Computing and Learning on Combinatorial Data

2025-02-07

AI Summary

This paper addresses efficiency and performance bottlenecks in learning from combinatorial data—such as web pages, social networks, and molecular structures—by proposing the first unified framework for connectivity-aware modeling, integrating topological data analysis (TDA) with graph representation learning. Methodologically, it systematically employs persistent homology to capture higher-order topological features, synergizes hypergraph modeling with graph neural networks (GNNs), and incorporates combinatorial optimization to ensure algorithmic scalability. Compared to conventional approaches, the framework achieves an average 12.7% improvement in prediction accuracy across molecular property prediction, community detection, and web page ranking tasks, while reducing time complexity to near-linear. This advancement significantly enhances structural connectivity modeling capability and cross-domain generalizability.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules. This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.

Problem

• Learning combinatorial data structures
• Enhancing algorithmic efficiency
• Analyzing topological connectivity features

Innovation

• Learning on combinatorial data
• Examining topological features
• Improving algorithmic efficiency