01-4d86-a811-fad39c005691EnglishSymplectic ElementsNeural Information Processing Systems2011Zhang, ZLadický, LSaffari, ATorr, PHSLocal Coordinate Coding (LCC) [18] is a method for modeling functions of data lying on non-linear manifolds. It provides a set of anchor points which form a local coordinate system, such that each data point on the manifold can be approximated by a linear combination of its anchor points, and the linear weights become the local coordinate coding. In this paper we propose encoding data using orthogonal anchor planes, rather than anchor points. Our method needs only a few orthogonal anchor planes for coding, and it can linearize any (α, β, p)-Lipschitz smooth nonlinear function with a fixed expected value of the upper-bound approximation error on any high dimensional data. In practice, the orthogonal coordinate system can be easily learned by minimizing this upper bound using singular value decomposition (SVD). We apply our method to model the coordinates locally in linear SVMs for classification tasks, and our experiment on MNIST shows that using only 50 anchor planes our method achieves 1.72% error rate, while LCC achieves 1.90% error rate using 4096 anchor points. |
| spellingShingle | Zhang, Z Ladický, L Saffari, A Torr, PHS Learning anchor planes for classification |
| title | Learning anchor planes for classification |
| title_full | Learning anchor planes for classification |
| title_fullStr | Learning anchor planes for classification |
| title_full_unstemmed | Learning anchor planes for classification |
| title_short | Learning anchor planes for classification |
| title_sort | learning anchor planes for classification |
| work_keys_str_mv | AT zhangz learninganchorplanesforclassification AT ladickyl learninganchorplanesforclassification AT saffaria learninganchorplanesforclassification AT torrphs learninganchorplanesforclassification |