Topology Structure Analysis of High Dimensional Dataset by Flattening Deformation of Data Manifold

A new analysis method for high dimensional sets is proposed by autonomous deforming of data manifolds. The deformation is guided by two kinds of virtual interactions between data points. The flattening of data manifold is achieved under the elastic and repelling interactions, meanwhile the topological structure of the manifold is preserved. The proposed method provides a novel geometric viewpoint on high-dimensional data analysis. Experimental results prove the effectiveness of the proposed method in dataset structure analysis.