  Spectral kernel methods are techniques for transforming data into a
coordinate system that efficiently reveals the geometric structure - in
particular, the "connectivity" - of the data. These methods depend on certain
tuning parameters. We analyze the dependence of the method on these tuning
parameters. We focus on one particular technique - diffusion maps - but our
analysis can be used for other methods as well. We identify the population
quantities implicitly being estimated, we explain how these methods relate to
classical kernel smoothing and we define an appropriate risk function for
analyzing the estimators. We also show that, in some cases, fast rates of
convergence are possible even in high dimensions.
