We characterize the intrinsic complexity of a set in a metric space by the least dimension of a linear space that can approximate the set to a given tolerance. This is dual to the characterization using Kolmogorov n-width, the distance from the set to the best n-dimensional linear space. We characterize the intrinsic complexity of a set of random vectors (via principal component analysis a.k.a. singular value decomposition) and random fields (via Karhunen–Loève expansion) as well as solutions to partial differential equations of various type.
Back to Workshop III: Geometry of Big Data