DynoGraph: Dynamic Graph Construction for Nonlinear Dimensionality Reduction

Most well-known graph-based dimensionality re-duction algorithms, such as t-SNE and UMAP, use a two-step approach: first to construct a graph out of the high-dimensional data and then to embed the graph into the low-dimensional space. The main challenges of these algorithms include how to construct a good graph and how to maintain the similarity structure of the high-dimensional data in the low-dimensional space. This study proposes DynoGraph, a novel algorithm called Dynamic Graph Construction for Nonlinear Dimensionality Reduction, to address these two challenges. First, we develop an adaptive neighborhood graph construction method that accurately captures the intrinsic geometry of the high-dimensional data. Second, for the first time, we introduce a dynamic graph modification process during dimensionality reduction, ensuring that the data structure in the low-dimensional space faithfully reflects the high-dimensional data. For vertex pairs that are connected by edges in high-dimensional space exhibit far apart in low-dimensional space, additional edges are inserted to strengthen the connection between them. Conversely, for vertex pairs that are not connected in high-dimensional space exhibit close together in the low-dimensional space, edges are deleted to reduce the connection between them. These adjustments help to update their positions in subsequent embeddings, aligning them toward the high-dimensional data. Extensive experiments have demonstrated the superiority of DynoGraph against various comparative algorithms in tasks such as visualization, classification and clustering.