Evolutionary Manifold Learning for Automated Extraction of Data Topology

The focus of manifold learning is to reduce the dimensionality of data. Typically, the geometric properties of the resulting manifold are only indirectly controlled, making them difficult to evaluate or manipulate during learning before the manifold is obtained. Dynamical tuning of manifold geometry solves the problem of complex manual topology assignment for data. This paper presents the method of extracting a geometry as a distance graph for data with minimum Dirichlet energy using an evolutionary algorithm, which demonstrates improved generalization over traditional manifold regularization. The effectiveness of the proposed approach is confirmed by validation on MNIST and Mammoth datasets.