SIG-NET: Exploring the interface between SIGnal processing and NETwork science

The qualitative step forward that Complexity Science has experienced in the last years is directly related to an increase of computation capacity, enabling the possibility of running large scale simulations and handling large amounts of (empirical) data: the so called Big Data paradigm. It is fundamental to come along with new methods and insights to deal, store and extract information from large amounts of data.
These datasets naturally come in two different types. First, from the time evolution of some financial indicator or the irregular motion of turbulent fluids to the waveform signal of speech, complex systems produce incredibly complicated univariate/multivariate time series, whose hidden structure should be processed and analysed using fast and novel approaches. Second, the intertwined architecture of the interaction patterns of complex systems is naturally represented and modeled in terms of graphs -a paradigmatic of this approach being the brain, modeled by single units (neurons) connected by edges that model synaptic connections. These distributed processing systems usually lay at the edge between order and randomness (the so-called complex network paradigm) and come in different flavours (undirected/directed, static/temporal, monolayer/multilayer). Each of these two families of datasets have its own mathematical corpus that deals with the description and characterisation of these data, namely signal processing and network science.

The working hypothesis of this project is that information encoded or hidden in a data set can be retrieved by mapping such data set into an alternative mathematical representation, where the extraction of information may be eventually simpler. As such, we aim to explore what new information can be extracted by mapping time series into graphs and therefore using network science to characterise signals and their underlying dynamics: in short, to make graph-theoretical time series analysis. We are also interested in the dual problem, namely extracting time series from graphs and therefore using the tools of time series analysis and signal processing to describe, compare and classify networks of many kinds: a signal processing of graphs.

We will consider specific methods (visibility algorithms, Markov chain theory, fluctuation analysis) and will be able to define and validate new graph-theoretical measures to describe signals and new signal-theoretic measures to describe graphs, as well as to build a mathematically sound and solid theory to relate these two approaches.

Ultimately, the results of our research will be implemented in a software whose input is a time series/complex network and whose output is a set of key features which describe the object under study from several angles (both the signal processing and graph theoretic angle). These features will then feed automatic classifiers for pattern recognition and data analytics.

This proposal will have impact on several academic, technological and industrial actors, as well as an impact on UK's societal welfare.

- A dedicated webpage will be hosted by the School of Mathematical Sciences containing the description and findings of the project, serving as a hub to catalyse the transfer of knowledge between academia and industry and to make outreach (via the publication of blog-like summaries of the most relevant research results).

- The school will host of a workshop on nonlinear time series analysis and networks, bringing together time series analysis practitioners, UK national and international scientists working on nonlinear time series analysis and data mining, and UK interested industrial partners.

Specific impact is expected at four levels:

(i) Fostering Interdisciplinarity in academia:
The research agenda on visibility algorithms is currently having a large impact in different scientific fields beyond applied mathematicians or theoretical physicists, including neuroscience, physiology, socio-economics, computer science, or applied physics, to cite some. We pretend to consolidate such impact within this project by both providing mathematical rigour to the method (WP1), by widening its spectrum of features (WP2) and by validating it in realistic scenarios of data classification (WP3).

(ii) Impact on clinical and biomedical realm:
An aspect of particular importance is the possibility of developing, as an outcome of the research involving analysis and classification of physiological time series, non-invasive diagnosis & clinical tests. Previous research on visibility algorithms suggest that this application is realistic and specific case tests will be addressed within WP3, in the context of implementing our feature based extraction and classification tool and validating in classification of cardiac diseases and cancer phenotypes. We have an ongoing collaboration with the Cancer Institute (Statistical Cancer Genomics Group) at UCL, which we plan to strengthen also within WP3 of this project.

(iii) Impact on software and telecommunication sectors:
We will collaborate (WP3) with Dr. Jordi Luque from Telefonica R&D (who is a partner in this fellowship) in validating the visibility network features for speaker recognition, mood and personality traits detection, these being classification problems of genuine research and long-term commercial interest for Telefonica, as expressed in their statement of support.

(iv) Societal welfare:
The ultimate beneficiary is UK society, whose welfare shall be increased as a consequence of the development of new tools for data analysis, as these have a direct impact in societal challenges such as healthcare or economic resilience, as acknowledged in the case for support. We will also use the webpage to make scientific outreach, making press releases and publishing non technical papers on the blog section of the site, much in the spirit of the Systems and Signals group blog at Imperial College London (http://systems-signals.blogspot.co.uk). Note that the PI belongs to the School's outreach committee, and has an independent track record of publishing scientific results in popular media such as newspapers, science magazines, and science websites. Furthermore, previous steps of this research have received press coverage in French magazine "La recherche" or in the popular "IEEE circuits and systems magazine".