Efficient tracking of the dominant eigenspace of a normalized kernel matrix, part I: the algorithm
Geert Gins, Ilse Y.M. Smets, Jan Frans M. van Impe · International Conference Information Processing · 2006
Various state-of-the-art machine learning problems rely on kernel based methods. These kernel methods have the ability to solve highly nonlinear problems by reformulating them in a linear context. Hereto, the dominant eigenspace of a (normalized) kernel matrix is often required. Unfortunately, due to the computational requirements of the existing kernel methods, this eigenspace can only be obtained for relatively small data sets. This paper, the first in a series of two, focuses on a kernel based method for large data sets. More specifically, a tracking algorithm for the dominant eigenspace of a normalized kernel matrix is proposed. This tracking algorithm consists in an updating step followed by a downdating step, and allows to estimate the evolution of the dominant eigenspace over time. The performance assessment of the proposed algorithm will be discussed in the second paper of this series [2].