SS-GUMAP, SL-GUMAP, SSSL-GUMAP: Fast UMAP Algorithms for Large Graph Drawing

Abstract

UMAP is a popular neighborhood-preserving dimension reduction (DR) algorithm. However, its application for graph drawing has not been evaluated. Moreover, a naive application of UMAP to graph drawing would include O(nm) time all-pair shortest path computation, which is not scalable to visualizing large graphs. In this paper, we present fast UMAP-based for graph drawing. Specifically, we present three fast UMAP-based algorithms for graph drawing: (1) The SS-GUMAP algorithm utilizes spectral sparsification to compute a subgraph G' preserving important properties of a graph G, reducing the O(nm) component of the runtime to O(n^2 log n) runtime; (2) The SSL-GUMAP algorithm reduces the kNN (k-Nearest Neighbors) graph computation from $O(n \log n)$ time to linear time using partial BFS (Breadth First Search), and the cost optimization runtime from O(n) time to sublinear time using edge sampling; (3) The SSSL-GUMAP algorithm combines both approaches, for an overall O(n) runtime. Experiments demonstrate that SS-GUMAP runs 28% faster than GUMAP, a naive application of UMAP to graph drawing, with similar quality metrics, while SL-GUMAP and SSSL-GUMAP run over 80% faster than GUMAP with less than 15% difference on average for all quality metrics. We also present an evaluation of GUMAP to tsNET, a graph layout based on the popular DR algorithm t-SNE. GUMAP runs 90% faster than tsNET with similar neighborhood preservation and, on average, 10% better on quality metrics such as stress, edge crossing, and shape-based metrics, validating the effectiveness of UMAP for graph drawing.