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The University of Southampton
Mathematical Sciences

Research project: Multi-dimensional Scaling in Complex Networks

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Multi-Dimensional Scaling is a popular research topic of common interest in many disciplines including statistics, computational chemistry and biology, and optimization.

It is a set of methods of discovering ``hidden’’ structures in multi-dimensional data to make scientific decisions by analysing the input data, which are typically a matrix of dissimilarities or distances. For example, in a complex network, the path length is often used to measure the distance between two nodes. However, such distances are rarely Euclidean, which is used in the classical MDS methods. This project aims to establish matrix optimization models and algorithms for MDS that use different types of distances. In particular, the project will design efficient numerical algorithms for visualizing data in complex networks. There are a few aspects to look into. One may focus on general optimization models and fast algorithms. Alternatively, one may want to look at some real applications that would need particular types of algorithms. This project has scientific significance and practical values for not only providing new theory and methods for MDS, but also offering new elements for the cross areas of statistics, optimization, and computer science.

Related research groups

Operational Research
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