The parameter ϵ represents a scale at which distances are meaningful: if ∥x i -x j ∥ >> ϵ the similarity metric becomes negligible. Following some normalization (see Diffusion Maps in Appendix B.1), the non-harmonic eigenvectors of the kernel matrix are known as diffusion coordinates and scaled by corresponding eigenvalues, providing a new coordinate system for the dataset. Diffusion coordinates with a low eigenvalue can be discarded, and it is the remaining diffusion coordinates that provide a set of global, collective latent variables to describe underlying low-dimensional structures. For data sampled on a manifold, diffusion maps can also be thought of as a discrete approximation of the Laplace-Beltrami operator on the manifold . By identifying a low-dimensional manifold, data points are automatically organized along new coordinates that parameterize this manifold, facilitating subsequent operations.