Estimating the effective dimension of large biological datasets using Fisher separability analysis

Abstract

Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a recently introduced dimensionality estimator, based on analysing the separability properties of data points, on several benchmarks and real biological datasets. We show that the introduced measure of ID has performance competitive with state-of-the-art measures, being efficient across a wide range of dimensions and performing better in the case of noisy samples. Moreover, it allows estimating the intrinsic dimension in situations where the intrinsic manifold assumption is not valid.