Dimensionality Reduction with Adaptive Kernels

1 A kernel determines the inductive bias of a learning algorithm on a specific data set, and it is beneficial to design specific kernel for a given data set. In this work, we propose a kind of new kernel, called Locality-Adaptive-Kernel (LAKE), which adaptively measures the data similarity by considering the geometrical structure of the data set. In theory, we prove that the LAKE is a special marginalized kernel; and intuitively, when the local kernel in LAKE is constrained to be linear, it has the explicit semantic of merging multiple local linear analyzers into a single global nonlinear one. We show in a toy problem that the kernel principal component analysis with LAKE well captures the intrinsic nonlinear principal curve of the data set. Moreover, a large set of experiments are presented to verify that the classification performance is sensitive to the kernel variation; and the extensive face recognition experiments on different databases demonstrate that KPCA and KDA based on LAKE...

• Type: Conference
• Year: 2006
• Where: ICPR
• Authors: Shuicheng Yan, Xiaoou Tang
• Keywords: Computer Vision, ICPR 2006, Kernel Principal Component, Special Marginalized Kernel, Specific Kernel