Open AccessTopology Structure Analysis of High Dimensional Dataset by Flattening Deformation of Data Manifold
Author(s) -
Xiaodong Zhuang,
Nikos E. Mastorakis
Publication year - 2021
Publication title -
international journal of mathematics and computers in simulation
Language(s) - English
Resource type - Journals
ISSN - 1998-0159
DOI - 10.46300/9102.2021.15.29
Subject(s) - flattening , manifold (fluid mechanics) , topological data analysis , deformation (meteorology) , topology (electrical circuits) , manifold alignment , computer science , nonlinear dimensionality reduction , mathematics , algorithm , artificial intelligence , physics , engineering , combinatorics , mechanical engineering , astronomy , meteorology , dimensionality reduction
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.