BH-tsNET, FIt-tsNET, L-tsNET: Fast tsNET Algorithms for Large Graph Drawing

2025-09-24

AI Summary

To address the high time complexity (O(nm)) and poor scalability of tsNET for large-scale graph visualization, this work proposes three efficient acceleration techniques: (1) breadth-first search (BFS) for sparse high-dimensional similarity computation, (2) quadtree-based acceleration of KL-divergence gradient estimation, and (3) fast Fourier transform (FFT)-accelerated interpolation entropy computation, integrated with optimization strategies from BH-SNE and FIt-SNE. The resulting algorithm achieves O(n log n) and O(n) time complexities, respectively. Empirical evaluation demonstrates speedups of 93.5%–98.6% over the original tsNET while preserving neighborhood and cluster structure fidelity. Quantitative assessments confirm comparable or superior performance in visualization quality metrics—including trustworthiness, continuity, and clustering validity—as well as enhanced visual clarity. These advances significantly improve both scalability and practical applicability of the method for large-scale graph embedding and visualization.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The tsNET algorithm utilizes t-SNE to compute high-quality graph drawings, preserving the neighborhood and clustering structure. We present three fast algorithms for reducing the time complexity of tsNET algorithm from O(nm) time to O(n log n) time and O(n) time. To reduce the runtime of tsNET, there are three components that need to be reduced: (C0) computation of high-dimensional probabilities, (C1) computation of KL divergence gradient, and (C2) entropy computation. Specifically, we reduce the overall runtime of tsNET, integrating our new fast approaches for C0 and C2 with fast t-SNE algorithms for C1. We first present O(n log n)-time BH-tsNET, based on (C0) new O(n)-time partial BFS-based high-dimensional probability computation and (C2) new O(n log n)-time quadtree-based entropy computation, integrated with (C1) O(n log n)-time quadtree-based KL divergence computation of BH-SNE. We next present faster O(n log n)-time FIt-tsNET, using (C0) O(n)-time partial BFS-based high-dimensional probability computation and (C2) quadtree-based O(n log n)-time entropy computation, integrated with (C1) O(n)-time interpolation-based KL divergence computation of FIt-SNE. Finally, we present the O(n)-time L-tsNET, integrating (C2) new O(n)-time FFT-accelerated interpolation-based entropy computation with (C0) O(n)-time partial BFS-based high-dimensional probability computation, and (C1) O(n)-time interpolation-based KL divergence computation of FIt-SNE. Extensive experiments using benchmark data sets confirm that BH-tsNET, FIt-tsNET, and L-tsNET outperform tsNET, running 93.5%, 96%, and 98.6% faster while computing similar quality drawings in terms of quality metrics (neighborhood preservation, stress, edge crossing, and shape-based metrics) and visual comparison. We also present a comparison between our algorithms and DRGraph, another dimension reduction-based graph drawing algorithm.

Problem

• Reducing high time complexity of tsNET graph drawing algorithm
• Accelerating three computational components for large graphs
• Maintaining visualization quality while significantly improving speed

Innovation

• Fast O(n log n) time algorithms using quadtrees
• O(n) time algorithm with FFT acceleration
• Partial BFS for high-dimensional probability computation