Autonomous Dimension Reduction by Flattening Deformation of Data Manifold under an Intrinsic Deforming Field

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data points. The flattening of data manifold is achieved as an emergent behavior under the elastic and repelling interactions between data points, meanwhile the topological structure of the manifold is preserved. To overcome the uneven sampling (or "short-cut edge") problem, the soft neighborhood is proposed, in which the neighbor degree is defined and adaptive interactions between neighbor points is implemented. The proposed method provides a novel geometric viewpoint on dimension reduction. Experimental results prove the effectiveness of the proposed method in dimension reduction, and implicit feature of data sets may also be revealed.