Efficient tracking of the dominant eigenspace of a normalized kernel matrix, part II: performance assessment
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 second in a series of two, focuses on a kernel based method for large data sets. More specifically, it investigates the performance of a tracking algorithm for the dominant eigenspace of a normalized kernel matrix, proposed in the first paper of this series [2]. It is found that the tracking algorithm yields a satisfactory approximation of the dominant eigenspace. The loss in accuracy with respect to batch SVD calculations is by far compensated by the minimal computational and memory requirements per iteration step, being O(nm) and O(nm), respectively, resulting in a drastic reduction in computation time.