Testing the robustness of manifold learning on examples of thinned-out data

Manifold learning can only be successful if enough data is available. If the data is too sparse, the geometrical and topological structure of the manifold extracted from the data cannot be recognised and the manifold collapses. In this paper we used data from a simulated two-dimensional double pendulum and tested how well several manifold learning methods could extract the expected manifold, a two-dimensional torus. The experiments were repeated while the data was down sampled in several ways to test the robustness of the different manifold learning methods. We also developed a neural network-based deep autoencoder for manifold learning and demonstrated that it performed in most of our test cases similarly or better than traditional methods such as principal component analysis and isomap.