Learning intrinsic dimension and intrinsic entropy of high-dimensional datasets

Populations of measurements of objects such as faces, genes or internet data traces, lie in lower dimensional manifolds of their high dimensional embedding spaces, e.g. face images, gene microarrays, or multivariate time series records. Knowing the intrinsic dimension and relative entropy of these manifolds is important for discovering structure, classifying differences, or performing dimensionality reduction (compression). In this paper we apply a new family of entropic graph methods to the estimation of intrinsic dimension and entropy of datasets supported on synthetic manifolds and of a high dimensional dataset of handwritten digits.