Year: 2018
Type: preprint
Abstract: Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in diverse areas, including, e.g., image processing and social networks. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics and thus come with no guarantees. Classic graph distances such as, e.g., the chemical and the CKS distance are arguably natural and intuitive, and are indeed also metrics, but they are intractable: as such, their computation does not scale to large graphs. We define a broad family of graph distances, that includes both the chemical and the CKS distance, and prove that these are all metrics. Crucially, we show that our family includes metrics that are tractable. Moreover, we extend these distances by incorporating auxiliary node attributes, which is important in practice, while maintaining both the metric property and tractability.
Source: arXiv (Cornell University)
Authors: Bento, Jose, Ioannidis, Stratis
Institutions: Boston College, Northeastern University
Language: English
Topic: Graph Theory and Algorithms
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: BIGDATA: F: Collaborative Research: Design and Computation of Scalable Graph Distances in Metric Spaces: A Unified Multiscale Interpretable Perspective, BIGDATA: F: Collaborative Research: Design and Computation of Scalable Graph Distances in Metric Spaces: A Unified Multiscale Interpretable Perspective
OpenAlex ID: W2963174716