A Geometrical Characterization on Feature Density of Image Datasets

Recently, the interpretability and verification of deep learning have attracted enormous attention from both academic and industrial communities, aiming to gain users’ trust and ease their concerns. To guide learning procedures or data operations carried out in a more interpretable way, in this paper, we put a similar perspective on image datasets, the inputs of deep learning. Based on manifold learning, we work out an interpretable geometrical characterization on the curvity of manifolds to depict the feature density of datasets, which is represented with the ratio of the Euclidean distance and the geodesic distance. It is a noteworthy characteristic of image datasets and we take the dataset compression and enhancement problems as application instances via sample credit assignment with the geometrical information. Experiments on typical image datasets have justified the effectiveness and enormous prospect of the presented geometrical characteristic.