  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.
