Link Prediction with Continuous-Time Classical and Quantum Walks

Author:

Goldsmith Mark12,Saarinen Harto12,García-Pérez Guillermo1234,Malmi Joonas134,Rossi Matteo A. C.1356ORCID,Maniscalco Sabrina123456

Affiliation:

1. Algorithmiq Ltd., Kanavakatu 3 C, FI-00160 Helsinki, Finland

2. Complex Systems Research Group, Department of Mathematics and Statistics, University of Turku, FI-20014 Turku, Finland

3. QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, FI-00014 Helsinki, Finland

4. InstituteQ-The Finnish Quantum Institute, University of Helsinki, FI-00014 Helsinki, Finland

5. QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland

6. InstituteQ-The Finnish Quantum Institute, Aalto University, FI-00076 Aalto, Finland

Abstract

Protein–protein interaction (PPI) networks consist of the physical and/or functional interactions between the proteins of an organism, and they form the basis for the field of network medicine. Since the biophysical and high-throughput methods used to form PPI networks are expensive, time-consuming, and often contain inaccuracies, the resulting networks are usually incomplete. In order to infer missing interactions in these networks, we propose a novel class of link prediction methods based on continuous-time classical and quantum walks. In the case of quantum walks, we examine the usage of both the network adjacency and Laplacian matrices for specifying the walk dynamics. We define a score function based on the corresponding transition probabilities and perform tests on six real-world PPI datasets. Our results show that continuous-time classical random walks and quantum walks using the network adjacency matrix can successfully predict missing protein–protein interactions, with performance rivalling the state-of-the-art.

Funder

Emmy.network foundation

Academy of Finland via the Centre of Excellence program

Academy of Finland via the Postdoctoral Researcher program

Academy of Finland

Publisher

MDPI AG

Subject

General Physics and Astronomy

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