Kernel methods such as Spectral Clustering and Kernel PCA
are unsupervised learning algorithms that perform a non-linear
dimensionality reduction. These methods are based on the eigen
decomposition of a NXN matrix, where N is the number of examples.
A greedy approximation of that matrix can be done in order to
handle larger problems and accelerate computation.
The idea is to approximate in the feature space some of the points
by a linear combination of a subset of the N points.