Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field

A self-organized geometric model is proposed for data dimension reduction to improve the robustness of manifold learning. In the model, a novel mechanism for dimension reduction is presented by the autonomous deforming of data manifolds. The autonomous deforming vector field is proposed to guide the deformation of the data manifold. The flattening of the data manifold is achieved as an emergent behavior under the virtual elastic and repulsive interaction between the data points. The manifold's topological structure is preserved when it evolves to the shape of lower dimension. The soft neighborhood is proposed to overcome the uneven sampling and neighbor point misjudging problems. The simulation experiment results of data sets prove its effectiveness and also indicate that implicit features of data sets can be revealed. In the comparison experiments, the proposed method shows its advantage in robustness.