Normalization and preimage problem in gaussian kernel PCA

Nicolas Thorstensen (1, 2, 3) , Florent Ségonne (1, 2, 3) , Renaud Keriven (1, 2, 3)

1 CERTIS - Centre d'Enseignement et de Recherche en Technologies de l'Information et Systèmes
2 imagine [Marne-la-Vallée]
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

Kernel PCA has received a lot of attention over the past years and showed usefull for many image processing problems. In this paper we analyse the issue of normalization in Kernel PCA for the pre-image problem. We present a geometric interpretation of the normalization process for the gaussian kernel. As a consequence, we could formulate a correct normalization criterion in centered feature space. Furthermore, we show how the proposed normalization criterion improves previous pre-image methods for the task of image denoising.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Nicolas Thorstensen, Florent Ségonne, Renaud Keriven. Normalization and preimage problem in gaussian kernel PCA. ICIP, Oct 2008, San Diego, United States. pp.741-744. ⟨hal-00835106⟩