The pre-image problem in kernel methods.
In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is noniterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Evaluations on performing kernel PCA and kernel clustering on the USPS data set show much improved performance.
Kwok
James Tin-yau
JT
Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. jamesk@cs.ust.hk
Tsang
Ivor Wai-hung
IW
D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003198:Computer Simulation; D003661:Decision Support Techniques; D005246:Feedback; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated / Q000379:methods*; D025341:Principal Component Analysis