2021 IEEE SPS Cycle 2 Virtual School on
Networked Federated Learning: Theory, Algorithms and Applications
28.3. - 01.04.2022
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Prof. Konstantin Avratchenkov, INRIA Lecture: Basics of spectral graph theory Abstract: Questions related to the spectra of graph matrices, such as adjacency matrix, Laplacian and normalized Laplacian,
naturally appear in the analysis of consensus algorithms, graph-based semi-supervised learning and network sampling.
In this lecture, we first review the basic properties of spectra of graph matrices. Then, we explain the elements
of the two main methods of random matrix theory: the method of moments and the method of Stieltjes transform.
Finally, we describe the spectra of graph matrices associated with Erdos-Renyi graph, stochastic block model
and random geometric graphs. Presenter: Konstantin Avrachenkov received Master degree in Control Theory from St. Petersburg
State Polytechnic University (1996), Ph.D. degree in Mathematics from University of South
Australia (2000) and Habilitation (Doctor of Science) from University of Nice Sophia
Antipolis (2010) in Computer Science. Currently, he is a Director of Research at INRIA
Sophia Antipolis, France. He is an associate editor of International Journal of Performance
Evaluation, Probability in the Engineering and Informational Sciences, ACM TOMPECS,
Stochastic Models and IEEE Network Magazine. He has won 5 best paper awards. His main
research interests are Markov chains, Markov decision processes, stochastic games, matrix
analysis and singular perturbations. He applies these methodological tools to the modeling
and control of networks and to design data mining and machine learning algorithms. |