Участники Зеркальной лаборатории выступили на конференции The 5th International Conference on Quaternion Matrix Computations with Applications
Участники проекта «Кватернионы, геометрические алгебры и приложения», реализуемого Лабораторией геометрической алгебры и приложений (НИУ ВШЭ, Москва) совместно с международной научно-исследовательской лабораторией «Многомасштабное математическое моделирование и компьютерные вычисления» (СВФУ, Якутск) в рамках проекта Зеркальных лабораторий НИУ ВШЭ, представили ряд докладов на международной конференции The 5th International Conference on Quaternion Matrix Computations with Applications (ICQMC 2025), которая проходила с 9 по 12 мая в Qufu Normal University, Цюйфу, Китай.
В научный комитет конференции вошли Цзян Тунсун (участник проекта Зеркальной лаборатории со стороны СВФУ; профессор, Университет Линьи, Китай), В.И. Васильев (руководитель проекта Зеркальной лаборатории со стороны СВФУ; профессор, заведующий кафедрой “Вычислительные технологии” СВФУ, Якутск) и Д.С. Широков (руководитель проекта Зеркальной лаборатории со стороны НИУ ВШЭ). В организационный комитет вошли участники проекта Зеркальной лаборатории со стороны СВФУ: Ван Ган, Чжан Дун и Го Чжэньвэй.
Программа конференции: program_qufu
На конференции был представлен доклад руководителя проекта «Кватернионы, геометрические алгебры и приложения» со стороны НИУ ВШЭ:
Доклад: Dmitry Shirokov, 'On calculation of spin group elements in terms of Clifford algebras, quaternions, and split-quaternions', 10 мая 2025 (онлайн).
Аннотация доклада: We present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then in some special cases explicitly using matrices, quaternions, and split-quaternions. The different formalisms are convenient for different possible applications in physics, engineering, and computer science.
Выступления участников проекта «Кватернионы, геометрические алгебры и приложения» со стороны СВФУ:
Доклад: Цзян Тунсун, 'A Novel Strategy for Color Image Denoising Using Quaternion SVD and Its Application to Bearing Weak Fault Diagnosis', 10 мая 2025
Аннотация доклада: Color short-time Fourier transform (STFT) image is commonly used in bearing fault diagnosis to highlight fault features. However, without additional denoising, fault information in STFT image is often obscured by non-fault related signal components and significant noise. While the quaternion model has shown effectiveness in color image denoising, existing quaternion color image denoising methods are not as applicable to STFT images in weak fault scenarios because they fail to extract fault features amid interference from non-fault related components and strong noise. In this talk, we introduce a novel bearing weak fault diagnosis method that utilizes a quaternion color image denoising scheme to analysis STFT image for the first time. This method comprises two stages: first, a new and fast quaternion singular value decomposition (QSVD) algorithm which is based on the real representation of a quaternion matrix is proposed for computing the singular components (SCs) of a pure quaternion matrix which represents an STFT image; second, an indicator, which is defined as fault energy ratio (FER), is introduced to select fault related SCs and mitigate the interference of non-fault related components and noise by leveraging fault characteristics in frequency domain. Results from both simulated analyses and real experimental signals demonstrate that the new and fast QSVD algorithm is more efficient than several existing QSVD algorithms, and the proposed bearing fault diagnosis method is effective in signal denoising even when fault features are weak.
Доклад: Го Чжэньвэй, 'A novel color face recognition and reconstruction scheme based on split quaternion principal component analysis', 11 мая 2025.
Аннотация доклада: Principal component analysis (PCA), as an effective data dimensionality reduction scheme, plays an important role in the fields of image processing, machine learning, and other complex data analysis. However, this scheme can only be effectively used for grayscale image processing. To overcome this limitation, color principal component analysis (CPCA) and quaternion principal component analysis (QPCA) have been successively proposed for color image processing. In this report, the split quaternion principal component analysis (SQPCA) scheme is established by the real representation of a split quaternion matrix, which is effectively used for color face recognition and reconstruction. The experimental results show that, compared with PCA, CPCA, and QPCA, our proposed scheme not only better preserves the intrinsic connection among the red, green, and blue color channels, but also has higher recognition accuracy, clearer reconstructed image, and achieves the goal of data dimensionality reduction effectively.
Доклад: Чжан Дун, 'Two efficient algorithms for the commutative quaternion equality constrained least squares problem', 11 мая 2025.
Аннотация доклада: With the development of the applied discipline of commutative quaternions, the commutative quaternion equality constrained least squares (CQLSE) problem is gaining more and more attention as an effective tool. However, the knowledge gap in numerous CQLSE problems is now unresolved. This talk, by means of the complex representation matrix of a commutative quaternion matrix, first studies the QR decomposition and generalized singular value decomposition (GSVD) of commutative quaternion matrices, and gives the corresponding theorems and algorithms. In addition, the algorithms for solving the CQLSE problem based on QR decomposition and GSVD of commutative quaternion matrices are presented in this talk. Finally, numerical experiments show the effectiveness of the algorithms proposed in this talk.