Cluster analysis is about finding groups in data. It has applications in various areas such as biology, medicine, marketing, computer science, psychology, archeology, sociology. The aim of the proposed project is to address cluster validation, which is a fundamental problem in cluster analysis. Cluster validation refers to both the evaluation of the quality of a clustering and the determination of the number of clusters. The main idea is to develop a systematic catalogue of cluster validity indexes and to explore their properties, so that a user can match the requirements of a given application of cluster analysis by an appropriate set or aggregation of criteria. This is original, because most existing literature on cluster validation advertises "one criterion fits it all"-approaches ignoring the specific aims of clustering. Given such a catalogue, a number of clusters in a given application can be determined by specifying a set of minimum requirements or by aggregating criteria with weights depending on the clustering aim. The quality of these approaches will be investigated. The methods will be generalised to clusterings where some data ("outliers") are not assigned to any cluster. For benchmarking the quality of cluster analysis methods, the given criteria will be used to explain the performance of different clustering methods on benchmark data sets from the characteristics of the true known clusterings of the data sets. The developed approaches to determine the number of clusters will be used for deciding about the number of biological species present in data sets with genetic information.

The aim of this network is to establish the UK as the world leading authority in the joint area of Computational Statistics and Machine Learning (CompStat & ML) by advancing communication, interchange and collaboration within the UK between the disciplines of Computational Statistics (CompStat) and Machine Learning (ML). The UK has tremendous research strength and depth that is widely acknowledged as world leading in both the individual areas of Computational Statistics and Machine Learning. Despite each of these fields of research developing, largely, independently and having their own separate journals, international societies, conferences and curricula both areas of investigation share a common theoretical foundation based on the underlying formal principles of mathematical statistics and statistical inference. As such there is a natural diffusion of concepts, research and individuals between both disciplines. This network will seek to formalise as well as enhance this interchange and in the process capitalise on important synergies that will emerge from the combined and shared research agendas of CompStat & ML.

The aim of this network is to establish the UK as the world leading authority in the joint area of Computational Statistics and Machine Learning (CompStat & ML) by advancing communication, interchange and collaboration within the UK between the disciplines of Computational Statistics (CompStat) and Machine Learning (ML). The UK has tremendous research strength and depth that is widely acknowledged as world leading in both the individual areas of Computational Statistics and Machine Learning. Despite each of these fields of research developing, largely, independently and having their own separate journals, international societies, conferences and curricula both areas of investigation share a common theoretical foundation based on the underlying formal principles of mathematical statistics and statistical inference. As such there is a natural diffusion of concepts, research and individuals between both disciplines. This network will seek to formalise as well as enhance this interchange and in the process capitalise on important synergies that will emerge from the combined and shared research agendas of CompStat & ML.

The CDT will train the next generation of leaders in statistics and statistical machine learning, who will be able to develop widely-applicable novel methodology and theory, as well as create application-specific methods, leading to breakthroughs in real-world problems in government, medicine, industry and science. The research will focus on the development of applicable modern statistical theory and methods as well as on the underpinnings of statistical machine learning. The research will be strongly linked to applications. There is an urgent national need for graduates from this CDT. Large volumes of complicated data are now routinely collected in all sectors of society, encompassing electronic health records, massive scientific datasets, governmental data, and data collected through the advent of the digital economy. The underpinning techniques for exploiting these data come from statistics and machine learning. Exploiting such data is crucial for future UK prosperity. However, several reports from government and learned societies have identified a lack of individuals able to exploit this data. In many situations, existing methodology is insufficient. Off-the-shelf approaches may be misleading due to a lack of reproducibility or sampling biases which they do not correct. Furthermore, understanding the underlying mechanisms is often desired: scientifically valid, interpretable and reproducible results are needed to understand scientific phenomena and to justify decisions, particularly those affecting individuals. Bespoke, model-based statistical methods are needed, that may need to be blended with statistical machine learning approaches to deal with large data. Individuals that can fulfill these more sophisticated demands are doctoral level graduates in statistics who are well versed in the foundations of machine learning. Yet the UK only graduates a small number of statistics PhDs per year, and many of these graduates will not have been exposed to machine learning. The Centre will bring together Imperial and Oxford, two top statistics groups, as equal partners, offering an exceptional training environment and the direct involvement of absolute research leaders in their fields. The supervisor pool will include outstanding researchers in statistical methodology and theory as well as in statistical machine learning. We will use innovative and student-led teaching, focussing on PhD-level training. Teaching cuts across years and thus creates strong cohort cohesion not just within a year group but also between year groups. We will link theoretical advances to application areas through partner interactions as well as through a placement of students with users of statistics. The CDT has a large number of high profile partners that helped shape our application priority areas (digital economy, medicine, engineering, public health, science) and that will co-fund and co-supervise PhD students, as well as co-deliver teaching elements.