Registration Number
0224U033194,
(0124U003512)
, R & D reports
Title
Application of quaternions in Laplacian constrained Gaussian graphical models and graphical neural networks
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Моделі графових нейронних мереж
Head
Kyrchei Ivan I., Доктор фізико-математичних наук
Registration Date
20-12-2024
Organization
Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine
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Investigation of the sparse graph Laplacian estimation problem, as well as its generalization to complex- and quaternion-valued directed, undirected, mixed Laplacian graphs, with the aim of using them for applications where strongly connected feature tuples (or vectors) are considered as complex signals, RGB values images or three-dimensional locations of points in space.
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A detailed combinatorial description of the determinants of the adjacency matrices for a cycle and a path graph in the case of quaternionic graphs of unit gain is given. The properties of the spectra of matrices associated with a quaternionic unit graph with gains are established, and models of quaternionic graph neural networks are constructed.
A combinatorial description of the determinant of the adjacency matrix of an arbitrary quaternionic graph of unit gain is obtained, and it is expressed in terms of the determinants of basic subgraphs, cycles, and paths.
The problem of the determinant of a quaternionic matrix with noncommutative elements is solved within the framework of the theory of noncommutative column-row determinants. The proposed method can be applied to various types of gain graphs.
Product Description
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Pelykh Volodymyr O.
Taistra Yurii V.
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2024-12-20
