Computing and Learning on Combinatorial Data

TL;DR

This paper explores methods for learning and computing on combinatorial data, emphasizing the importance of connectivity and topological features to enhance algorithmic performance in various data structures.

Contribution

It introduces novel approaches to analyze and utilize connectivity and topological features in combinatorial data for improved learning and computation.

Findings

Enhanced algorithms leveraging connectivity features

Improved computational efficiency on combinatorial datasets

Better learning performance through topological analysis

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.