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Communication Dans Un Congrès Année : 2023

Learning in RKHM: a $C^*$-Algebraic Twist for Kernel Machines

Yuka Hashimoto
  • Fonction : Auteur
Masahiro Ikeda
  • Fonction : Auteur
Hachem Kadri

Résumé

Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning in RKHS and vvRKHS to reproducing kernel Hilbert $C^*$-module (RKHM), and show how to construct effective positive-definite kernels by considering the perspective of $C^*$-algebra. Unlike the cases of RKHS and vvRKHS, we can use $C^*$-algebras to enlarge representation spaces. This enables us to construct RKHMs whose representation power goes beyond RKHSs, vvRKHSs, and existing methods such as convolutional neural networks. Our framework is suitable, for example, for effectively analyzing image data by allowing the interaction of Fourier components.
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hal-04523913 , version 1 (27-03-2024)

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Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri. Learning in RKHM: a $C^*$-Algebraic Twist for Kernel Machines. International Conference on Artificial Intelligence and Statistics (AISTATS), Apr 2023, Valencia, Spain. ⟨hal-04523913⟩
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