Feature extraction using low-rank approximations of the kernel matrix

In this work we use kernel subspace techniques to perform feature extraction. The projections of the data onto the coordinates of the high-dimensional space created by the kernel function are called features. The basis vectors to project the data depend on the eigendecomposition of the kernel matrix which might become very high-dimensional in case of a large training set. Nevertheless only the largest eigenvalues and corresponding eigenvectors are used to extract relevant features. In this work, we present low-rank approximations to the kernel matrix based on the Nystrom method. Numerical simulations will then be used to demonstrate the Nystrom extension method applied to feature extraction and classification. The performance of the presented methods is demonstrated using the USPS data set.