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Local Isomorphism to Solve the Pre-image Problem in Kernel Methods

8 years 5 months ago
Local Isomorphism to Solve the Pre-image Problem in Kernel Methods
Kernel methods have been popular over the last decade to solve many computer vision, statistics and machine learning problems. An important, both theoretically and practically, open problem in kernel methods is the preimage problem. The pre-image problem consists of finding a vector in the input space whose mapping is known in the feature space induced by a kernel. To solve the preimage problem, this paper proposes a framework that computes an isomorphism between local Gram matrices in the input and feature space. Unlike existing methods that rely on analytic properties of kernels, our framework derives closed-form solutions to the pre-image problem in the case of non-differentiable and application-specific kernels. Experiments on the pre-image problem for visualizing cluster centers computed by kernel k-means and denoising highdimensional images show that our algorithm outperforms state-of-the-art methods.
Dong Huang, Yuandong Tian, Fernando DelaTorre
Added 01 May 2011
Updated 01 May 2011
Type Journal
Year 2011
Where CVPR
Authors Dong Huang, Yuandong Tian, Fernando DelaTorre
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