Functional Object Data Analysis and its Applications

Lead Research Organisation: University of Warwick
Department Name: Statistics

Abstract

When linguists are trying to determine how different languages are related or neuroscientists wish to know how one part of the brain is associated with another, how to analyse data which is both complex and massive is a fundamental question. However, an area of Statistics, namely Functional Data Analysis, where the data is described as mathematical functions rather than numbers or vectors, has recently been shown to be very powerful in these situations.

This fellowship aims to take functional data analysis and advance it so that much more complex data can be investigated. This will require establishing a careful statistical framework for the analysis of such functions even in situations where the functions have strict relationships. By considering the underlying mathematical spaces which the functions lie in, it is possible to construct valid statistical procedures, which preserve these relationships, such as the functions needing to be positive definite or the functions needing to be related by a graph or network.

As an example, comparison between different languages (for example, how is French quantitatively different from Italian) can be carried out in the framework of functional data but not without considering specifically how the data should be analysed to take into account its particular properties. For example in trying to find a path from one language to another, it would be sensible to try to only go via other feasible acoustic sounds. This turns out to be mathematically related to shape analysis, a simple example of which might be how to describe going from London to Sydney. The shortest path is through the centre of the Earth, but this is not sensible, so you have to go round the world. Establishing links between shape analysis and functional data is a major aim of this fellowship.

In addition, most brain analysis currently splits the brain up into lots of elements know as voxels, and then analyses these voxels one by one. However, the brain is really one object (or complex 3-D object) which should be analysed together. This is another example of functional data and the methods developed in this fellowship will enable the analysis of the brain as a single object. This will be done by examining the types of dependence between observations in brain imaging data, and using these to build such an object. Of particular interest will be the analysis of brain connections resulting from particular tasks which will require a mixture of functional data analysis and graphical or network analysis. However, before this can be done and the resulting insights into the brain found, the statistical methods required to do this need to be developed.

Planned Impact

There are three main areas of impact from this fellowship.

Firstly there are the academic disciplines associated with the projects within the fellowship. The main academic beneficiary will be statistical science, not simply those working on Functional Data Analysis, but also those in the other areas of shape analysis and network or graphical modelling, as well as applied statisticians making use of methodology in these areas. However, those working in the application areas under investigation will also greatly benefit from the methodology developed. This is evidenced by the strong support shown by the three non-statisticians who have written letters to say that they feel the research will benefit their groups and disciplines more generally.

Secondly, there are the non academic counterparts of those mentioned above. Statistics is a discipline where statisticians working outside academia outnumber those within, and the methodology developed here will be of benefit to these statisticians in government and industry as well, particularly as software development is a critical part of the dissemination of this research. For clinical neuroscientists and speech technologists, the resulting application driven research that will be undertaken will also be of considerable use, and dissemination through mediums such as subject specific journals will allow them to make use of the results.

Finally, there is the wider public engagement that a project of this kind will engender. The ideas of using statistics to determine linguistic relations such that ancient languages can be reheard or so that the function of the brain in particular settings can be understood is something that will naturally be of wide interest, given the public fascination with science. Making full use of this engagement opportunity through webcasts and public lectures will help to engage the public in the work undertaken.

Publications

10 25 50

Related Projects

Project Reference Relationship Related To Start End Award Value
EP/K021672/1 01/07/2013 31/12/2013 £836,309
EP/K021672/2 Transfer EP/K021672/1 01/01/2014 04/09/2017 £795,226
 
Description This is the first six months of a 5 year continuing fellowship which took place at Warwick prior to the PI moving to Cambridge.

The fellowship, called Functional Object Data Analysis and its Applications, is associated with the analysis of non-traditional statistical data, particularly data which can be characterised as continuous functions, often in multidimensions such as images.

To date, the research has been very successful. The project has developed a rigorous statistical theory for the analysis of functional data constrained to be on a manifold, while has also developed image based methods for clinical trials. In neuroimaging, the project has developed novel methods for the analysis of Positron Emission Tomography images such both functional data analysis and sequential monte carlo. It is also pioneering the field of statistical phonetics, and has produced the first synthetic statistically valid intermediate Romance languages.
Exploitation Route The findings are already being used by those in Neuroimaging and those in Linguistics. In some nascent collaborations in Cambridge, the findings on using SMC in PET models are being used to examine data from people with serious brain injury. Linguists are using the methods to produce a historical sound family tree from the models we have postulated.
Sectors Communities and Social Services/Policy,Digital/Communication/Information Technologies (including Software),Education,Energy,Environment,Healthcare,Government, Democracy and Justice,Manufacturing, including Industrial Biotechology,Culture, Heritage, Museums and Collections,Pharmaceuticals and Medical Biotechnology

URL http://www.statslab.cam.ac.uk/~jada2/FODAA.html
 
Description The major results from this project so far are their use to generate synthetic sounds from ancient languages which can give insights into how mathematics can play a role in humanities. In addition, work on linking functional data to time series has enabled a new benchmarking system being proposed for the Office for National Statistics. This is now being further investigated by their statisticians for possible implementation on a wide variety of economic time series.
First Year Of Impact 2014
Sector Communities and Social Services/Policy,Digital/Communication/Information Technologies (including Software),Education,Healthcare,Culture, Heritage, Museums and Collections,Pharmaceuticals and Medical Biotechnology
Impact Types Cultural,Societal,Economic

 
Description Roundtable Discussion on the Bean Review of Economic Statistics
Geographic Reach National 
Policy Influence Type Participation in a national consultation
 
Description EPSRC Centres for Maths in Healthcare
Amount £1,923,014 (GBP)
Funding ID EP/N014588/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 03/2016 
End 02/2020
 
Description Programme Grant
Amount £2,750,890 (GBP)
Funding ID EP/N031938/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 06/2016 
End 05/2022
 
Description Cambridge Research Magazine 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact The Cambridge Research Magazine - Research Horizons - ran an article on our research. This focused on the use of statistics and linguistics to recreate ancient languages. This was picked up by international media and the Daily Mail ran a long article on the ideas (see other entry).
Year(s) Of Engagement Activity 2016
URL https://issuu.com/uni_cambridge/docs/issue_30_research_horizons/1?e=1892280/36314892
 
Description Daily Mail Article 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact The Daily Mail picked up the story detailed as well in the submission from the Cambridge Research Magazine. This has led to contacts from across the world about the research.
Year(s) Of Engagement Activity 2016
URL http://www.dailymail.co.uk/sciencetech/article-3698184/Listen-mother-language-Researchers-recreate-w...
 
Description Science Museum Exhibition 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact The research from this award was the basis for a week-long exhibit at the Science Museum in London as part of the LMS Mathematics Footfall Festival. In particular we showed how mathematics and statistics can be used to investigate lost languages.
Year(s) Of Engagement Activity 2015
URL http://www.sciencemuseum.org.uk/about-us/press/nov-2015/mathematics-festival