Learning Eigenfunctions of Similarity: Linking Spectral Clustering and Kernel PCA
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 dened with respect to a density model. This suggests a new approach to unsupervised learning in which abstractions (such as manifolds and clusters) that represent the main features of the data density are extracted. Abstractions discovered at one level can be used to build higher-level abstractions. This paper also discusses how these abstractions can be used to recover a quantitative model of the input density, which is at least useful for evaluative and comparative purposes.