The University of Bath is inviting applications for the following PhD project commencing in October 2021.
Funding is available to candidates who qualify for ‘Home’ fee status. Following the UK’s departure from the European Union, the rules governing fee status have changed and, therefore, candidates from the EU/EEA are advised to check their eligibility before applying. Please see the Funding Eligibility section below for more information.
This project aims to investigate a variety of learning problems related to graphs. The focus is on the design and analysis of algorithms that are simple, work well in practice, and have provable theoretical guarantees. Tools from discrete probability and linear algebra will be used to achieve this goal.
One of the topics at the centre of this project will be graph clustering. The aim of graph clustering is to partition the vertices of a graph into subsets (called clusters) so that vertices belonging to the same cluster represent objects that are closely related. Practical applications of graph clustering include community detection in social networks, image segmentation, and the analysis of biological data.
Despite graph clustering being a well-studied problem, most graph clustering algorithms identify very similar clusters: ones that correspond to regions of the graph with many connections on the inside and few connections towards the outside. Only recently some work has been devoted in trying to investigate new typologies of clusters. For example, Cucuringu et al. [1] study clusters in directed graphs that are characterised by particular patterns in the direction of the edges.
A goal of the project would be to define new notions of clusters in both directed and undirected graphs, and develop algorithms to efficiently identify such clusters.
Another topic related to the project is semi-supervised learning on graphs: we possess label information for a subset of the vertices, and we would like to extend this information to the rest of the graph. Despite simple algorithms that work well in practice have been known for almost two decades, strong theoretical guarantees for such algorithms are still missing. A goal of the project would be to bridge the gap between the theory and practice of semi-supervised learning and, potentially, design new improved algorithms.
Candidate Requirements:
Applicants should hold, or expect to receive, a First Class or good Upper Second Class Honours degree (or the equivalent). A master’s level qualification would also be advantageous.
Non-UK applicants must meet our English language entry requirement.
Enquiries and Applications:
Informal enquiries are welcomed and should be directed to Dr Luca Zanetti, [Email Address Removed].
Formal applications should be made via the University of Bath’s online application form for a PhD in Mathematics.
More information about applying for a PhD at Bath may be found on our website.
Funding Eligibility:
In order to be considered for a studentship, you must qualify as a ‘Home’ student. In determining ‘Home’ student status, we follow the UK government’s fee regulations and guidance which, when available, will be set out by the UK Council for International Student Affairs (UKCISA) on their website. At the time of advertising this project, the fee regulations for 2021/22 have not yet been published, but we expect (subject to confirmation) that the main categories of students generally eligible for ‘Home’ fee status will be:
- UK nationals (who have lived in the UK, EU, EEA or Switzerland continuously since September 2018)
- Irish nationals (who have lived in the UK or Ireland continuously since September 2018)
- EU/EEA applicants with settled status in the UK under the EU Settlement Scheme (who have lived in the UK continuously since September 2018)
- EU/EEA applicants with pre-settled status in the UK under the EU Settlement Scheme (who have lived in the UK, EU, EEA, Switzerland or Gibraltar continuously since September 2018)
- Applicants with indefinite leave to enter/remain in the UK (who have been resident in the UK continuously since September 2018)
EU/EEA citizens who live outside the UK are unlikely to be eligible for ‘Home’ fees and funding.
Additional information may be found on our fee status guidance webpage, on the GOV.UK website and on the UKCISA website.
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