Hybrid Integrated Dimensionality Reduction Method Based on Conformal Homeomorphism Mapping

Abstract

Based on the theories of Riemannian surface, Topology and Analytic function, a novel method for dimensionality reduction is proposed in this paper. This approach utilizes FCA to merge highly correlated features to obtain approximate independent new features in the locally, and establishes a conformal homomorphic function to realize global dimensionality reduction for text data with the manifold embed in the Hausdorff space. During the process of dimensionality reduction, the geometric topological structure information of the original data is preserved through conformal homomorphism function. This method is characterized by its simplicity, effectiveness, low complexity, and it avoids the neighbor problem in nonlinear dimensionality reduction and it is conducive to the outlier data. Moreover, it has extensible for new text vectors and new feature from sub-vectors of new text vectors, and incremental operation without involving existing documents. The mapping function exhibits desirable properties resulting in stable, reliable, and interpretable dimensionality reduction outcomes. Experimental results on both construction laws and regulations dataset and toutiao text dataset demonstrate that this dimensionality reduction technique is effective when combined with the typical classification method of Random Forest, Support Vector Machine, and Feedforward Neural Network.