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# Learning Dynamic Connectivities and Signal Recovery over Graphs

The emerging field of graph signal processing (GSP) provides the analysis of large data sets via graph theory tools, where the structure of the data is illustrated by a graph topology.

Mahmoud Ramezani-Mayiami

PhD Candidate

Mahmoud Ramezani-Mayiami will defend his PhD thesis Learning Dynamic Connectivities and Signal Recovery over Graphs 25 August 2023.

Ramezani-Mayiami has followed the PhD Programme at Faculty of Engineering and Science, with spesialisation in ICT.

## Summary of the thesis:

The real-world applications generate rapidly growing volumes of structured data, e.g., brain-computer interface measurements, social networks activities, gene network data, patient records of healthcare systems, and financial data. Storing and analyzing these data sets are easier when the underlying data structure is considered. The emerging field of graph signal processing (GSP) provides the analysis of large data sets via graph theory tools, where the structure of the data is illustrated by a graph topology. To be more technical, each graph vertex or graph node represents an entity of the system. A sequence of data is generated by each entity over time. For example, let us consider the Facebook friendship network. Every person has his/her own profile which is connected to others. In this example, everyone is an entity of the network, and these connections are the links in the Graph topology of the network. Now assume that for a limited number of people, e.g., 1000, we count the number of received “likes” every day. If we collect all 1000 values in a vector of values, this is the “like signals” for that day. In graph signal processing, we call it the “graph signal”. Now assume that we repeat it for one year, then we have 365 graph signals. This is the information that can be collected easily from the network but still, we do not know how these “likes” are propagated through the network or how the number of likes of one person is related to others. The main contribution of this Ph.D. thesis is to find these connections/relations between the data that we have. It is not just about Facebook data, and we can think about other things, like the following:

•  How the weather temperature of one city propagates to other cities and is it possible to predict the temperature of one location based on its neighbors?
•  How does the price of one stock affect the others in the market? Is it possible to predict the share price of one company by looking at its competitor or alliances?
• From a political perspective, how is the voting decision propagated? For example, what is the graphical propagation of the effect of a speech on people’s minds?

And many more! Just think about a real-world situation in which you have some information over time from different perspectives and you can find how these perspectives are related to each other.