2021/10/21 by Xiaodong Zhuang, Zhuang, Xiaodong
Computer Science · Engineering · #Advanced Vision and Imaging #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Image Processing Techniques and Applications #Machine Learning (cs.LG) #Optical measurement and interference techniques
paper · pdf · doi:10.48550/arxiv.2110.10938
openalex publication_date 2021/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.