Embedding Learning-Based Nonlinear Neighborhood-Preserving Dimensionality Reduction for Numerical Data

The complex nonlinear structure, large volume, and high redundancy of real high-dimensional data pose great challenges to data analysis and utilization. Currently, various nonlinear approaches have been used to reduce data dimensionality. However, current methods mainly face dual challenges, including the inefficiency in handling large-scale numerical data with implicit correlations, and the prohibitive computational costs of constructing complete neighborhood graphs for correlation preservation. In this paper, we propose a nonlinear Dimensionality Reduction (DR) framework to address these issues, which is based on embedding learning and designed to efficiently generate Vectors’ Embedding (VecE) of numerical matrices. First, an approximate algorithm is proposed to construct the neighborhood of numerical data rapidly by optimizing the top-k nearest neighbors (KNN). Second, a novel random sampling algorithm is proposed to extract the context of each vector from the constructed neighborhood, thus recognizing the intrinsic structural feature of the input data. Finally, an elaborate objective is designed to learn the embedding of the input numerical data from the extracted context, with the goal of maximizing the retention of data structural features in low-dimensional space. The computational complexity of VecE is also analyzed to illustrate its effectiveness. Extensive experiments on eight real-world datasets demonstrate that VecE outperforms most popular dimensionality reduction methods in terms of computational efficiency, while achieving acceptable accuracy and demonstrating excellent scalability to large-scale datasets.