A family of tractable graph metrics
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 an...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Applied Network Science |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/s41109-019-0219-z |
| _version_ | 1831723532951748608 |
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| author | José Bento Stratis Ioannidis |
| author_facet | José Bento Stratis Ioannidis |
| author_sort | José Bento |
| collection | DOAJ |
| description | 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 distance and the Chartrand-Kubiki-Shultz 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 Chartrand-Kubiki-Shultz distances, 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. |
| first_indexed | 2024-12-21T04:05:02Z |
| format | Article |
| id | doaj.art-8c40c42d23714888b0d264ee0964704c |
| institution | Directory Open Access Journal |
| issn | 2364-8228 |
| language | English |
| last_indexed | 2024-12-21T04:05:02Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Applied Network Science |
| spelling | doaj.art-8c40c42d23714888b0d264ee0964704c2022-12-21T19:16:37ZengSpringerOpenApplied Network Science2364-82282019-11-014112710.1007/s41109-019-0219-zA family of tractable graph metricsJosé Bento0Stratis Ioannidis1Department of Computer Science, Boston CollegeDepartment of Electrical and Computer Engineering, Northeastern UniversityAbstract 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 distance and the Chartrand-Kubiki-Shultz 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 Chartrand-Kubiki-Shultz distances, 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.http://link.springer.com/article/10.1007/s41109-019-0219-zMetric spacesGraph distancesGraph matchingGraph isomorphismConvex optimizationSpectral algorithms |
| spellingShingle | José Bento Stratis Ioannidis A family of tractable graph metrics Applied Network Science Metric spaces Graph distances Graph matching Graph isomorphism Convex optimization Spectral algorithms |
| title | A family of tractable graph metrics |
| title_full | A family of tractable graph metrics |
| title_fullStr | A family of tractable graph metrics |
| title_full_unstemmed | A family of tractable graph metrics |
| title_short | A family of tractable graph metrics |
| title_sort | family of tractable graph metrics |
| topic | Metric spaces Graph distances Graph matching Graph isomorphism Convex optimization Spectral algorithms |
| url | http://link.springer.com/article/10.1007/s41109-019-0219-z |
| work_keys_str_mv | AT josebento afamilyoftractablegraphmetrics AT stratisioannidis afamilyoftractablegraphmetrics AT josebento familyoftractablegraphmetrics AT stratisioannidis familyoftractablegraphmetrics |