In this paper, we show a direct equivalence between spectral clustering and kernel PCA, and how both are special cases of a more general learning problem, that of learning the principal eigenfunctions of a kernel, when the functions are from a Hilbert space whose inner product is defined with respect to a density model. This defines a natural mapping for new data points, for methods that only provided an embedding, such as spectral clustering and Laplacian eigenmaps. The analysis also suggests new approaches to unsupervised learning in which abstractions such as manifolds and clusters that represent the main features of the data density are extracted.