Learning with Transformation Invariant Kernels

Walder, C; Chapelle, O

アイテム詳細

登録内容を編集ファイル形式で保存

一時保存へ追加

タグ情報を表示リリース履歴を表示詳細要約

公開

報告書

Learning with Transformation Invariant Kernels

MPS-Authors

/persons/resource/persons84294

Walder, C
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

External Resource

There are no locators available

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

フルテキスト (公開)

MPIK-TR-165.pdf
(出版社版), 362KB

付随資料 (公開)

There is no public supplementary material available

引用

Walder, C., & Chapelle, O.(2007). Learning with Transformation Invariant Kernels (165). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

引用: https://hdl.handle.net/11858/00-001M-0000-0013-CC0D-9

要旨

Abstract. This paper considers kernels invariant to translation, rotation and dilation. We show that no non-trivial
positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite
(c.p.d.) ones. Accordingly, we discuss the c.p.d. case and provide some novel analysis, including an elementary
derivation of a c.p.d. representer theorem. On the practical side, we give a support vector machine (s.v.m.) algorithm
for arbitrary c.p.d. kernels. For the thin-plate kernel this leads to a classifier with only one parameter (the
amount of regularisation), which we demonstrate to be as effective as an s.v.m. with the Gaussian kernel, even
though the Gaussian involves a second parameter (the length scale).