Kernel-methods are popular tools in machine learning and statistics that can be implemented in a simple feed-forward neural network. They have strong connections to several psychological theories. For example, Shepard‘s universal law of generalization can be given a kernel interpretation. This leads to an inner product and a metric on the psychological space that is different from the usual Minkowski norm. The metric has psychologically interesting properties: It is bounded from above and does not have additive segments. As categorization models often rely on Shepard‘s law as a model for psychological similarity some of them can be recast as kernel-methods. In particular, ALCOVE is shown to be closely related to kernel logistic regression. The relationship to the Generalized Context Model is also discussed. It is argued that functional analysis which is routinely used in machine learning provides valuable insights also for psychology.