ABSTRACT
At first glance, it is not at all obvious what form spectral methods for learning might take. The connection between spectra and semisupervised learning can perhaps most readily be seen by thinking back to label propagation, and specifically our picture of label propagation as doing an interpolation of label information from boundaries across the interior of the graph. With spectral methods, the idea is to construct an interpolation in the form of a “standing wave.” Accordingly, we begin with a discussion of wave-shaped functions, specifically harmonics (not to be confused with the harmonic functions of chapter 10) that arise from simple harmonic motion.
