The Laplacian spectral classifier

We develop a novel classifier in a kernel feature space defined by the eigenspectrum of the Laplacian data matrix. The classification cost function is derived from a distance measure between probability densities. The Laplacian data matrix is obtained based on a training set, while test data is mapped to the kernel space using the Nystrom routine. In that space, the test data is classified based on the angle between the test point and the training data class means. We illustrate the performance of the new classifier on synthetic and real data.