## Introduction

Modern data, even though large and high-dimensional, often contains 'simple' structure, with only a few degrees of freedom. Leveraging this structure allows for the design of efficient algorithms to collect, process, and communicate the data. For example, a large but low-rank matrix can be completed after observing relatively few of its entries at random. Alternatively, in social networks, the wealth of interaction patterns can be insightfully represented as a few clusters of individuals. Moreover, the ability of deep learning to generalise for unseen data relies on such low-dimensional structure. Many more such examples exist across a variety of applications and scientific disciplines.

## Aims

This Interest Group is dedicated to the study and development of tools that can produce low-dimensional representations of large and complex data sets, and to the application of such tools across a variety of domains. Our goal will be to improve state-of-the-art and to enable collaboration between members of the interest group, as well as between researchers across the wider scientific community.

In addition to any theoretical underpinnings, we also strive to develop fast and scalable algorithms for such problems, borrowing tools from a wide range of areas such as: network analysis, graph representation learning, time series clustering and anomaly detection, deep learning, stochastic and distributed optimisation, compressed sensing, (numerical) linear algebra, (high-dimensional) statistics, approximation theory, probability and others. We will also explore specific themes such as generalisation errors for deep neural networks.

An area of particular interest is that of inverse problems on graphs. In order to model complex and heterogeneous data, a prominent approach is to represent the data as a graph. Graphs have received significant attention over the last decade, and numerous methods have been proposed for analyzing their low-dimensional structure. The structural properties of such graphs can be used to model interactions within a network, or to capture geometric and statistical information about the data itself. Areas of focus include instances where the empirical data is incomplete or inconsistent, and one exploits the underlying structure (e.g., low-rank structure) to design scalable algorithms that are robust to noise and sampling sparsity.

## How to get involved

## Organisers

### Dr Mihai Cucuringu

Turing Fellow## Researchers

### Andrew Elliott

Lecturer in Statistics, University of Glasgow### Dr Brooks Paige

Turing Fellow### Professor Gesine Reinert

Turing Fellow### Professor Renaud Lambiotte

Turing Fellow## Contact info

## External researchers

**Andrea Pizzoferrato**, University of Bath**Florian Klimm**, Max Planck Institute for Molecular Genetics**Francois Lafond**, University of Oxford**Giorgos Bouritsas**, Imperial College London**Karel Devriendt**, University of Oxford**Luca Zanetti**, University of Cambridge**Martin Lotz**, University of Warwick**Pier Luigi Dragotti**, Imperial College London**Stephane Chretien**, Turing Visiting researcher, National Physical Laboratory, University of Lyon**Shuaib Choudhry**, University of Warwick**Wei Dai**, Imperial College London**Xiaowen Dong**, University of Oxford**Yijie Zhou**, University of Warwick