Autonomous Dimension Reduction by Flattening Deformation of Data Manifold under an Intrinsic Deforming Field
This work addresses dimension reduction for data analysis, offering a novel geometric approach that is incremental in improving upon existing methods.
The authors tackled the problem of dimension reduction by proposing a method that autonomously deforms data manifolds using a deforming vector field based on virtual interactions between points, achieving flattening while preserving topology. Experimental results demonstrated its effectiveness in dimension reduction and potential for revealing implicit data features.
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.