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Master internship
4-6 months, spring 2020

Online novelty detection in multivariate graph signals
Application to hyperspectral imaging 

Detecting changes in network-structured time series data is of utmost importance in critical applications as diverse as detecting denial of service attacks against online service providers, or monitoring energy and water supplies. We recently devised an online change-point detection algorithm that fully benefits from the recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. The algorithm is able to detect anomalous clusters of activity over time in streaming scalar data measured at each node of the graph in a distributed manner across nodes. A natural extension is to tackle the case where the measurement at each node is vectored value. This paves the way to many applications such as detection of changes in hyperspectral images where a node is associated to each pixel, the graph models spatial dependences between pixels and each node is associated to the corresponding spectrum. The internship will focus on theoretical aspects related to the development of a multivariate detection algorithm, including multivariate graph signal processing, and practical application to change detection in multi temporal hyperspectral images.

To apply for this intership, please contact me with a CV.

Location: Lagrange Lab., Campus Valrose, University Côte d'Azur, Nice (downtown), France

PhD Scholarship
Available now

Distributed adaptation and learning over graph signals 

For the past 5 years, there has been a major and persistent interest for the treatment of big data, in response to a radical change in our information societies. Many applications involving these big data are structured by a network and require real-time actions given their chrono-sensitive constraints. Telecommunication networks and power grids monitoring are typical examples. Many scientific disciplines are also involved, from Sciences of the Universe to Neuroscience. These systems consist of a large number of agents or nodes linked by a connection topology. These agents can potentially interact dynamically to accomplish a task. Data flows are massive and their properties are likely to evolve over time. The graphs themselves are dynamic.

The aim of the thesis is to propose new adaptive, distributed and collaborative learning methods on large dynamic graphs in order to extract structured information from data flows acquired or transiting at the nodes of these graphs. Key learning tasks considered in the thesis will include online regression for graph time series prediction, network topology learning and novelty detection.

The first lock concerns the size of the graphs. The example of the SKA radio-telescope studied in the lab is emblematic since it should total 2.5 million antennas spread over an area from South Africa to Australia. For such situations, it is essential to develop processing and learning methods that support scalability by being natively distributed over the nodes. The second lock concerns the temporality of the data. Some data flows require online analysis to adapt to time-varying dynamics and respond to time-critical process constraints.

The PhD student will propose a family of learning methods operating on temporal signals structured by dynamic graphs. These methods will be natively distributed on the nodes of the graphs, will operate in an online manner and will enjoy adaptive capabilities to meet temporal constraints. In order to obtain performance guarantees, these methods will be systematically accompanied by a thorough study with random matrix theory. This powerful tool, never used in this context although perfectly indicated for inference on random graphs, will offer new perspectives. Finally, these methods will be confronted with two state-of-the-art observation techniques in which two of the partners of the project are involved and have data: radioastronomy with the giant instrument SKA (Obs Cote d'Azur) for images reconstruction and calibration, and magnetoencephalography neuro-imaging (NeuroSpin, CEA Saclay) for the characterization of anatomical connectivity of distinct functional regions of the cortex.

To apply for this PhD scholarship, please contact me with a CV.

Location: Lagrange Lab., Campus Valrose, University Côte d'Azur, Nice (downtown), France